Mathematics is a creative pursuit so it's not surprising that there are communalities between maths and art in all its forms. In this episode we explore the intersection between maths and art with physicist Andrzej Herczyński and mathematician Paul Glendinning.

Andrzej Herczyński

Andrzej and Paul were two of the organisers of the workshop Space, scale and scaling in art, which recently took place at the Isaac Newton Institute for Mathematical Sciences in Cambridge. We find out about the rich dialogue that can ensue between artists and mathematicians, how maths and physics can help us understand the power of art and how we perceive it, and provide insights into how a particular piece of art was made.

The Space, scale and scaling in art workshop was part of a larger research programme funded by the National Science Foundation on the intersection of science and art.

You can see Agnes Martin's painting Morning, which is mentioned in this episode, here (though the digital version does not do it justice). To see Jackson Pollock's works, which are also discussed in this episode, go to the Jackson Pollock website. The image above has been generated by AI.

Paul Glendinning

To find out more about some of the topics mentioned in this episode, see the following articles:

• Fractal expressionism looks at fractal structures in works by the abstract expressionist Jackson Pollock.

To see all our content on maths and art see here, and for everything on maths and music see here.

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 our 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 of the most fascinating figures in the history of mathematics was Srinivasa Ramanujan, a self-taught Indian genius who formed a remarkable relationship with the Cambridge mathematician GH Hardy. Ramanujan was interested in problems in number theory, which are often easy to state, but incredibly difficult to prove. One amazing thing about Ramanujan's work is that it still finds applications today, in areas you'd never imagine are linked to number theory. An  example is the study of black holes, those gravitational monstrosities that lie at the centres of galaxies.

We will explore this surprising link in an upcoming episode, but for now we revisit a 2018 interview with mathematician Ken Ono (pictured above), who was an advisor and associate producer on the well-known film about Ramanujan, The man who knew infinity. Talking to Plus Editor Rachel Thomas, Ken explores just what made Ramanujan's work so special and the piece of mathematics that is relevant to black holes. Rachel talked to Ken at the Royal Society's celebration of the centenary of Ramanujan's election as a Fellow of the Royal Society.

You can also read an article accompanying this podcast, which looks at the mathematics relevant to black holes. For more about Ramanujan's mathematics, and Ken's research into it, see Ramanujan surprises again. To find out more about the Spirit of Ramanujan project, which Ken mentions in this episode, see here.

In this episode of Maths on the move we look at some favourite pieces of maths we have worked on so far this year. From a revolutionary new tile to new insights in topology, and from fooling cancer cells to bringing mathematical research into the classroom, we hope there's something interesting there for everyone. 

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

• A tip of the hat: Celebrating an aperiodic monotile — meeting the discoverers of the hat

To find out more about our work with the JUNIPER network of disease modellers see here and to find out more about our work with the maths4DL research project see here.

It's always exciting to have a glimpse at new mathematics and technology as they take shape.  In this podcast we talk to Georg Maierhofer, from the University of Oxford, about an exciting new idea that is only just emerging  – physics informed neural networks  (PINNs for short) – where you add in the laws of physics to machine learning methods. 

We have been able to sit in on a number of meetings of our colleagues from Maths4DL (the Mathematics for Deep Learning research group) as they explore this idea.   Georg explains why PINNs are a bit like learning golf, tells us about the exciting opportunities and challenges, and why the key part to developing new ideas is getting the right people together at the right time.

You can find more about the machine learning and the some of the work that Maths4DL is doing at https://plus.maths.org/maths4dl, including our recent podcast How does AI work?  and our collection Predicting the weather with artificial intelligence.

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.

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.