Maths on the Move
- Folgen
- 100
- Erscheint
- wöchentlich
- Letzte Folge
- 10. Nov. 2026
Über den Podcast
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
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Henry Bradford: AI versus mathematicians
There has been a lot of discussion about AI proofs, some of which we have covered earlier in this podcast series. But what actually happens when an AI proof is announced? How much credit should be assigned to …
Shownotes
There has been a lot of discussion about AI proofs, some of which we have covered earlier in this podcast series. But what actually happens when an AI proof is announced? How much credit should be assigned to human work? How much is hype? We spoke to Henry Bradford, our colleague at the University of Cambridge, about his experience after OpenAI announced a new result in his field of mathematics, concerning non-sofic groups. Through this case-study, he explains the mathematical ideas, as well as the ethical and practical questions that come up with the rise of AI technologies and their use in mathematics.
You might also like:
- An overview of groups
- A short explainer of the Navier-Stokes equations
- A summary of the 2026 International Congress of Mathematicians
If you would like to find out more about the mathematics involved in the result Henry is talking about, listen to the Director's cut, a longer version of this episode. You can also find out more in the accompanying article.
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
Henry Bradford: AI versus mathematicians (Director's Cut)
There has been a lot of discussion about AI proofs, some of which we have covered earlier in this podcast series. But what actually happens when an AI proof is announced? How much credit should be assigned to …
Shownotes
There has been a lot of discussion about AI proofs, some of which we have covered earlier in this podcast series. But what actually happens when an AI proof is announced? How much credit should be assigned to human work? How much is hype? We spoke to Henry Bradford, our colleague at the University of Cambridge, about his experience after OpenAI announced a new result in his field of mathematics, concerning non-sofic groups. Through this case-study, he explains the mathematical ideas, as well as the ethical and practical questions that come up with the rise of AI technologies and their use in mathematics.
You might also like:
- An overview of groups
- A short explainer of the Navier-Stokes equations
- A summary of the 2026 International Congress of Mathematicians
This is the Director's cut version of this podcast episode, with more detail about the maths involved. Alternatively, you can listen to the original or you can find out more in the accompanying article.
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
Chris Budd: Did AI prove the Navier-Stokes Millennium Problem?
Recently, Open AI announced that one of their systems had proved one of the hardest maths problems in the world – the Navier-Stokes Millennium Problem, which comes with a million dollar reward. Naturally it has …
Shownotes
Recently, Open AI announced that one of their systems had proved one of the hardest maths problems in the world – the Navier-Stokes Millennium Problem, which comes with a million dollar reward. Naturally it has shaken the maths world, but there’s still a lot of confusion about what has actually been proved and how. To get to the bottom of it, we knew exactly who to ask: Chris Budd OBE, a Professor at the University of Bath and long-time Plus collaborator. Chris has worked on the Navier-Stokes equations and currently co-leads the Maths for Deep Learning research project and he tells us what it has been like on the mathematical/AI frontline.
This is a rapidly developing area – since recording this podcast it has been established that the Open AI result does not apply to the Navier-Stokes equations in full generality (i.e. without forcing). We are continuing to follow developments and will be sharing updates as more information is released. In fact, we will have a number of other episodes in this podcast series about AI and maths, so make sure you are following for more!
You might also like:
- An article on Navier-Stokes and AI
- A quick overview of the Navier-Stokes equations
- A collection of articles and podcasts on AI and mathematical proof
- All of our work with Chris on maths and deep learning
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
Joe Hilton: Striking the balance with health economics
Should a life-saving, but expensive, cancer drug be made available on the NHS even though it only benefits very few people? Or should the money be allocated to drugs that lower blood pressure, which help vast …
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Should a life-saving, but expensive, cancer drug be made available on the NHS even though it only benefits very few people? Or should the money be allocated to drugs that lower blood pressure, which help vast swathes of the population? For the final episode of this season, we spoke to Joe Hilton, a health economist, to understand more about how difficult decisions like this one are made.
Joe is a research fellow in mathematical modelling at the Manchester Centre for Health Economics and a 2025 JUNIPER Fellow. JUNIPER is a network of researchers across the UK working to prepare the country for the public health challenges of the future. We spoke to Joe at JUNIPER’s annual meeting to understand more about the role of maths and economics in healthcare. He also talked us through his path into this job and what it was like going into research into health policy in 2020 at the very start of the pandemic!
To find out more about the mathematics of health, you might enjoy:
- This article about about how mathematical models are used in epidemiology
- An exploration of how you can use maths to understand disease spread in a hospital
- Another podcast on how modellers work between maths and medicine
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
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.
Meet a Mathematical Family
“He asked me this question because I'm his sister and he loves me.” Mathematics can often be seen as a solitary endeavour, but as this quote from one of our latest podcast guests show, that is far from the …
Shownotes
“He asked me this question because I'm his sister and he loves me.”
Mathematics can often be seen as a solitary endeavour, but as this quote from one of our latest podcast guests show, that is far from the truth. In this episode, we learn how a new proof has developed from one young mathematician talking to his sister – and then collaborating with their father and close family friend. We spoke to Roman Sauer and Uri Bader – and Uri’s two children Saar and Shaked – after they had attended a residential research programme at the Isaac Newton Institute where they had worked together and proved a rigidity result around symmetries and group theory. We spoke to all four of them to understand the result, what it was like working together, and how they each got into maths.
Please note, this episode includes more technical mathematical descriptions than is standard for our podcasts so you may want a strong cup of coffee before you dive in!
To find out more about the maths discussed in this episode, you might like:
- An introduction to group theory
- A very short overview of symmetry and groups
- A podcast on group theory
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
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.
Ramin Zabih: Welcome to the ArXiv
In this episode, we meet the CEO of one of the most important institutions in mathematics - arXiV. Around since 1991, the website is a publicly accessible home for mathematical research before it is officially …
Shownotes
In this episode, we meet the CEO of one of the most important institutions in mathematics - arXiV. Around since 1991, the website is a publicly accessible home for mathematical research before it is officially published in journals. Around 1,000 articles are published on arXiv every day — it has hosted everything from the proof of the Poincaré Conjecture to some of the newest research from AI companies like DeepSeek and Gemini.
We spoke to Ramin Zabih, a Professor at Cornell Tech and Interim Chief Executive Officer at ArXiv, about the organisation and how it supports the very best of mathematical research. Ramin explains why early access is so important, the site’s role in making maths more robust, and why arXiv can publish things that journals can’t. Particularly importantly, he talks about the impact of AI on arXiv’s work.
To learn more:
- Watch a recording of Ramin speaking at the INI
- What is the Poincaré conjecture?
- Another approach to the current state of artificial intelligence in mathematics
- All of our content on artificial intelligence
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
James Fergusson: AI and data intensive science
What is the potential of artificial intelligence (AI) in scientific research? In this episode, Cambridge Professor James Fergusson talks about some cutting-edge research which addresses this question. James is …
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What is the potential of artificial intelligence (AI) in scientific research? In this episode, Cambridge Professor James Fergusson talks about some cutting-edge research which addresses this question. James is Director of the Infosys-Cambridge AI Centre, an innovative partnership between traditional academia and industry. James showed us how AI is quickly becoming the most effective tool for some kinds of data analysis, and even highlighted successful experiments he ran using AI to write research papers.
James is also Executive Director of the University of Cambridge's new Master's programme in Data Intensive Science, which is training up the next leaders in the field. He talked us through the programme’s benefits, the institutional approach to AI and the best ways to advance the field.
If you'd like to find out more, you might be interested in:
- An introduction to artificial intelligence
- Are we entering the 'centaur-stage' of maths and AI?
- All of our content on AI
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
Ulrich Sperhake and Seppe Staelens: Boson stars
Welcome to the latest episode of Maths on the Move! In this episode we spoke to Cambridge Professor of Theoretical Physics Ulrich Sperhake and his graduate student, Seppe Staelens, about boson stars …
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Welcome to the latest episode of Maths on the Move! In this episode we spoke to Cambridge Professor of Theoretical Physics Ulrich Sperhake and his graduate student, Seppe Staelens, about boson stars: hypothetical objects that might be masquerading as black holes.
Our conversation with Ulrich and Seppe marked the tenth anniversary of the first detection of gravitational waves. As Ulrich explained back then, gravitational waves "opened our ears to the Universe in a waveband in which we have been 100% deaf up to now" and they also help us understand black holes and boson stars. In this podcast Seppe and Uli explain more, taking us to the frontiers of current research..
To find out more about the topics discussed in this podcast, you might like:
- A short explainer of gravitational waves
- Gravitational waves reveal cosmic hum: another podcast with Ulrich
- Dark stars: an article on gravitational waves and boson stars
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
Holly Krieger: The dynamics of numbers
Plus is based at the Maths Faculty at the University of Cambridge so we have lots of opportunities to talk to interesting mathematicians about their work and their working lives. This week we speak to Holly …
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Plus is based at the Maths Faculty at the University of Cambridge so we have lots of opportunities to talk to interesting mathematicians about their work and their working lives. This week we speak to Holly Krieger, who is a professor here in a podcast that we originally produced for the Maths Faculty.
Holly works in the overlap of two areas of mathematics: number theory – which is famous for problems such as Fermat's Last Theorem – and complex dynamics, which gives rise to beautiful fractals. This intersection is known as arithmetic dynamics and it's an exciting, relatively young area of research. Holly's work has been very successful, being awarded several prestigious prizes. And she is also known for her appearances on the Numberphile channel where she has shared the beauty of maths in a range of areas, from centrifuge to the Mandelbrot set.
Holly told us about how she came to her current research, the benefits of a career in maths, advice for younger mathematicians, and her appearances on Numberphile.
Find out more about:
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
Hannah Fry wins Leelavati Prize!
Hannah Fry, Cambridge's first Professor of the Public Understanding of Mathematics, has been awarded the Leelavati Prize at this year's International Congress of Mathematicians (ICM). The Leelavati Prize is …
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Hannah Fry, Cambridge's first Professor of the Public Understanding of Mathematics, has been awarded the Leelavati Prize at this year's International Congress of Mathematicians (ICM). The Leelavati Prize is awarded every four years by the International Mathematical Union and Infosys for outstanding contributions for increasing public awareness of mathematics.
We talked to Hannah in the run-up to the ICM about how she feels about being awarded the prize, the role of mathematics in culture, and her favourite experience as a maths communicator.
As Hannah puts it, "I feel as though there are these wonderful secrets that are completely invisible to almost everybody in the world who are mathematicians and it doesn’t make sense to me we would keep them to ourselves — I feel as though I have this really good bit of gossip that I just want to share."
To hear Hannah talk about her favourite mathematical moment, which is mentioned in this episode, see this podcast recorded when she became Professor of the Public Understanding of Mathematics at the University of Cambridge.
You can see the part of Hannah Fry's RI Christmas lecture mentioned in this podcast on YouTube.
The photo of Hannah is courtesy of the Simons Foundation.
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
Julian Sahasrabudhe: The ICM 2026
We are continuing our conversations with mathematician colleagues at the University of Cambridge, part of the podcast we produce for the Maths Faculty here. Today we meet Julian Sahasrabudhe, Professor of …
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We are continuing our conversations with mathematician colleagues at the University of Cambridge, part of the podcast we produce for the Maths Faculty here. Today we meet Julian Sahasrabudhe, Professor of Mathematics, and one of the invited speakers at the International Congress of Mathematicians (ICM) in July this year.
The ICM is one of the biggest events in the mathematics world and is the host of several prizes, including the prestigious Fields Medal. Only mathematicians at the very forefront of research are invited to speak, so we were very excited to learn more about Julian's work.
We spoke to him about his path into mathematics, from his childhood dreams to his early career as a drummer, before he finally settled on maths. Julian also gave us a brief introduction to his work in the field of combinatorics and how it offers partnerships with other areas of maths.
The podcast mentions Maryna Viazovska, who won a Fields Medal in 2022. Julian discusses the link between Ramsey theory and her work on sphere packing, as in the image below (courtesy Greg A L, CC BY-SA 3.0).
Find out more about:
- Julian's work and its connections to sphere packings
- Combinatorics
- Other Cambridge mathematicians invited to speak at the 2026 ICM
- The 2022 ICM
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
Richard Samworth: The ICM 2026
We are very lucky to be based at the Centre for Mathematical Sciences at the University of Cambridge. To start our latest podcast season we bring you a series of conversations with our mathematician colleagues …
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We are very lucky to be based at the Centre for Mathematical Sciences at the University of Cambridge. To start our latest podcast season we bring you a series of conversations with our mathematician colleagues, part of the podcast we produce for the Maths Faculty here.
In our first podcast we meet Richard Samworth, Professor of Statistical Science and Director of the Statistical Laboratory. We spoke to him in the run up to the International Congress of Mathematicians (ICM), one of the biggest dates in the mathematical calendar, where the most prestigious prizes in maths, including the Fields Medals, are awarded. Held every four years, the ICM features the world's leaders in the field and celebrates the diversity of today’s mathematics. Only mathematicians whose work is of the highest international standard are invited to speak at the week-long event, and Richard is one of the invited speakers at the ICM this July!
Richard's contributions to statistics have been recognised with numerous honours and awards. In 2025, he won two prestigious prizes in the space of 24 hours – the David Cox Medal for Statistics and the Guy Medal in Silver.
We talked to Richard to find out more about the work he will be speaking about at the ICM, how his field of statistics is simultaneously very theoretical and very applied, and what he most values about being part of the mathematical community here in Cambridge.
Find out more about:
- Richard's work
- Other Cambridge mathematicians invited to speak at the 2026 ICM
- The 2022 ICM
- The history of the ICM
Maths on the Move, is the podcast from plus.maths.org. We speak to researchers from the frontiers of mathematical science so you can connect with the maths that shapes and explains our world. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.
Living Proof: Building digital hearts
Imagine if your doctor had a digital model of your heart, personalised to you and updated with your latest medical information. This isn't science fiction – this revolutionary healthcare is being tested now. In …
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Imagine if your doctor had a digital model of your heart, personalised to you and updated with your latest medical information. This isn't science fiction – this revolutionary healthcare is being tested now. In this podcast we speak to Steven Niederer, who leads the CVDNet project developing and testing these ideas, and his colleague Richard Wilkinson, from the University of Nottingham.
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.
Living Proof: Céline Broeckaert and Frank Verstraete
"I have learnt that even if you are not a master in mathematics and science you are still able to grasp the essence." This is Céline Broeckaert talking, believe it or not, about the famously difficult theory of …
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"I have learnt that even if you are not a master in mathematics and science you are still able to grasp the essence."
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.
Adventures in Model Land
You are blue, and are surrounded by other blue people: swirling together in a dot, identical and indistinguishable. From somewhere above you hear the ticking of a clock, and suddenly find yourself and some of …
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You are blue, and are surrounded by other blue people: swirling together in a dot, identical and indistinguishable. From somewhere above you hear the ticking of a clock, and suddenly find yourself and some of your fellows pulled upwards, sucked through a tube arcing high above...
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.
Living Proof: Kevin Buzzard and proof assistants
There's been a lot of talk recently about whether artificial intelligence is becoming just as good as maths as humans are. But quietly in the background there's been another development regarding the use of …
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There's been a lot of talk recently about whether artificial intelligence is becoming just as good as maths as humans are. But quietly in the background there's been another development regarding the use of computers in maths. It involves proof assistants: computer programmes that can check whether a mathematical proof is correct; whether it can be derived from a set of basic axioms of mathematics using only the rules of logic.
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.
Living Proof: Moustapha Fall
In this episode of the Living Proof podcast we're delighted to meet Moustapha Fall. Moustapha is the Center President of the African Institute for Mathematical Sciences (AIMS) in Senegal and winner of a …
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In this episode of the Living Proof podcast we're delighted to meet Moustapha Fall. Moustapha is the Center President of the African Institute for Mathematical Sciences (AIMS) in Senegal and winner of a prestigious Ramanujan Prize for Young Mathematicians from Developing Countries. He also plays an important role on the international stage as Member-at-Large of the Executive Committee of the International Mathematical Union.
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.
Living proof: Codina Cotar and some amazing mathematical art
Earlier this year the the anomalous mathematical patterns sci-art competition attracted some jaw-dropping entries. The competition was held in connection to the Stochastic systems for anomalous diffusion …
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Earlier this year the the anomalous mathematical patterns sci-art competition attracted some jaw-dropping entries. The competition was held in connection to the Stochastic systems for anomalous diffusion research programme which took place at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge last year.
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.
Topological data analysis with Michael Hill
The mathematical area of topology is all about figuring out what truly defines a shape. Famously, topologists consider a coffee cup to be the same as a doughnut because one can be turned into the other without …
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The mathematical area of topology is all about figuring out what truly defines a shape. Famously, topologists consider a coffee cup to be the same as a doughnut because one can be turned into the other without cutting or gluing — what defines and relates these two shapes for a topologist is that they have a single hole.
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.
David Tong and 100 years of quantum mechanics
Welcome to the new season of the Maths on the Move podcast! We start the season with theoretical physicist David Tong of the University of Cambridge looking at an important milestone in the history of physics …
Shownotes
Welcome to the new season of the Maths on the Move podcast!
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
Liz Fearon: Co-producing mathematics with the public
We may not notice it, but mathematics impacts our lives on a daily basis. Mathematical models inform policy decisions around the economy and public health. They are used to understand climate change and how to …
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We may not notice it, but mathematics impacts our lives on a daily basis. Mathematical models inform policy decisions around the economy and public health. They are used to understand climate change and how to respond to it. They are vital in the design of public buildings and spaces. They are even used to try and prevent crime.
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
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.
Living proof: Hunting through higher dimensions with Zhouli Xu
On May 30th 2024 seminar goers at Princeton University witnessed a thrilling moment. The mathematician Zhouli Xu of the University of California, LA, announced that, together with colleagues he had sorted out …
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On May 30th 2024 seminar goers at Princeton University witnessed a thrilling moment. The mathematician Zhouli Xu of the University of California, LA, announced that, together with colleagues he had sorted out the 126th dimension. Not in general, but in regards to a problem that has taunted mathematicians since the 1960s. The problem involves strange shapes and is called the Kervaire invariant problem, after the mathematician Michel Kervaire.
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:
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.
Brainstorming AI with Maths4DL
The capabilities of artificial intelligence may appear to be galloping ahead, but there are still many challenges that need to be solved. Last month we joined members of the Maths4DL research project for a …
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The capabilities of artificial intelligence may appear to be galloping ahead, but there are still many challenges that need to be solved. Last month we joined members of the Maths4DL research project for a hackathon — an intensive two-day brainstorming session designed to figure out how one might teach machine learning techniques for solving differential equations and how best to test those techniques.
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.
Meet your digital twin
Imagine we could have a digital version of our entire body which could help us, and our doctors, decide what life style is good for us, predict which diseases we might get, and how to best treat them? In short …
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Imagine we could have a digital version of our entire body which could help us, and our doctors, decide what life style is good for us, predict which diseases we might get, and how to best treat them? In short, what if we could all have our very own digital twin?
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.
Living proof: The meaning is in the arrows with Adina Goldberg
In this podcast we hope to give you some interesting information. This information is encoded in terms of 0s and 1s – the classical bits in your computer or phone. But what if instead we were using a quantum …
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In this podcast we hope to give you some interesting information. This information is encoded in terms of 0s and 1s – the classical bits in your computer or phone. But what if instead we were using a quantum computer? Then we'd be dealing with quantum bits, or qubits, opening up exciting new possibilities. And quantum information theory is the area of mathematics that explores how we can do that.
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.
Postcard from Oslo: Masaki Kashiwara and the 2025 Abel Prize
From sunny parks to banquets in castles – come with us on an exciting adventure in Oslo as we join the celebrations for the 2025 Abel Prize! We meet Masaki Kashiwara, winner of this year's prize, who tells us …
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From sunny parks to banquets in castles – come with us on an exciting adventure in Oslo as we join the celebrations for the 2025 Abel Prize! We meet Masaki Kashiwara, winner of this year's prize, who tells us about the importance of collaborations and creating new things. Ragni Piene, previous chair of the Abel Prize Committee, gives us a look behind the scenes. And Andrea D'Agnolo, one of Masaki Kashiwara's most recent collaborators, celebrates his friend and fellow bridge-builder between mathematical worlds.
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
Living proof: A conversation with Sarah Hart
Sarah Hart is a mathematician who is interested, not just in the maths itself, but also its connections to other areas of culture and art. She's done an amazing number of things throughout her career — from …
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Sarah Hart is a mathematician who is interested, not just in the maths itself, but also its connections to other areas of culture and art. She's done an amazing number of things throughout her career — from research in pure mathematics and heading up a maths department, to being the first woman Gresham Professor of Geometry and President of the British Society for the History of Mathematics.
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.
Rob Eastaway: Shakespeare's mathematical life and times
One thing we all have in common is that we did maths at school. Those of us from the English speaking world most likely also did Shakespeare at school. Do these two things have anything in common? It turns out …
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One thing we all have in common is that we did maths at school. Those of us from the English speaking world most likely also did Shakespeare at school. Do these two things have anything in common?
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?
Living proof: Diving into maths with Emmy Noether
Every now and again, and more often than you'd think, the work of mathematics overlaps with the world of theatre and film. This happened again recently when the Isaac Newton Institute for Mathematical Sciences …
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Every now and again, and more often than you'd think, the work of mathematics overlaps with the world of theatre and film.
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.
The Abel Prize 2025
Last Wednesday, March 26, 2025, this year's Abel Prize was awarded to the Japanese mathematician Masaki Kashiwara. The Abel Prize is one of the most prestigious honours in mathematics. It is awarded every year …
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Last Wednesday, March 26, 2025, this year's Abel Prize was awarded to the Japanese mathematician Masaki Kashiwara. The Abel Prize is one of the most prestigious honours in mathematics. It is awarded every year by the Norwegian Academy of Science and Letters and comes with a prize money of over £550,000.
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.
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