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

• The website of the COMMET project

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

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

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

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

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.

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.

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.

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

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.

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?