Maths on the Move

Afleveringen

1. Chris Budd: Did AI prove the Navier-Stokes Millennium Problem?

   3 november 2026 · 31 min

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   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. Lees meer

   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.

2. Joe Hilton: Striking the balance with health economics

   1 september 2026 · 27 min

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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. Lees meer

   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.

3. Meet a Mathematical Family

   25 augustus 2026 · 27 min

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   “He asked me this question because I'm his sister and he loves me.” Lees meer

   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.

4. Ramin Zabih: Welcome to the ArXiv

   18 augustus 2026 · 22 min

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   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. Lees meer

   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.

5. James Fergusson: AI and data intensive science

   11 augustus 2026 · 22 min

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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. Lees meer

   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.

6. Ulrich Sperhake and Seppe Staelens: Boson stars

   4 augustus 2026 · 42 min

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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. Lees meer

   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.

7. Holly Krieger: The dynamics of numbers

   28 juli 2026 · 28 min

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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. Lees meer

   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:

   Holly's work

   Number theory

   Fermat's Last Theorem

   Mandelbrot set

   Holly's appearances on Numberphile

   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.

8. Hannah Fry wins Leelavati Prize!

   23 juli 2026 · 27 min

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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. Lees meer

   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.

9. Julian Sahasrabudhe: The ICM 2026

   14 juli 2026 · 25 min

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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. Lees meer

   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.

10. Richard Samworth: The ICM 2026

    7 juli 2026 · 23 min

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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. Lees meer

    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.

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