Richard is one of the organisers of the long research programme, Representing, calibrating & leveraging prediction uncertainty from statistics to machine learning (RCL), held earlier this year at the Isaac Newton Institute for the Mathematical Sciences (INI).

We first spoke to Steven back in 2019 when he helped organise the Fickle Heart programme at the INI. In this podcast, Richard and Steven tell us about digital twins, digital hearts, and how the RCL programme and CVDNet build on the work started back in 2019 with the Fickle Heart programme.

You can find out more about some of the ideas discussed in this podcast in these short introductions:

• Maths in a Minute: Mathematical models
• Maths in a Minute: Differential equations
• Maths in Minute: Machine learning

This content was produced as part of our collaborations with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.

This is Céline Broeckaert talking, believe it or not, about the famously difficult theory of quantum mechanics. Céline knows what she's talking about. She's not a physicist, in fact she's a Romance languages scholar, author and playwright. Yet she's written a book about quantum mechanics together with her physicist husband Frank Verstraete, Leigh Trapnell Professor of Quantum Physics at the University of Cambridge. The book is called Why Nobody Understands Quantum Physics - and everyone needs to know something about it. And it's good timing: quantum mechanics celebrates its 100th birthday this year.

In this episode of Living Proof we talk to Céline and Frank about the book, what it was like writing it, and what their different backgrounds brought to the project.

We met Céline and Frank at the Isaac Newton Institute for Mathematical Sciences in Cambridge, where Frank is co-organising the research programme Quantum field theory with boundaries, impurities, and defects.

For a brief introduction to quantum mechanics see A ridiculously short introduction to some very basic quantum mechanics. To find out more about the overlap of maths and art, see here.

This content forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

Intrigued? That is a description of one of Jess Enright's adventures in her mathematical models. This is an exciting new approach that researchers are using to invite people into the worlds of their models, both to communicate their research to the people outside of academia, but also for the researchers themselves to reflect on what aspects of reality these models actually do, and don't, describe.

These adventures in model land build on the work of Erica Thompson in her book, Escape from Model Land: how mathematical models can lead us astray and what we can do about it. Any mathematical description of a process in the world around us is a mathematical model: whether it's describing the processes in our climate, the spread of a disease through a population or the movement of water across a landscape. They are incredibly useful and key to research in modern mathematics and science. But these mathematical models are, by necessity, simplifications of the real world.

Erica's book inspired geoscientist Chris Skinner to use principles of role-playing games to explore and communicate mathematical models. And this approach was a perfect fit with Jess' experience building board games to communicate her research - we event get to play some in this podcast at the huge UK Games Expo in Birmingham earlier this year!

Jess Enright, along with Emma Gort Tarrus, in action at the UK Games Expo in Birmingham earlier in 2025. (Photo: Rachel Thomas)

In this podcast we talk to Jess (a reader in the school of Computing Science at the University of Glasgow and member of the JUNIPER partnership of disease modellers from across the UK), Chris (an independent geoscientist and researcher and a visiting fellow at York St John University)and Erica (Associate Professor of Modelling for Decision Making at University College, London) about their explorations of these ideas.

You can find out more information about the ideas discussed in the podcast here:

• Maths in a Minute: Mathematical model – a brief and an accessible introduction to mathematical models and where they are used.
• Escape from Model Land: how mathematical models can lead us astray and what we can do about it – Erica's book
• Adventures in Model Land– the framework, developed by Chris, Erica and Jess, together with Liz Lewis, Rolf Hut and Sam Illingworth, for exploring mathematical models using table-top role-play games
• You can find some of the adventures in model land and other games that Jess took to the UK Games Expo in Birmingham

This podcast is part of our collaboration with JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium. JUNIPER comprises academics from the universities of Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster, who are using a range of mathematical and statistical techniques to address pressing questions about the control of COVID-19. You can see more content produced with JUNIPER here.

In this episode of Living proof we meet Kevin Buzzard, an expert on proof assistants at University College London. Kevin explains what proof assistants are, how using them is like playing a computer game, and why they turn maths into a highly collaborative pursuit. He also tells us about his effort to get a proof assistant to check one of the most famous results in all of mathematics — Fermat's Last Theorem — and how proof assistants and AI may team up to provide a powerful tool.

We met Kevin in the summer when he was taking part in a research programme called Big Proof at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge. This programme, which attracted some of the best minds in modern mathematics, followed on from a pioneering workshop on the same topic which took place at the INI in 2017.

To find out more about the topics mentioned in this podcast, see the following articles:

• Proof assistants — This two part article, written by our brilliant summer intern Ben Watkins, is based on the interview with Kevin Buzzard and explores what proof assistants are.
• Maths in a Minute: Coding with Lean — Here's a simple walk-through of how to use a proof assitant called Lean.
• Pure maths in crisis? — In this article from 2019 Kevin Buzzard explains why he thinks that the standard of proof in research maths might not be as high as mathematicians would like to believe.
• How to (im)prove mathematics — This article explores how the simple notion of counting ends in a revolutionary new way of doing maths using proof assistants. This article is based on a talk by Terence Tao at a 2024 workshop at the INI which celebrated the mathematics of Tim Gowers as well as his 60th birthday.
• A very old problem turns 30! — This article explores Fermat's famous last theorem as well as the mathematics its proof has given rise to. It comes with a podcast featuring Andrew Wiles, who proved the result, and people who are now working on its legacy.
• You can find more background reading in our collection on proof assistants.

This content forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

Moustapha talks to us about about the amazing institution that is AIMS, about his outreach activities and advice for budding mathematicians, and about the challenges that face mathematicians in sub-Saharan Africa.

You can find the IMU-ICIAM report on fraudulent publishing, which Moustapha mentions in the podcast, here. The same team of authors has also drawn up recommendations on how to fight fraudulent publishing.

In this episode of Maths on the Move we talk to Codina Cotar, who co-organised the INI programme and helped put on the competition. Codina explains the maths which served as inspiration and discusses some of the winning entries. From coffee to quantum mechanics and from dance to diffusion, find out how mathematics, nature and art are inextricably linked.

Note that the in-person exhibition at the INI is now scheduled for March 2026.

The entries discusses in this podcast are shown below. To find out more about some of the mathematical topics mentioned in this podcast see:

• The Sci-art competition - This article explores some of the mathematics behind the competition, including randomness, diffusion, and many particle systems.
• The Fields Medals 2022: Maryna Viazovska - This article looks at the mathematics of sphere packings, which won a Fields Medal for the mathematician Maryna Viazovska.
• Maths in a Minute: Fluid dynamics - A very bried introduction to the mathematics of liquids and gases.
• A ridiculously short introduction to some very basic quantum mechanics - This article does what the title suggests.
• A brief history of quantum field theory - A deeper look at the theory that arose from quantum mechanics.

Dye Diffusion in Water by Henrique Biasi. Find out more here.

A microcosm of milk by Christian Casaljay. Find out more here.

Work by Lilia Bakanova, which which won the category for textile, sculpture and other medium. Find out more here.

As you might imagine, if you have ever tried to drink coffee out of a doughnut, topology has traditionally been part of pure mathematics. Topological data analysis (TDA), however, opens up a world of applications by applying ideas from topology to vast data sets, helping us to understand their "shape" and draw out important features.

In this episode of Maths on the Move we talk to algebraic topologist Michael Hill about some of the fascinating uses of topological data analysis — from understanding breast cancer to making sure that voting is fair.

We talked to Michael after he gave a brilliant Rothschild lecture at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge. He was at the INI to attend the research programme Equivariant homotopy theory in context.

To find out more about the topics mentioned in this podcast see:

• Maths in a minute: Topology — a quick introduction to topology.
• Understanding life with topology — a quick introduction to TDA and some of its uses.
• Euromaths: Heather Harrington — An episode of our Maths on the move podcast giving and introduction to topological data analysis.
• Watch Mike Hill's Rothschild lecture at the INI.
• Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival - The paper by Nicolau, Levine and Carlesson, mentioned by Michael in the podcast, which uses TDA to identify a novel type of breast cancer.
• The Data and Democracy Lab — mentioned by Mike in the podcast.

Also, here is an image illustrating the intuition behind topological data analysis. As discs drawn around a bunch of points arranged in a circle increase in radius, they eventually overlap to form a ring, and later overlap to form a single blob.

This podcast forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

We start the season with theoretical physicist David Tong of the University of Cambridge looking at an important milestone in the history of physics: the 100th birthday of quantum mechanics which we celebrate this year. David tells us why a new theory was needed, which of the many strange aspects of quantum mechanics is, in his opinion, the most significant, and that Erwin Schrödinger had a tendency to be grumpy.

David also tells us how quantum mechanics links to quantum field theory, the language in which all of modern physics is formulated, and reveals some mysterious connections between very different areas of physics — such as the theory of black holes and fluid mechanics. Join us in a wavy dance from the very small to the very large!

For some background and further reading and viewing see:

• David Tong's series of text books
• A ridiculously short introduction to some very basic quantum mechanics
• A brief history of quantum field theory
• Heisenberg's uncertainty principle
• Maths in a Minute: Black holes
• What is general relativity? Plus asks David Tong
• Sean Carroll's Mindscape podcast featuring David Tong

It seems reasonable, then, that the mathematical models should reflect people's interaction with each other and their environment, and that they should take account of people's perspectives and priorities. In this episode of Maths on the Move we talk to Liz Fearon, an epidemiologist  at University College London, about a pioneering new project which aims to involve people in the production of mathematical models from the start, treating them as valued and equal members of the research team. Liz tells out about the motivation behind the project, how it works, and what she hopes to achieve.

To find out more about topics mentioned in this podcast see:

• Co-production of mathematical models — the article accompanying this podcast

• The website of the COMMET project

• Disease modelling for beginners — our introduction to some basic concepts in infectious disease modelling

• The inequalities of COVID-19 — our article exploring the role of the pandemic in amplifying social inequalities

• Tracing mpox — our article about modelling the spread of mpox.

This podcast is part of our collaboration with JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium. JUNIPER comprises academics from the universities of Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster, who are using a range of mathematical and statistical techniques to address pressing questions about the control of COVID-19. You can see more content produced with JUNIPER here.

In this episode of Maths on the Move Zhouli takes us on a trip into higher dimensions, giving us a gist of what this long-standing problem is all about and retracing some of the long, and sometimes arduous, journey towards a proof. We met Zhouli when he visited our neighbours at the Isaac Newton institute for Mathematical Sciences (INI) in Cambridge to take part in a research programme called Equivariant homotopy theory in Context.

To find out more abut the topics discussed in this podcast see:

• Maths in a minute: Topology
• The hypersphere in four dimensions
• Telescope topology

This content forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

In this episode of Maths on the Move, Maths4DL members Yolanne Lee from University College London, Georg Maierhofer from the University of Cambridge, and Chris Budd OBE from the University of Bath tell us all about the hackathon, the science behind it, and what it was like to participate in those ambitious but exciting 48 hours.

For a brief introduction to machine learning see Maths in a minute: Machine learning and neural networks and for a brief introduction to differential equations see Maths in a minute: Differential equations. You might also like:

• Our podcast featuring Yolanne Lee talking about her work as a Maths4DL researcher,
• Our podcast featuring Georg Maierhofer talking about physics informed neural networks, as well as the accompanying article,
• Our article AI and GoPro physics featuring the work of Nathan Kutz who is mentioned in this podcast.

This content is part of our collaboration with the Mathematics for Deep Learning (Maths4DL) research programme, which brings together researchers from the universities of Bath and Cambridge, and University College London. Maths4DL aims to combine theory, modelling, data and computation to unlock the next generation of deep learning. You can see more content produced with Maths4DL here.

The idea isn't quite as sci-fi as it sounds. A gigantic scientific effort called the Physiome Project is about piecing together a mathematical description of the entire physiology of the human body. Once this has been achieved to a sufficient level digital twins will be a spin-off.

In this podcast we revisit an interview we did back in 2019 with Steven Niederer, who was then Professor of Biomedical Engineering at King's College London but has since moved to a new position at Imperial College London as Chair of Biomedical Engineering. Niederer told us about the physiome project, about how the fitbits many of us own are a very first step towards a digital twin, and about how you can model individual human organs such as the heart. We also challenge ourselves to explain differential equations in one minute.

You can find out more about maths and medicine, differential equations and mathematical modelling on Plus.

We met Niederer in 2019 when he helped to organise a research programme at the Isaac Newton Institute for Mathematical Sciences in Cambridge.

The music in this podcast comes from the artist Oli Freke. The track is called Space Power Facility.

This podcast forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

Adina Goldberg was one of the participants at a recent research programme in this area at the Isaac Newton Institute for Mathematical Sciences (INI). In this episode of Living proof, our podcast produced in collaboration with the INI, we speak to Adina about her work and how her intriguing motto – "the meaning is in the arrows" – applies to her research, her career path, and the way she looks at life.

You can find out more about quantum information in this short introduction and delve into the details of information theory in this collection of content.  

Make sure you visit Adina's website to find out more about her work and her fascinating career. Since we recorded this podcast Adina has finished her PhD – congratulations Dr Goldberg!

This podcast forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

You can read more about Masaki Kashiwara's work in our article, and you can listen to a recent podcast where we spoke to Helge Holden, Chair of the Abel Prize committee, about the Abel Prize and about Masaki Kashiwara's work.  And can you see all our reporting on every Abel Prize since it was first awarded in 2003 here.

Thanks to the musicians  Peter Baden, Astrid Garmo and Liv Lande for playing such wonderful music in the Abel Prize ceremony which you'll hear a little taste of in this podcast.  And thank you to all the Abel Prize team, including Unni Irmelin Kvam, Pål Petterson, Marina Tofting and Anne Lise Stranden for inviting us to Abel Week and for such a fantastic celebration!

Photo of Masaki Kashiwara is copyright Thomas B. Eckhoff/DNVA and used with permission

Sarah has also written a fascinating book, called Once upon a time: The wondrous connections between mathematics and literature, and she gave a talk at this year's Cambridge Festival, with the intriguing title Life in Lilliput – The Mathematics of Fictional Realms. The talk was the contribution to the Festival of the Isaac Newton Institute for Mathematical Sciences (INI). Sarah also participates in the Modern History of Mathematics research programme that is currently taking place at the INI.

In this episode of Living proof, produced in collaboration with the INI, Sarah tells us about the many things she has done and how they all fit together, and gives some advice for budding mathematicians of all ages: keep pursuing all the things you love doing, and one day it may turn out that they all fit together.

To find out more about some of the things mentioned in this podcast see the fllowing links:

• Sarah Hart: Once upon a prime — In this episode of our Maths on the Move podcast Sarah talks about her book and the connections between maths and literature.
• Maths in three minutes: Groups — This article gives a brief introduction to Sarah's research area.
• Life in Lilliput – The Mathematics of Fictional Realms — Click this link to watch a recording of Sarah's Cambridge Festival talk at the INI.
• Sarah Hart at Gresham College — Click this link to watch Sarah's Gresham College public lectures.

This podcast forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

It turns out that they do! Our friend Rob Eastaway, author and Director of the amazing Maths Inspiration project, has written a book called Much Ado About Numbers: Shakespeare's mathematical life and times. In this episode of Maths on the Move, Rob tells us about some of the many instances of maths appearing in Shakespeare's work. He also tells us about the mathematical climate that Shakespeare lived in. Among other things, it included a mathematical revolution, saw music as a subfield of maths, and gave rise to the word "trivial" so much beloved by mathematicians. The book is out in paperback now.

To find out more about some of the topics mentioned in this episode, see the following links:

• The fabulous positional system is an article exploring the nature of our number system.
• Rob's Gresham College lecture explores some of the topics mentioned in this podcast and in his book.
• Maths Inspiration runs inspiring and interactive maths shows for teenagers.
• Finally, here are reviews of some of Rob's books:
  • The hidden mathematics of sport (with John Haigh)
  • Maths for mums and dads (with Mike Askew)
  • More maths for mums and dads (with Mike Askew)
  • How long is a piece of string? (with Jeremy Wyndham)
  • Mindbenders and brain teasers (with David Wells)
  • How to take a penalty (with John Haigh)
  • How many socks make a pair?

This happened again recently when the Isaac Newton Institute for Mathematical Sciences (INI) organised a staging of the play Diving into math with Emmy Noether. Noether was a pure mathematician whose results made waves far beyond her field. Albert Einstein called her a "creative mathematical genius". 

The play is produced by Portrait Theater Vienna in co-operation with Freie Universität Berlin, directed by Sandra Schueddekopf, and features Anita Zieher as Emmy Noether. It was put on as part of the Modern History of Mathematics research programme that is currently taking place at the INI and the Inclusivity in the Mathematical Sciences workshop that was organised by the Newton Gateway to Mathematics in March 2025.

In this episode of Maths on the move we talk to historian of mathematics David E. Rowe, who provided scientific advice for the play, about the life and work of Emmy Noether, and about what it's like putting mathematics on stage.

You might also want to read our article Emmy Noether: A creative mathematical genius.

This content was produced as part of our collaborations with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.

In this episode of Maths on the Move we talk to Helge Holden, Chair of the Abel Prize Committee. Helge tells us about this year's winner, the history and purpose of the Prize, and how the winners are chosen. He also tells us why good mathematicians are needed in all sectors of science and beyond, and talks about the tragic story of the mathematician Niels Henrik Abel, after whom the Prize is named.

To find out more about some of the topics mentioned in this episode, see:

• The Abel Prize 2025: Masaki Kashiwara - An accessible look at some of Kashiwara's mathematics.
• The Chern Medal 2018: Masaki Kashiwara - Another look at Kashiwara's work written on the occasion of his winning the Chern Medal in 2018.
• What are groups and what are they good for? - An episode of the Maths on the Move podcast which explores group theory.
• Stubborn equations and the study of symmetry - An article which touches one of Niels Henrik Abel's most famous results.
• Journal für die reine und angewandte Mathematik - Also known as Crelle's journal, this publication is mentioned in the podcast.

In this episode of Maths on the Move we talk to mathematician Chris Budd who recently went to Parliament for something called Evidence Week, where he and other AI researchers talked with MPs and Peers from the House of Lords. Chris tells us about the discussions he had with politicians — about the worrying issue of bias in AI, its promising applications, for example in the medical arena, and also about the fact that AI is built on mathematics. A strong maths education, starting at primary school, is therefore essential if we're going to make the best of AI in the future.

Chris is Professor of Applied Mathematics at the University of Bath, co-lead of the research project Maths4DL, and Director of Knowledge Exchange for the Bath Institute for Mathematical Innovation. He attended Evidence week with a team of researchers which included Yolanne Lee, a Maths4DL PhD student who recently featured in another Maths on the Move episode. The image above shows, from left to right, Dáire O’Kane (Maths4DL), Jenny Power (IMI), Yolanne Lee (Maths4DL), and Alexandra Freeman, Baroness Freeman of Steventon.

To find out more about some of the topics discussed in this episode see

• AI be the judge: The use of algorithms in the criminal justice system
• Can AI help with breast cancer screening?
• Maths4DL AI policy brief: Black boxes of AI - watch maths open them

This podcast was produced as part of our collaboration with the Mathematics for Deep Learning (Maths4DL) research programme. Maths4DL brings together researchers from the universities of Bath and Cambridge, and University College London and aims to combine theory, modelling, data and computation to unlock the next generation of deep learning. You can see more content produced with Maths4DL here.

This episode is all about the communication of mathematics to the wider world, which is becoming ever more recognised as a priority within the maths community. We talk to Sara Khan, Communications Manager at the INI, about how this renowned research institute supports mathematics communication. And we revisit our interview with Hannah Fry who has just taken up her new role as Professor of the Public Understanding of Mathematics here at the University of Cambridge

As Hannah puts it,

"It's really important that people feel that [mathematics] is being done with them, not to them."

We also find out about Hannah's own research in her previous role as Professor for the Mathematics of Cities at University College London, and hear about her favourite mathematical moment.

To find out more about organisations and events in support of mathematics communication mentioned in this episode, see the following links:

• The Mathsci-comm network is funded by an INI Network grant and aims to connect those working in, and with a stake in, communicating complex mathematics and data science to a variety of non-expert audiences. The network is run by the Editors of plus.maths.org, Marianne Freiberger and Rachel Thomas, together with Maha Kaouri from the Newton Gateway to Mathematics
• Communicating mathematical and data sciences — what does success look like? was a workshop organised by the Mathsci-comm network, which took place at the INI in November 2024. Hannah Fry announced her move to Cambridge at this event.
• The Graduate training workshop for the Mathematical Sciences, organised by the Newton Gateway to Mathematics, took place at the INI in February 2025 and comprised a significant component dedicated to communication, delivered by the Editors of plus.maths.org, Marianne Freiberger and Rachel Thomas, together with Alison Kiddle and Katie Steckles. This followed a pilot event which took place in October 2024.
• Talking maths in public (TMiP) is a conference which runs in the UK every two years, for people who work in, or otherwise participate in, communicating mathematics to the public. TMiP 2025 will take place at the University of Warwick on 28th - 30th August 2025, with the option to participate online.

This content was produced as part of our collaborations with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.

In this episode of Maths on the Move we talk to this year's winner of the Otto Neugebauer Prize, Reinhard Siegmund-Schultze, who has worked on and written about mathematicians who fled Nazi Germany. Reinhard tells us about the motivation for his work, how the Nazi regime impacted mathematics and mathematicians, and what future historians might say about the mathematics of today.

This content was produced with kind support from the London Mathematical Society.

In this podcast we talk to Benjamin Walker from University College London, and to Adam Townsend and Andrew Krause from Durham University, who together created this online solver of partial differential equations.  Such equations describe how quantities change over space and time and therefore used throughout science to describe processes that play out in the real world — from the transmission of airborne viruses to the flow of water during a flood. Ben, Andrew and Adam tell us about their motivation for building VisualPDE and what they can do with it.

We met Ben, Andrew and Adam through the Mathsci-comm network for people who communicate maths and data science to non-expert audiences. As you can see by playing with the simulation below, VisualPDE  is a great tool for communicating maths research to non-experts, as well as allowing mathematicians to quickly simulate what their mathematical models can tell them.

Adam is also part of the team behind the brilliant Chalkdust, a magazine for the mathematically curious. Why not order the latest issue for a Christmas gift?

Suppose that lots of people are sitting in a sealed room and one of them is infectious. We'll assume that the infectious person is constantly producing virus-laden particles that spread out around them and lose their potency over time. The simulation below shows what this might look like. The colour corresponds to the concentration or amount of the virus in the air.

With VisualPDE, we're not just limited to watching a simulation: we can interact with it too. Clicking in the room will introduce some viral particles to the air, as if someone with an infection had coughed (coughing is actually a lot more complicated and is the focus of lots of research). Try clicking to see what difference a cough can make.

Though each cough introduces some virus to the room, it looks like it quickly decays away until we can't even tell it was there. So, does this mean we shouldn't be worried about a cough?

To explore this further, let's look at the probability (or chance) of getting an infection, which is related but not equal to the virus concentration. Specifically, we'll look at the chance of catching the virus assuming that you'd been in the same location for the duration of the simulation. With VisualPDE, we can do this by switching to the Probability View by pressing and choosing "Probability".

Now for the goldfish. People don't always stay still in the middle of rooms. Unsurprisingly, the movement of an infected individual can have a big impact on the spread of a virus. The next simulation is set up so that the source of the infection moves around the room, as if they were a waiter going between tables in a restaurant, perhaps. The air conditioner is turned off, so that the air in the room is still.

The Probability View shows the build-up of a ring of likely infections as the infectious person circles the room. A quick look at the Concentration View shows their circular path, leaving a trail of viral particles behind them.

To find out more about this simulation and how to explore it, go to the VisualPDE site.

The two scientific papers mentioned in the podcast are:

• Predicting the spatio-temporal infection risk in indoor spaces using an efficient airborne transmission model by Zechariah Lau, Ian M. Griffiths, Aaron English and Katerina Kaouri

• Turing Instabilities are Not Enough to Ensure Pattern Formation by Andrew L. Krause, Eamonn A. Gaffney, Thomas Jun Jewell, Václav Klika and Benjamin J. Walker 

In this episode of Maths on the Move we talk to two current Martingale scholars, Alexandra Sorinca and Malachy Reynolds, who have both just started their PhD at King's College London. We met them this summer at Solve for X, a mathematical modelling retreat delivered by the Martingale Foundation in partnership with the Newton Gateway to Mathematics and the Isaac Newton Institute for Mathematical Sciences (INI), which challenged teams of students to solve real-life maths problems posed by industry.  Solve for X is one of the activities the Martingale Foundation provides for its scholars. Alexandra and Malachy tell us about their challenges and also about what it's like being a Martingale scholar.

We also talk to Chloe Slevin, the Martingale Foundation's Communications Manager, who explains the Foundation's aims and gives useful advice for new applicants.

To find out more about the topics discussed in this podcast see Artificial intelligence and deep learning: Your questions answered.

This content is part of our collaboration with the Mathematics for Deep Learning (Maths4DL) research programme, which brings together researchers from the universities of Bath and Cambridge, and University College London. Maths4DL aims to combine theory, modelling, data and computation to unlock the next generation of deep learning. You can see more content produced with Maths4DL here.

In this episode of Maths on the Move Hannah explains how her interest in public engagement grew directly out of her work as a mathematician, talks about how she got into maths in the first place, and shares one of her favourite mathematical moments.

We were very proud that Hannah announced the news at an event we organised together with the Newton Gateway to Mathematics. It was called Communicating Mathematical and Data Sciences – What does Success Look Like? and took place at the Newton Institute for Mathematical Sciences (INI) on November 21, 2024. The event was part of the mathsci-comm network which aims to connect those working in, and with a stake in, communicating complex mathematics and data science to a variety of non-expert audiences. The network is supported by the INI — find out more here.

Image above: Lloyd Mann.

This content was produced as part of our collaborations with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.

But what is topological data analysis? And how might it help to understand proteins or diseases such as cancer? We find out with Heather Harrington a mathematician we met at the European Congress of Mathematics (ECM) this summer. Heather tells us how topological data analysis can produce a so-called barcode for a given data set which gives deep insights into its structure. Below are a couple of images illustrating a barcode to illustrate what we talk about in the podcast.

We attended the ECM with kind support of the London Mathematical Society (LMS). Heather gave the LMS lecture at the ECM.

You might also want to listen to more episodes of our Euromaths series which reports on the ECM.

Circles drawn around 20 points in the plane. If the radius r is less than r0, the circles are small enough to not overlap (left). Once the radius exceeds r0, but is smaller than r1, the circles overlap and together form a ring-like structure (middle). One the radius is larger than r1 the circles join up in the centre of this ring-like structure. What you see now is a single blob without a hole.

The barcode captures this information. For r < r0 there are 20 red lines indicating there are twenty connected components without holes. For r0 < r < r1 there is one green line indicating there is one connected component with one hole (the colours red and green differentiate between no hole and one hole). For r > r1 there is one red line indicating there is one connected component without a hole.

This content was produced with kind support from the London Mathematical Society.

We met Giovanni at the European Congress of Mathematics (ECM) in summer this year, which we attended with kind support of the London Mathematical Society. See here for more episodes of our Euromaths series which reports on the ECM.

To find out more about mathematical billiards on Plus see

• Chaos on the billiards table
• Playing billiards on doughnuts
• Playing billiards on strange tables

Here are a couple of academic papers by Forni and his collaborators:

• Weakly Mixing Billiards, J. Chaika, G. Forni
• Weak Mixing in rational billiards, F. Arana-Herrera, J. Chaika, G. Forni.

This content was produced with kind support from the London Mathematical Society.

Jessica tells us how to capture infinitely many snowflakes at the same time, the maths of symmetry and her work on representation theory, and why she likes doing handstands.

To find out a little more about Jessica's mathematics, as well as her gymnastics, see this video.

You might also like to look the following content relevant to topics discussed in the podcast:

• Groups: the basics
• Maths in a minute: Representing groups

This content was produced with kind support from the London Mathematical Society.

In this episode of Maths on the move Richard tells us about an amazing result he helped to prove to great acclaim, known as Ringel's conjecture, and why it's interesting to take graphs to the extreme.

You might also want to read this article about Richard's work. To find out more about the event at the Isaac Newton Institute in honour of Tim Gowers, which is mentioned in the podcast, see here.

This content was produced with kind support from the London Mathematical Society.

In this episode of Maths on the Move we talk to David about the book, touching on a huge range of topics — from double yolked eggs and the bay of pigs, to why it's useful to disagree and why uncertainty is personal. Enjoy!

To find out more about some of the topics mentioned in this episode see,

• When being wrong is right — on the "tell me why I'm wrong" approach
• Struggling with chance — on the philosophy of probability
• Freedom and physics — on randomness and free will

The strength of the Earth's gravity is measured by the gravitational constant g, one of the constants of nature. These constants are special not just when it comes to toast. If their values were just a tiny bit different, life as we know it couldn't exist. This begs the question of why — why are the constants fine-tuned for our existence? Some people have taken this fine-tuning as evidence of the existence of a god who wanted us to be here, but there's also another explanation: perhaps our Universe is just one of many, all with different values for the constants of nature? If such a multiverse exists, then the existence of our Universe within it is no longer surprising. It's just one of many.

All this reminded us of an interview we did in 2016 with astrophysicist Fred Adams at the FQXi international conference in Banff, Canada. In this episode of Maths on the move we bring you this interview. Adam tells us all about the multiverse and how knowledge about our own Universe can help us to calculate how many of those other universes could be similar to our own. We hope you enjoy it, but if it's too mind-boggling, have a piece of toast.

Fred Adams

In this episode of Maths on the move we revisit an interview with Domokos from all the way back in 2009.

We were reminded of this interview when we thought about what makes a good mathematical story and the story of the Gömböc has it all: beautiful mathematics, an exciting discovery, a beach holiday, romance (sort of) and even turtles. We hope you enjoy it!

You can read the article that accompanies this this episode here.

Gábor Domokos

You can find out more about groups in the following two collections Justin has produced:

• Groups: The basics
• Groups: A whistle-stop tour

You might also want to read Justin's article Explaining AI with the help of philosophy mentioned at the beginning of the podcast. It is based on an interview with Hana Chockler, a professor at King's College London, conducted at a recent event organised by the Newton Gateway to Mathematics and the Alan Turing Institute.

This article was produced as part of our collaborations with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.

First up is the eminent Avi Wigderson, who has won many prestigious mathematical prizes, including an Abel Prize in 2021. Avi gave a great talk at the ECM about the role of errors in mathematical proofs. Traditionally, mathematical proofs need to be absolutely waterproof and errors are anathema. But as Avi told us, if you allow a certain level of error to creep in, you can do amazing things. For example, you can construct zero knowledge proofs, which allow you to prove something without giving any information away about what you're proving. And you can construct proofs that even if they're very long, can be checked for correctness by just reading a few pages. Find out more in this episode of Maths on the move.

The photo of Avi Wigderson above is courtesy Cliff Moore/Institute for Advanced Study, Princeton, NJ USA/AbelPrize.

This content was produced with kind support from the London Mathematical Society.

In this episode of Maths on the move we talk to Livio about the new book. From creating life in the lab to searching for it on distant planets, Livio gives us a riveting whistelstop tour of research into the origin of life, here on Earth an elsewhere. Is Earth exceptional is out on September 10, 2024 in the US and on September 26, 2024 in the UK.

To get a taster of Livio's writing (which we think is very good) see a list of his Plus articles. We have also reviewed six of Livio's books:

• Galileo and the science deniers
• Why? What makes us curious
• Brilliant blunders
• Is god a mathematician?
• The equation that couldn't be solved
• The golden ratio

Marianne told us about her recent interview with Avi Widgerson – winner of the Abel Prize in 2021 and the most recent Turing Prize. Justin told us about  how the philosophical concept of causality can help us understand AI.  And Rachel tells us about the surprising phenomena of anti-diffusion and how it links the patterns we see on Juniper, staircases in our oceans and fusion reactors of the future.

We'll be back with  more podcasts in the Autumn, but here are some of our recommendations for your summer reading and listening pleasure!

Articles:

• How to (im)prove mathematics
• Fractal photo finish 
• Chaos on the billiard table 

Podcasts:

• Tying together black holes, quantum gravity and number theory
• The murmuration conjecture: finding new maths with AI
• From clicks to chords 

Books:

• Collision – Stories from the Science of CERN

This content was produced as part of our collaborations with the London Mathematical Society, the Isaac Newton Institute for Mathematical Sciences and the Newton Gateway to Mathematics. 

To find out we talk to mathematicians Kirsty Bolton, Assistant Professor at the University of Nottingham, and Ed Hill, a Warwick Zeeman Lecturer  at the University of Warwick.  Kirsty and Ed organised a recent workshop bringing together experts from across maths, data science, life sciences and social sciences to explore how mathematical models can be made more realistic by including human behaviour.  They tell us about both the mathematical and the communication challenges this brings, from the difficulty of learning the languages of other disciplines to the excitement of finding the sweet spot where experts from such different areas can work together to make progress.

Kirsty and Ed are both part of JUNIPER, a collaborative network of researchers from across the UK who work at the interface between mathematical modelling, infectious disease control and public health policy, and JUNIPER supported the workshop.

This podcast is part of our collaboration with JUNIPER, the Joint UNIversities Pandemic and Epidemiological Research network. JUNIPER is a collaborative network of researchers from across the UK who work at the interface between mathematical modelling, infectious disease control and public health policy. You can see more content produced with JUNIPER here.

So to celebrate the run-up to the ECM we've launched Euromaths, a miniseries of podcasts revisiting interviews with Fields Medallists who previously won an EMS prize. This week we hear from Maryna Viazovska who won a Fields Medal in 2022 and an EMS prize in 2020, talking about the theory of optimal transport and how it applies to a wide range of things, from crystals to clouds.

You can read about Maryna's work in this article. To listen to previous episodes of Euromaths click here.

This content was originally produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2022 International Congress of Mathematicians here.

So to celebrate the run-up to the ECM we've launched Euromaths, a miniseries of podcasts revisiting interviews with Fields Medallists who previously won an EMS prize. This week we hear from Artur Avila who won a Fields Medal in 2014 and an EMS prize in 2012, talking about the theory of optimal transport and how it applies to a wide range of things, from crystals to clouds.

You can read about Artur's work in this article. To listen to previous episodes of Euromaths click here.

This content was originally produced as part of our collaboration with the London Mathematical Society. You can find all our content on the 2014 International Congress of Mathematicians here.

So to celebrate the run-up to the ECM we've launched Euromaths, a miniseries of podcasts revisiting interviews with Fields Medallists who previously won an EMS prize. This week we hear from Alessio Figalli who won a Fields Medal in 2018 and an EMS prize in 2012, talking about the theory of optimal transport and how it applies to a wide range of things, from crystals to clouds.

You can read about Alessio's work in this article. To listen to previous episodes of Euromaths click here.

This content was originally produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2018 International Congress of Mathematicians here.

So to celebrate the run-up to the ECM we've launched Euromaths, a miniseries of podcasts revisiting interviews with Fields Medallists who previously won an EMS prize. This week we hear from James Maynard who won a Fields Medal in 2022 and an EMS prize in 2016, talking about is work on the fabled twin prime conjecture.

You can read about James's work in this short introduction and this in-depth article.

Click here to listen to last week's episode of Euromaths featuring Fields Medallist Hugo Duminil-Copin.

This content was originally produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2022 International Congress of Mathematicians here.

One of the interesting things that happens at an ECM is that the European Mathematical Society (EMS) awards ten prizes to mathematicians who are under the age of 35 at the start of the year the prizes are awarded. When looking through previous winners we noticed that quite a few winners of EMS prizes later go on to win a Fields Medal, one of the highest honours in mathematics, awarded every four years at the International Congress of mathematicians.

To celebrate the run-up to this year's ECM, we launch our Euromaths miniseries of podcasts, which revisits interviews with Fields Medallists from years past, who previously also won an EMS prize. We start the series by revisiting our interview with Hugo Duminil-Copin in 2022, when won a Fields Medal for his work transforming the mathematical theory of phase transitions in statistical physics. Hugo first won an EMS prize in 2016. We hope you enjoy the interview!

Hugo Duminil-Copin (Photo Matteo Fieni)

You can read about Hugo's work in this short introduction and this in-depth article.

This content was originally produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2022 International Congress of Mathematicians here.

In this podcast we speak to Yang-Hui He from the London Institute of Mathematical Sciences about his recent work on the evocatively titled murmuration conjecture. This exciting new conjecture came about due to both artificial and human intelligence, and reveals patterns in the prime numbers that look like flocks of birds. (You can also read more in the article that accompanies this podcast.)

A murmuration of starlings. Photo: Walter Baxter, CC BY-SA 2.0.

We were speaking to Yang as part of our coverage of the research programme, Black holes: bridges between number theory and holographic quantum information, held at the Isaac Newton Institute for Mathematical Sciences  in Cambridge.  The programme  brought together a fascinating array of experts in black holes and quantum theory, with mathematicians and computer scientists. You can read more in our coverage of the programme here.

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

Yang-Hui He (Photo Rajarshi Maiti – CC BY-SA 4.0)

You can find out more about the ideas we discussed with Yang in this podcast in the accompanying articles String theory: A promise from physics and String theory: Convincing mathematics. And stay tuned for the second part of our conversation with Yang in the next episode!

We were speaking to Yang about a research programme, Black holes: bridges between number theory and holographic quantum information, held at the Isaac Newton Institute for Mathematical Sciences  in Cambridge.  The programme  brought together a fascinating array of experts in black holes and quantum theory, with mathematicians and computer scientists. You can read more in our coverage of the programme here.

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

Andrzej Herczyński

Andrzej and Paul were two of the organisers of the workshop Space, scale and scaling in art, which recently took place at the Isaac Newton Institute for Mathematical Sciences in Cambridge. We find out about the rich dialogue that can ensue between artists and mathematicians, how maths and physics can help us understand the power of art and how we perceive it, and provide insights into how a particular piece of art was made.

The Space, scale and scaling in art workshop was part of a larger research programme funded by the National Science Foundation on the intersection of science and art.

You can see Agnes Martin's painting Morning, which is mentioned in this episode, here (though the digital version does not do it justice). To see Jackson Pollock's works, which are also discussed in this episode, go to the Jackson Pollock website. The image above has been generated by AI.

Paul Glendinning

To find out more about some of the topics mentioned in this episode, see the following articles:

• Fractal expressionism looks at fractal structures in works by the abstract expressionist Jackson Pollock.
• The Artist's fractal fingerprint explores Pollock's paintings further.
• Sine language looks at a song by our musician friend Oli Freke which explores the idea of sine waves, and how they relate to other concepts such as the Western tuning system known as equal temperament and even to ancient Greek cosmological ideas.
• Fractal music has composer Dmitry Kormann explaining how he brings fractal-like patterns to the very structure of his music, with beautiful results.
• Restoring profanity explores how the heat equation can help restore damaged art works.
• Where to stand to look at sculptures uses some simple geometry to find the perfect vantage point from which to take in a sculpture (or painting).

To see all our content on maths and art see here, and for everything on maths and music see here.

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

We will explore this surprising link in an upcoming episode, but for now we revisit a 2018 interview with mathematician Ken Ono (pictured above), who was an advisor and associate producer on the well-known film about Ramanujan, The man who knew infinity. Talking to Plus Editor Rachel Thomas, Ken explores just what made Ramanujan's work so special and the piece of mathematics that is relevant to black holes. Rachel talked to Ken at the Royal Society's celebration of the centenary of Ramanujan's election as a Fellow of the Royal Society.

You can also read an article accompanying this podcast, which looks at the mathematics relevant to black holes. For more about Ramanujan's mathematics, and Ken's research into it, see Ramanujan surprises again. To find out more about the Spirit of Ramanujan project, which Ken mentions in this episode, see here.

To find out more about the topics mentioned in this episode see the following articles:

• A tip of the hat: Celebrating an aperiodic monotile — meeting the discoverers of the hat
• Contagious maths — bringing epidemiological research into the classroom
• The mathematics of movement — what do cancer cells, birds, and whales have in common (and can a slime mould be intelligent)?
• Outraged by not knowing— new insights in topology with Oscar Randal-Williams

To find out more about our work with the JUNIPER network of disease modellers see here and to find out more about our work with the maths4DL research project see here.

We have been able to sit in on a number of meetings of our colleagues from Maths4DL (the Mathematics for Deep Learning research group) as they explore this idea.   Georg explains why PINNs are a bit like learning golf, tells us about the exciting opportunities and challenges, and why the key part to developing new ideas is getting the right people together at the right time.

You can find more about the machine learning and the some of the work that Maths4DL is doing at https://plus.maths.org/maths4dl, including our recent podcast How does AI work?  and our collection Predicting the weather with artificial intelligence.

This content is part of our collaboration with the Mathematics for Deep Learning (Maths4DL) research programme, which brings together researchers from the universities of Bath and Cambridge, and University College London. Maths4DL aims to combine theory, modelling, data and computation to unlock the next generation of deep learning. You can see more content produced with Maths4DL here.

At the same time our partners at the Isaac Newton Institute next door hosted one of our favourite physicists: Ben Allanach, Professor of Theoretical Physics at the University of Cambridge. Ben gave a talk called The force awakens: Quantum collisions, in which he explored experiments at the Large Hadron Collider (LHC), particle physics, as well as recent research results which suggested there may be a fifth force of nature, hitherto unknown to science.

For those who weren't able to attend Ben's talk we revisit an interview with him from last year, in which he explains this intriguing (and if true sensational) result about a potential new force.

The image above illustrates particle collisions at the LHC and is courtesy CMS.

This content now forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI). The INI is an international research centre in Cambridge which attracts leading mathematicians from all over the world. You can find all the content from the collaboration here.

In this episode of Maths on the move we talk to Kweku Abraham, member of Maths4DL, a research project which investigates deep learning, and postdoctoral researcher at the University of Cambridge. Kweku explains how machine learning works, why it's so powerful and whether there are any limits to what it can achieve, and the kind of maths he works on every day.

To find out more about the topics discussed in this episode, see Artificial intelligence and deep learning: Your questions answered.

This content is part of our collaboration with the Mathematics for Deep Learning (Maths4DL) research programme, which brings together researchers from the universities of Bath and Cambridge, and University College London. Maths4DL aims to combine theory, modelling, data and computation to unlock the next generation of deep learning. You can see more content produced with Maths4DL here.

A very interesting group of people came together to discuss this in January 2024. Policy makers, climate scientists, epidemiologists and mathematicians met at a workshop at the University of Oxford to discuss the impact of climate change on epidemics. We spoke to one of the organisers, Helena Stage, from the University of Bristol, about how exactly climate change impacts the spread of diseases, how maths can help and why it's so important to think globally.

Helena Stage

You can find out more about disease modelling and epidemiology in our library for beginners, or our work with JUNIPER (the Joint UNIversities Pandemic and Epidemiological Research network). And you can find out more about climate change and how maths can help in these articles and podcasts.

This podcast was produced as part of our collaborations with JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium, and the Isaac Newton Institute for Mathematical Sciences (INI), both of whom funded the workshop discussed in this episode.

JUNIPER comprises academics from the universities of Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster, who are using a range of mathematical and statistical techniques to address pressing question about the control of COVID-19. You can see more content produced with JUNIPER here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

In this episode of Maths on the move the Centre's Director of Research, Shaun Fitzgerald, tells us more about the Centre's work and its three-fold mission: to reduce emissions of greenhouse gases, to remove excess green house gases from the atmosphere, and to refreeze the Arctic.

You may also want to read the article accompanying this episode of Maths on the move. For more about mathematics and climate change, see here.

We hope you enjoy this final episode of the year and wish you all the best for next year! And remember: no matter how hard a piece of mathematics might be, there's always something in it that everyone can relate to!

To find out more about the topics mentioned in this episode see

• Fermat's last theoem
• Telescope topology
• From clicks to chords, the article and the the podcast
• Creating a low carbon energy network
• A 60% chance of rain: our podcast episode featuring climate scientist Tim Palmer
• Climate change and ready meals: Challenges for epidemiologists

To find out more about our collaboration with the Isaac Newton Institute see here, about our collaboration with the JUNIPER network see here, and about our collaboration with Maths4DL see here.

Chris and Lars tell us why decarbonising the energy network also resents huge mathematical challenges — and why the effort isn't unlike the Apollo mission that got people to the Moon in the 1960s.

You can read more about the topic discussed in this episode in this article.

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

(The sound effects used in this podcast are by jlozano and nemoDaedalus.)

You can read more about the travelling salesman problem, P versus NP, and cryptography on plus.maths.org

One thing we hadn't thought of, until 2013 that is, was that he could be the emotional centerpoint of a musical. The universal machine is a musical about Alan Turing's life and work that was staged in London in 2013. As part of our series about putting maths on stage and screen, we revisit our 2013 interview with the writer and director David Byrne, actor Richard Delaney, who played Turing, and assistant director Natalie York, to find out how you turn such a story, and the maths in it, into a musical.

We are very grateful to Dominic Brennan, who wrote the music for The universal machine, for giving us permission to use the track Building The Bombe Part Two from the show.

The universal machine poster detail.

For more information:

• You can read the original article accompanying this podcast and a review of The universal machine;
• You can find out more about the Enigma code and how it was cracked in Exploring the Enigma;
• You can read about morphogenesis in How the leopard got its spots;
• And there is more on Turing and his work in Alan Turing: ahead of his time and What computers can't do. These two articles also look at the halting problem which is related to the Entscheidungsproblem mentioned in the podcast.

You can also read about A disappearing number in this article. To find out more about Victoria Gould's career as an actor and mathematician, see this article or listen to last week's episode of Maths on the move.

Such a discovery would be quite a revolution, so we went to talk to our friend Ben Allanach, Professor of Theoretical Physics at the University of Cambridge, to find out more. Ben explained the science, gave us his personal hunch regarding the experimental results, and provided a fascinating glimpse into life at the cutting edge of physics.

Ben Allanach

To find out more about the topics explored in this podcast, see The physics of elementary particles and A brief introduction to quantum field theory. Click here to see all our content featuring Ben Allanach.

You can also read the article accompanying this podcast, and find out more about the play A disappearing number here.

We were inspired to revisit this episode when we met mathematical film maker Ekaterina Eremenko at this year's Heidelberg Laureate Forum. Eremenko's latest film, Solving the Bonnet problem, really gets across that mathematics is a dynamic, and sometimes dramatic, pursuit that can be well suited for the stage and screen. You can watch the trailer here.

David Berman

You can also read the articles that accompany this podcast: Kaluza, Klein and their story of a fifth dimension and The ten dimensions of string theory.

The result was announced this summer at a conference organised by Isaac Newton Institute for Mathematical Sciences in Cambridge (INI).

We talk to two of these mathematicians, Tomer Schlank and Jeremy Hahn, to get a gist of this high-powered result in pure mathematics, which is nevertheless wonderfully intuitive. So fasten your seatbelt and join us on a trip into the wonderful world of homotopy theory!

Jeremy Hahn                  Tomer Schlank

To read an article exploring the telescope conjecture and for some background reading, see here.

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI). The INI is an international research centre in Cambridge which attracts leading mathematicians from all over the world. You can find all the content from the collaboration here.

This podcast was originally released earlier this year when musician Ed Sheeran was in the news  as he was being sued for similarities between his song Thinking out loud from 2014, and Marvin Gaye's song Get it on from 1973. But, given the way we write music to fit into specific genres, is it possible to write unique music with the limited quantity of notes and chords available?

After first answering this question in this podcast, Oli has now written a brilliant article, From clicks to chords, where you can see some of the connections between maths and music come to life.   

You can find out more about the maths in music in Oli's articles other – How many melodies are there? and Sine language. And you can find more of Oli's music, and his book "Synthesizer Evolution", here!

The music in this podcast comes from, of course, Oli Freke! The track is called Funk Off.

Spare a thought for whales then, who have to put up with the constant noise caused by shipping and the construction of oil rigs and wind farms in the oceans. There are concerns that the noise pollution we cause bothers and confused the whales so much, it may even disrupt their ability to go on their annual migrations.

In this episode we talk to Stuart Johnston of the University of Melbourne in Australia who uses mathematics to understand the migration of whales and how it might be impacted by human generated noise. The ultimate aim is to figure out what we can do to mitigate the disruption we cause.

We met Stuart at a workshop on collective behaviour, which took place at the Newton Institute for Mathematical Sciences (INI) in Cambridge in August 2023. The workshop was part of a 6-month research programme on the mathematics of movement which is currently taking place at the INI.

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI). The INI is an international research centre in Cambridge which attracts leading mathematicians from all over the world. You can find all the content from the collaboration here.

Find out more about Coralie's writing, download a free PDF of the book, and find links to other online sellers here.

This podcast is part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

They did all this attending the Graduate Modelling Camp, which is organised every year by the Newton Gateway to Mathematics in Cambridge. The camp gives early career mathematicians a chance to experience life as a mathematical modeller by challenging them to solve problems posed by industry.

We talk to Chris Breward, who has been helping to run the modelling camp for many years, to PhD students Emily Cook, Julian Glover, and Michael Smah, who attended this year's camp, and to Ashleigh Hutchinson who took part as a mentor. They all enjoyed the camp immensely — find out why in this podcast!

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics. The INI is an international research centre in Cambridge which attracts leading mathematicians from all over the world. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.

In this podcast we find out what these new results mean, and why they're so exciting, with Michalis Agathos, Amelia Drew, and Ulrich Sperhake of the Stephen Hawking Centre for Theoretical Cosmology at the University of Cambridge. Join us on this fascinating, and slightly mind-bending, cosmic ride!

To find out more about the topics discussed in this podcast see:

• Maths in a minute: Gravitational waves
• Maths in a minute: Black holes
• Maths in a minute: Einstein's general theory of relativity

You might also want to listen to our recent podcast A new map of dark matter.

The illustration above is an artist's rendering of black hole binaries emitting gravitational waves, produced by Olena Shmahalo for NANOGrav and reproduced here under CC BY 4.0.

Sarah tells us about the links between poetry and mathematical proof, the maths of Moby dick and the The luminaries, and why mathematical patterns and references can enhance your enjoyment of a book even when you're not aware of them.

To find out more about the problem of squaring the circle, which is mentioned in this podcast, see Mathematical mysteries: Transcendental meditation. To find out more about conic sections, see here.

Wiles' announcement, 30 years ago today, was a thrilling moment in mathematical history. But Fermat's Last Theorem is not just the story of one person. Jack Thorne, who works on new mathematics that builds on Wiles' proof, told us that it is actually a story of people talking to each other over a period of centuries.

To celebrate 30 years since that exciting moment, we were lucky enough to speak with Andrew Wiles and Jack Thorne, and also to Tom Körner, who was there the day Wiles announced the proof.

This is a special joint episode with the INI's Living Proof podcast, made in collaboration with our friend Dan Aspel, from the INI.

You can find out more about Fermat's Last Theorem in the article that accompanies this podcast, and in this collection of further reading.

This podcast was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

We talked to Valerie at the Isaac Newton Institute for Mathematical Sciences in Cambridge where Valerie is currently co-organising a research programme on the mathematical theory and applications of multiple wave scattering. As we will find out, this has a huge range of applications, from understanding mayonnaise to making invisibility cloaks.

While Valerie is a professor at the University of Loughborough now, her career path has also involved work in industry and time out for kids, so we also asked her for some advice for women mathematicians and scientists wondering how to build their career.

This podcast was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from the collaboration here.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

You can find out more about the maths in music in Oli's articles – How many melodies are there? and Sine language. And you can find more of Oli's music, and his book "Synthesizer Evolution", here!

The music in this podcast comes from, of course, Oli Freke! The track is called Funk Off.

In this podcast we talk to Blake Sherwin about a brand new map of dark matter that has been produced by a consortium of scientists using data from the Atacama Cosmology Telescope which sits high up in the Chilean Andes. Sherwin is part of that consortium, and he is also Professor of Cosmology and Astrophysics the University of Cambridge and a member of the Stephen Hawking Centre for Theoretical Cosmology at Cambridge.

Sherwin tells us how you go about producing a map of something you can't see, in how far the new map solves the so-called crisis of cosmology, and whether we will ever find out what dark matter is made of.

To find out more about dark matter, read Maths in a minute: Dark matter and What is dark matter? And you can find all the details about the research by Blake, his PhD student Frank Qu, and their colleagues in their series of papers here, here and here.

The music in this podcast is by eusa and the track is called Plankton. you can find their music on Soundcloud.

Matt Keeling

----more----We're very pleased to host this episode of SBIDER Presents, one of the podcasts produced by the Zeeman Institute for Systems Biology & Infectious Disease Epidemiology Research (SBIDER). You can find out more about the work Matt Keeling is discussing in this podcast in our article Shining a light on COVID modelling. And you can hear more from Ed and Laura in our previous podcasts On the mathematical frontline: Ed Hill and Climate change and ready meals: Challenges for epidemiologists.

This podcast is part of our collaboration with JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium. JUNIPER comprises academics from the universities of Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster, who are using a range of mathematical and statistical techniques to address pressing questions about the control of COVID-19. You can see more content produced with JUNIPER here.

Algae going through their paces.  (Movies: Kirsty Wan and Raymond E. Goldstein, for more information see this paper)

In 2019 we visited Ray Goldstein, Schlumberger Professor of Complex Physical Systems at Cambridge, and he explained how algae manage to synchronise their so-called flagella, what this means for human physiology, and how it sheds light on the evolution of multi-cellular organisms from single-celled ones.

You can also read our article on Goldstein's work with volvocales, or watch an interview with Goldstein in this video.

Sound effects in this podcast are from Robinhood76 and 16HPanskaKanclirova_Victoria on freesound.org.

This podcast was partially funded by the European Mathematical Society.

Today's podcast was inspired by questions sent in by our friend Ash. To answer Ash's questions we take a trip to our favourite hotel, and we revisit our 2012 interview with our late boss, John D. Barrow, when we asked him – does infinity exist? Listen to the podcast to find out how infinity can corrupt the youth, why subtracting infinities can give you the right answer, and the weirdness that might be lurking out there in the cosmos...

Image created by FAVIO.

You can read more about infinity on plus.maths.org. And if you have a question about life, the universe and everything you'd like us to answer – email us as plus@maths.cam.ac.uk or contact us on twitter.

In this podcast we talk to researchers Helena Stage and Laura Guzmán-Rincón about two such questions. One concerns the fact that a warming climate allows disease-carrying mosquitoes to live in places they previously found too cold. The other asks how you might detect a hidden outbreak of food poisoning coming, for example, from ready meals having been contaminated way back in the production chain. Both require clever mathematical ideas and ingenious detective work.      

Helena and Laura are members of the JUNIPER modelling consortium. We met them at a JUNIPER research meeting which took place at the University of Warwick in March 2023.

This podcast is part of our collaboration with JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium.

JUNIPER comprises academics from the universities of Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster, who are using a range of mathematical and statistical techniques to address pressing question about the control of COVID-19. You can see more content produced with JUNIPER here.

Timandra Harkness – presenter, writer, comedian and Fellow of the Royal Statistical Society – told our friends Dan Aspel and Maha Kaouri her favourite maths joke in this episode of the Living Proof podcast from the Isaac Newton Institute for Mathematical Sciences.

Timandra Harkness

Timandra brilliantly chaired several sessions of the Communicating mathematics for the public event at the Newton Gateway to Mathematics. In this podcast Timandra spoke about how to make maths funny, and how she came to fall in love with mathematics from an arts and humanities background.

Oh and the punchline to Timandra's favourite joke? You'll have to listen to the podcast to find out!

00:00 – Introduction 00:44 – Welcome, discussing Communicating mathematics for the public 03:38 – Origins of Timandra's interest in maths, understanding "enough to ask the right questions" 07:50 – Discussing Timandra's book Big Data – Does Size Matter? 11:10 – Other current projects and shows, writing another book about "why everything is personalised" 13:13 – Mingling an arts background with a mathematics focus, "coming out as a closet mathematician" 17:10 – How do you make maths funny as a comedian? … "What's a statistician's favourite sandwich filling?" 21:10 – Future projects

This podcast was inspired by the Communicating mathematics for the public event at the Newton Gateway to Mathematics in January 2023.

(If that joke tickles your funny bone – try this one!)

This podcast is part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

Our friends Dan Aspel and Maha Kaouri spoke to Hannah for this episode of the Living Proof podcast from the Isaac Newton Institute for Mathematical Sciences. Hannah told them about her work helping to make government data more accessible, the common pitfalls of data accessibility and tips and tricks that can help. They also find our why more people used to get married at the end of the tax year...

Hannah Thomas speaking at the Communicating mathematics for the public event

00:00 – Introduction 00:44 – Welcome, discussing “Communicating Mathematics for the Public” (“as entertaining as Disneyland Paris and definitely more inspiring”) 04:20 – All about Government Analysis Function, a love of data journalism, career history 13:35 – Visualising data and making digital information accessible 21:40 – Common accessibility pitfalls 24:20 – Plans for the future… e-learning resources

This podcast was inspired by the Communicating mathematics for the public event at the Newton Gateway to Mathematics in January 2023. For more information we strongly recommend you watch Hannah's talk from that event, Data Visualisation and Digital Accessibility: What We Can Do to Help.

This podcast is part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

Following on from the Communicating mathematics for the public event at the Newton Gateway to Mathematics we spoke to the INI's Dan Aspel about our work in this episode of the Living Proof podcast. You can find all the content from our collaboration here.

Communicating from the mathematical frontiers - from plotting a path to the highest peak to exploring the hidden depths.

00:00 – Introduction 00:44 – Welcome, discussing Communicating Mathematics for the Public, the importance of trustworthiness 05:30 – Who you're speaking to vs what you're saying 07:38 – Making higher mathematics accessible to audiences: "any bit of mathematics either comes from somewhere, or is going somewhere, or both" 14:20 – Are there incommunicable subjects? 16:55 – The rarity of maths "headlines" 19:25 – The partnership between INI and Plus magazine – why is it important? 23:25 – Are some topics inherently more interesting? 25:26 – What is the end goal of maths communication? "I would love it if people could see how maths is everywhere… that maths is a language of rhythms and patterns" 30:00 – Looking to the future

This podcast was inspired by the Communicating mathematics for the public event at the Newton Gateway to Mathematics in January 2023. You can watch our talk from that event, Trust, time and truth, that was about our collaboration with JUNIPER modelling consortium.

This podcast is part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

We finally met Tom when we were both speaking at the Communicating mathematics for the public event in January 2023 at the Newton Gateway to Mathematics in Cambridge. In this podcast Tom tells us about providing a bridge between policy and mathematics, the importance of transparency, and the joy of the R number being discussed at the hairdressers.

This episode is part of On the mathematical frontline, a special series of the Plus podcast which explores the work of mathematicians grappling with the unprecedented challenge of studying a live pandemic unfolding in front of their eyes. In this series we interview our colleagues in the JUNIPER modelling consortium, whose research and insights have fed into SPI-M and SAGE - the Scientific Advisory Group for Emergencies, both of whom advise the UK government on the scientific aspects of the COVID-19 pandemic.

You can watch Tom's talk on the Challenges in Communicating the Results of SAGE's Covid Modelling, and you can find all our work covering COVID-19 here.

This podcast is part of our collaboration with JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium.

JUNIPER comprises academics from the universities of Cambridge, Warwick, Bristol, Exeter, Oxford, Manchester, and Lancaster, who are using a range of mathematical and statistical techniques to address pressing question about the control of COVID-19. You can see more content produced with JUNIPER here.

We were very happy to start 2023 with catching up with David (the first time in person since the pandemic!) at the Communicating mathematics for the public event that we were both speaking at in the Newton Gateway to Mathematics in Cambridge. We hope you enjoy this interview with him from 2015, where he gives us some of his favourite snippets from the book, and some easy ways you can think more critically about statistics. (You can also watch our interview as a video or read the associated article.)

Donald Sadoway

Hope is on the horizon in the form of liquid metal batteries. At a recent event organised by the Newton Gateway to Mathematics in Cambridge we met Donald Sadoway who played a very important role in pioneering these batteries. In this podcast he talks to us what they are and why they are better, when they'll be commercially available, and why sometimes it's best to ignore the experts.

To watch a talk given by Sadoway at the Newton Gateway event go to the Newton Gateway website. And to find out more about magnetohydrodynamics, a theory that has been used to describe liquid metal batteries, go here.

Tim Palmer.

We were lucky enough to meet Palmer at a recent event organised by the Newton Gateway to Mathematics In Cambridge. In this podcast we talk to Palmer about this call for a "CERN for climate change" and why climate forecasting requires so much computing power in the first place. Palmer also tells us about a technique for dealing with uncertainty called ensemble forecasting, and what his work has taught him about uncertainty more generally, as it crops up in many areas of life and nature.

Tim Palmer's new book on the science of uncertainty, The primacy of doubt, is published by Oxford University Press. To learn more about climate models see this article. To learn about weather forecasting see this article, and to read about uncertainty more general click here.

This podcast was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

Or are they? Today would have been our wonderful boss, John D. Barrow's, 70th birthday. And to celebrate him and his work we look at the answer to this question in today's podcast.

John D. Barrow (Image credit: Tom Powell)

Over time, since these constants were discovered, people had hoped to find a theory, a great theory of everything, that would explain why these particular values had arisen. However, as John explains in this podcast, developments in recent decades, in areas such as string theory, have shown that these constants could take any value. And this provided the motivation for studying whether such constants might be changing in value.

John, together with the astronomer John Webb, initiated an observational programme looking at the light produced by quasars in the distant Universe. They developed new techniques to analyse the light to test if certain constants had the same value near a quasar as they did in laboratories here on Earth.

You can find out more about this aspect of John’s work in this podcast, and read more in his accompanying article: Are the constants of nature really constant? And you can find out more about some of John's other work and interests in his many Plus articles.

This interview was recorded in 2009 as part of our celebration of the International Year of Astronomy 2009, where we tried to answer the questions everyone wanted to ask about the Universe

For this week's episode we delve back far into our archive to hear from Paul Shepherd from the University of Bath, an expert in building football stadiums such as the famous Emirates stadium in London. In this interview, first recorded back in 2007, he tells us about what kind of things are important in building a stadium, how maths is an integral part of the design process, and why his work required him to listen to Belgian techno.

The Emirates Stadium, home of the Arsenal football club. (Photo Arne Müseler – CC BY-SA 3.0 DE)

You can hear more about the maths behind famous sporting buildings in our recent podcast How the velodrome found its form. And you can find out much more about the maths behind football and sports, and behind engineering and architecture here on Plus.

In this podcast Yuriy speaks to the INI's Dan Aspel and shares his experience of the Russian invasion of Ukraine, and why the work of a mathematicians is always possible.

We are very pleased to host this episode of the Living Proof podcast as part of our collaboration with the wonderful INI.

In this podcast Nataliya tells her story in conversation with the INI's Dan Aspel.

We are very pleased to host this episode of the Living Proof podcast as part of our collaboration with the wonderful INI.

This podcast was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) – you can find all the content from our collaboration here. The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. It attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.

On our way to the writing workshops we were running with these women, we walked past six inspiring portraits of female mathematicians from Cambridge. These form part of the Women of Mathematics photo exhibition, which celebrates female mathematicians from institutions throughout Europe. It's been a great pleasure revisiting our our 2017 Women of Mathematics interviews with these mathematicians about their work and their mathematical lives in this special series of podcasts.

Today's podcast is the final one of this series, and we are very pleased to revisit our interview with Carola-Bibiane Schönlieb, now professor of applied mathematics and a very good friend of us here at plus.maths.org. Carola works on the interface between machine learning and the mathematics of image analysis.

You can read more about some of Carola's recent work, including how artificial intelligence can support medical doctors in their work, and the INTEGRAL project, a collaboration with Indian researchers on how machine learning can make sense of the vast amounts of remote sensing data that is available to help conserve forests and improve life in cities.

To find a transcript and video of this interview, meet the other female mathematicians, and find out more about the exhibition, see here.

Holly Krieger (Photograph by Henry Kenyon)

You can find more about Krieger's prize winning work in Dynamic numbers and you see her talk about complex numbers and dynamical systems in our collection Complex numbers: Why do we love them?

To find a transcript and video of this interview, meet the other female mathematicians, and find out more about the exhibition, see here.

In this interview, first recorded to celebrate the addition of six portraits of Cambridge mathematicians to the Women of Mathematics photo exhibition, Gog told us about the buzz of mathematical research, and how maths can help you do good in the world.

To find a transcript and video of this interview, meet the other female mathematicians, and find out more about the exhibition, see here. And you can read more about the work of Gog and her JUNIPER colleagues here.

To find a transcript and video of this interview, meet the other female mathematicians, and find out more about the exhibition, see here. And you can read more about Davis' recent prize-winning research in our article On the road to dark energy (with chameleons).

In this podcast we revisit our 2017 interview with Nilanjana Datta - now a professor in quantum information theory., who told us why she loves maths and also about some of the challenges she has faced as a female mathematician.

You can see all the Cambridge portraits and find out more about the work and mathematical lives of these women here. And stay tuned to this podcast for the rest of the interviews with these brilliant women of mathematics over the coming weeks.

The music in this podcast comes from the band eusa. The track is called Plankton.

On our way to the writing workshops we were running with these women, we walked past six inspiring portraits of female mathematicians from Cambridge. These form part of the Women of Mathematics photo exhibition, which celebrates female mathematicians from institutions throughout Europe. When the University of Cambridge hosted the exhibition in 2017, we had the opportunity to interview these Cambridge mathematicians about their work and their mathematical lives.

In this podcast we revisit our 2017 interview with Natalia Berloff, Professor of Applied Mathematics, who told us why maths is like a treasure hunt, and shared some of her adventures in the world of maths.

You can see all the Cambridge portraits and find out more about the work and mathematical lives of these women here.  And stay tuned to this podcast for the rest of the interviews with these brilliant women of mathematics over the coming weeks.

The music in this podcast comes from the band eusa. The track is called Plankton.

Yoshua Bengio (Photo copyright: Heidelberg Laureate Forum Foundation)

We'll find out how such agency helps us learn, what it could mean for computers to have it too, and hear about Bengio's work introducing it into an area of machine learning called deep learning.

And, in honour of the mathematician Ron Graham who sadly passed away in July 2020, we celebrate our very favourite number, Graham's number, by telling you about it in just one minute.

You can find out more about Bengio's take on agency in this series of articles, about machine learning in this article, and about Graham's number in this article.

The music in the podcast is by Oli Freke and the track is called Line-1. You can listen to more of Oli's music on Soundcloud.

This podcast was produced as part of our collaboration with the Isaac Newton Institute (INI) – you can find out more of our work with the INI here.

How can a machine learn to distinguish a picture of a cat from a picture of a dog?

At the Heidelberg Laureate Forum in 2019, Chris Budd, Professor of Applied Mathematics at the University of Bath, talked us through the basics of how these learning machines tick.  While Raj Reddy, Turing Award winner and artificial intelligence pioneer, talked to us about his grand challenges in artificial intelligence, and why time travel and immortality might be easier to achieve than creating a machine that rivals human intelligence.

To find out more about machine learning, its history, and some of the moral questions it raises, read the series of articles based on Chris' Gresham College lectures. 

The music in this podcast is from Oli Freke, and the track is called "Experimental 5". You can find his music at soundcloud.

This podcast, first published in August 2020, was partially funded by the European Mathematical Society.

Sir Chris Hoy leads the GB Cycling Team during the official opening of the Velodrome (Photograph by David Poultney)

We hope you enjoy revisiting this conversation, and you can find out more in this accompanying article. Good luck to all the athletes completing in the 2022 Commonwealth Games!

June Huh. Photo: Lance Murphey.

In this podcast, which comes to you from the opening days of the ICM 2022 in Helsinki, we talk to Huh about is relatively late start in mathematics, about maths you can "feel and touch", and why maths mirrors who we are as a species.

You can read about Huh's work in this short introduction and this in-depth article. See here for all our coverage of the prizes awarded at the ICM 2022.

This content was produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2022 International Congress of Mathematicians here.

Hugo Duminil-Copin (Photo Matteo Fieni, used with permission)

In this podcast, which comes to you from a beautiful lake on day two of the ICM 2022 in Helsinki, we talk to Duminil-Copin about how his work in statistical physics brings together his two loves – maths and physics.

You can read about Duminil-Copin's work in this short introduction and this in-depth article. See here for all our coverage of the prizes awarded at the ICM 2022.

This content was produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2022 International Congress of Mathematicians here.

James Maynard (Photo by Ryan Cowan, used with permission)

In this podcast, which comes to you from the opening day of the ICM 2022 in Helsinki, we talk to Maynard about his love for numbers and groundbreaking progress towards something that has eluded mathematician for a very long time: a proof of the twin prime conjecture.

You can read about Maynard's work in this short introduction and this in-depth article. See here for all our coverage of the prizes awarded at the ICM 2022. And to hear from the other Fields Medallists check out existing and upcoming podcast episodes.

This content was produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2022 International Congress of Mathematicians here.

This year's Congress is a little different – it is being held as a fully virtual event with only the prize ceremonies and lectures taking place in-person in Helsinki, Finland on 5 and 6 July. The rest of the schedule fascinating talks from across the spectrum of maths will take place online over the coming week.

In this podcast we tell you all the winners of all the prizes being announced today at the ICM and bring you an interview with one of them: Maryna Viazovska, who has won a Fields Medal for a ground-breaking result in the theory of sphere packings. Viazovska is only the second woman to receive a Fields Medal, following on from Maryam Mirzakhani, who won it in 2014.

Maryna Viazovska. Photo: Matteo Fieni.

You can find out more about Viazovska's work in our short introduction or our more in-depth article.

To read about the work of all the prize winners, see here. And to hear from the other Fields Medallists watch out for upcoming podcast episodes.

This content was produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2022 International Congress of Mathematicians here.

We are fortunate to have been able to interview the prize winners in advance of the conference, but that’s top secret and we won’t be revealing the winners till they are announced publicly in Helsinki next week!  We're really looking forward to sharing our interviews with you when we meet them in person in Helsinki next week, where we will also bring you all the news from the ICM itself.

But in the meantime, to get us in the mood, let's revisit the 2018 ICM that took place in Rio de Janeiro in Brazil.  It was a brilliant conference and the podcast you are about to hear was recorded on that very first days of the 2018 ICM, when all the big prizes were announced.  You can find all our coverage of the past three ICM’s by going  to plus.maths.org and searching for "ICM".  

And stay tuned for our special series of podcasts, Maths on the Red Carpet, starting next week, that will bring you all our reporting from this years International Congress of Mathematicians.  But for now - enjoy the sounds of the Brazilian forest in this podcast revisiting the exciting first days of the 2018 ICM....