Maths on the Move

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.