Maths on the Move

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.

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.

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.

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.

“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.

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.

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.

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.

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: 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.

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.