Last weekend our friends and neighbours at the Centre for Mathematical Sciences at the University of Cambridge put on a great event: the Mathematics Discovery Day, part of the Cambridge Festival. Among the may hands-on activities, games and pop-up explorations were the hugely popular, and well-attended, workshops for students delivered by our colleagues Liz and Charlie from NRICH. Our brilliant colleague Julia Hawkins herded academics and volunteers, juggled props and generally made sure that everything went smoothly.

At the same time our partners at the Isaac Newton Institute next door hosted one of our favourite physicists: Ben Allanach, Professor of Theoretical Physics at the University of Cambridge. Ben gave a talk called The force awakens: Quantum collisions, in which he explored experiments at the Large Hadron Collider (LHC), particle physics, as well as recent research results which suggested there may be a fifth force of nature, hitherto unknown to science.

For those who weren't able to attend Ben's talk we revisit an interview with him from last year, in which he explains this intriguing (and if true sensational) result about a potential new force.

The image above illustrates particle collisions at the LHC and is courtesy CMS.

This content now forms part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI). The INI is an international research centre in Cambridge which attracts leading mathematicians from all over the world. You can find all the content from the collaboration here.

Artificial intelligence has made astonishing progress in the last few years. Perhaps surprisingly, all of the amazing things we've seen, from ChatGPT to generative AI, are powered by same mathematical technique: machine learning, and in particular deep learning.

In this episode of Maths on the move we talk to Kweku Abraham, member of Maths4DL, a research project which investigates deep learning, and postdoctoral researcher at the University of Cambridge. Kweku explains how machine learning works, why it's so powerful and whether there are any limits to what it can achieve, and the kind of maths he works on every day.

To find out more about the topics discussed in this episode, see Artificial intelligence and deep learning: Your questions answered.

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.

We’re now all very aware that climate change is not just a problem for the future – 2023 was officially the hottest year on record ever. And as well as impacting our lives through food security, flooding and drought, climate change can also impact our health by the impact it can have on the spread of diseases.

A very interesting group of people came together to discuss this in January 2024. Policy makers, climate scientists, epidemiologists and mathematicians met at a workshop at the University of Oxford to discuss the impact of climate change on epidemics. We spoke to one of the organisers, Helena Stage, from the University of Bristol, about how exactly climate change impacts the spread of diseases, how maths can help and why it's so important to think globally.

Helena Stage

You can find out more about disease modelling and epidemiology in our library for beginners, or our work with JUNIPER (the Joint UNIversities Pandemic and Epidemiological Research network). And you can find out more about climate change and how maths can help in these articles and podcasts.

This podcast was produced as part of our collaborations with JUNIPER, the Joint UNIversity Pandemic and Epidemic Response modelling consortium, and the Isaac Newton Institute for Mathematical Sciences (INI), both of whom funded the workshop discussed in this episode.

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 question about the control of COVID-19. You can see more content produced with JUNIPER 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.

Could we make the clouds brighter so they reflect more of the Sun's warming rays back into space to keep us cooler? Or make Arctic ice thicker so it lasts longer over the summer? These ideas might sound slightly fantastical, but they're active research areas at the Centre for Climate Repair which has recently become our neighbour here at the Centre for Mathematical Sciences at the University of Cambridge.

In this episode of Maths on the move the Centre's Director of Research, Shaun Fitzgerald, tells us more about the Centre's work and its three-fold mission: to reduce emissions of greenhouse gases, to remove excess green house gases from the atmosphere, and to refreeze the Arctic.

You may also want to read the article accompanying this episode of Maths on the move. For more about mathematics and climate change, see here.

In this, the last episode of Maths on the move for this year, we look back on 2023 and forward to 2024. We talk about some highlights in our coverage of this year's mathematics, and some of the exciting things to come next year. It's a crazy journey featuring breakthroughs in pure maths, the maths of music and Ed Sheeran, renewable energy sources, the maths of justice, and the epidemiology of climate change.

We hope you enjoy this final episode of the year and wish you all the best for next year! And remember: no matter how hard a piece of mathematics might be, there's always something in it that everyone can relate to!

To find out more about the topics mentioned in this episode see

• Fermat's last theoem

To find out more about our collaboration with the Isaac Newton Institute see here, about our collaboration with the JUNIPER network see here, and about our collaboration with Maths4DL see here.

To help mitigate climate change the UK government has pledged to decarbonised UK electricity supply by 2035. That's a huge science and engineering challenge on a very tight deadline. In this episode we talk to two people who know all about the challenges involved: Chris Dent, Professor of Industrial Mathematics, and Lars Schewe, Reader in Operational Research, both of the University of Edinburgh. Both helped to organise an intensive two week "deep dive" workshop on the Mathematics and statistics for low carbon energy systems earlier this year as part of a longer research programme at the Isaac Newton Institute for Mathematical Sciences (INI) in Cambridge.

Chris and Lars tell us why decarbonising the energy network also resents huge mathematical challenges — and why the effort isn't unlike the Apollo mission that got people to the Moon in the 1960s.

You can read more about the topic discussed in this episode in this article.

This content was produced as 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.

We continue our series about bringing maths to the stage and screen by going back to 2012 when we were lucky enough to host the UK premiere of the Travelling Salesman, here at the Centre for Mathematical Sciences, our home. It is an unusual movie: despite almost every character being a mathematician there's not a mad person in sight. Moreover, the plot centres on one of the greatest unsolved problems in mathematics, does P = NP? Timothy Lanzone, the writer and director, tells us about creating drama from mathematics, and we discuss the maths behind the movie.

(The sound effects used in this podcast are by jlozano and nemoDaedalus.)

You can read more about the travelling salesman problem, P versus NP, and cryptography on plus.maths.org

When you think of Alan Turing you might think of his work breaking the Enigma code in World War II. Or you might think of his work that helped build the foundations of computer science and mathematical logic. Or you might even think of his groundbreaking work in mathematical biology on morphogensis which helps explain animal patterns.

One thing we hadn't thought of, until 2013 that is, was that he could be the emotional centerpoint of a musical. The universal machine is a musical about Alan Turing's life and work that was staged in London in 2013. As part of our series about putting maths on stage and screen, we revisit our 2013 interview with the writer and director David Byrne, actor Richard Delaney, who played Turing, and assistant director Natalie York, to find out how you turn such a story, and the maths in it, into a musical.

We are very grateful to Dominic Brennan, who wrote the music for The universal machine, for giving us permission to use the track Building The Bombe Part Two from the show.

The universal machine poster detail.

For more information:

• You can read the original article accompanying this podcast and a review of The universal machine;

This is the second part of our mini series focussing on mathematics coming to life on stage and in film. We revisit our 2008 interview with mathematician and actor Victoria Gould and mathematician Marcus DuSautoy, who were both involved in the development of the play A disappearing number produced by Complicité. The play explores the fascinating collaboration between the mathematicians GH Hardy and Srinivasa Ramanujan. Find out how theatre can embody, not just the story of the people involved, but also the mathematics itself.

You can also read about A disappearing number in this article. To find out more about Victoria Gould's career as an actor and mathematician, see this article or listen to last week's episode of Maths on the move.

In the summer we came across news coverage claiming that scientist were on the verge of discovering a fundamental force of nature they hadn't previously known about. This would be a fifth force, in addition to gravity, electromagnetism, and the strong and weak nuclear forces.

Such a discovery would be quite a revolution, so we went to talk to our friend Ben Allanach, Professor of Theoretical Physics at the University of Cambridge, to find out more. Ben explained the science, gave us his personal hunch regarding the experimental results, and provided a fascinating glimpse into life at the cutting edge of physics.

Ben Allanach

To find out more about the topics explored in this podcast, see The physics of elementary particles and A brief introduction to quantum field theory. Click here to see all our content featuring Ben Allanach.