We're getting excited for the summer here but before we all head off on holidays we catch up with Marianne in Spain at the European Congress of Mathematics, and Justin and Rachel in the UK having just attended some fascinating events in London and Cambridge held by the Isaac Newton Institute of Mathematical Sciences and the Newton Gateway.

Marianne told us about her recent interview with Avi Widgerson – winner of the Abel Prize in 2021 and the most recent Turing Prize. Justin told us about  how the philosophical concept of causality can help us understand AI.  And Rachel tells us about the surprising phenomena of anti-diffusion and how it links the patterns we see on Juniper, staircases in our oceans and fusion reactors of the future.

We'll be back with  more podcasts in the Autumn, but here are some of our recommendations for your summer reading and listening pleasure!

Articles:

• How to (im)prove mathematics
• Fractal photo finish 
• Chaos on the billiard table 

Podcasts:

• Tying together black holes, quantum gravity and number theory
• The murmuration conjecture: finding new maths with AI
• From clicks to chords 

Books:

• Collision – Stories from the Science of CERN

This content was produced as part of our collaborations with the London Mathematical Society, the Isaac Newton Institute for Mathematical Sciences and the Newton Gateway to Mathematics. 

How we behave can have far greater impacts than just on our own daily lives.  For example who we interact with and whether we get vaccinated affects how diseases spread through the community.  So if we are going to use maths to try to understand such a challenge facing society, we need to make sure we include human behaviour in our mathematical models.  But how do you mathematically describe the messiness of human behaviour? 

To find out we talk to mathematicians Kirsty Bolton, Assistant Professor at the University of Nottingham, and Ed Hill, a Warwick Zeeman Lecturer  at the University of Warwick.  Kirsty and Ed organised a recent workshop bringing together experts from across maths, data science, life sciences and social sciences to explore how mathematical models can be made more realistic by including human behaviour.  They tell us about both the mathematical and the communication challenges this brings, from the difficulty of learning the languages of other disciplines to the excitement of finding the sweet spot where experts from such different areas can work together to make progress.

Kirsty and Ed are both part of JUNIPER, a collaborative network of researchers from across the UK who work at the interface between mathematical modelling, infectious disease control and public health policy, and JUNIPER supported the workshop.

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.

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
• Contagious maths — bringing epidemiological research into the classroom
• The mathematics of movement — what do cancer cells, birds, and whales have in common (and can a slime mould be intelligent)?
• Outraged by not knowing— new insights in topology with Oscar Randal-Williams

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
• Telescope topology
• From clicks to chords, the article and the the podcast
• Creating a low carbon energy network
• A 60% chance of rain: our podcast episode featuring climate scientist Tim Palmer
• Climate change and ready meals: Challenges for epidemiologists

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

We're very excited to be going to this year's European Congress of Mathematics (ECM), which will take place in Seville, Spain, in July! We noticed that mathematicians who win one of the prizes awarded at the ECM by the European Mathematical Society quite often go on to win a Fields Medal, one of the highest honours in mathematics.

So to celebrate the run-up to the ECM we've launched Euromaths, a miniseries of podcasts revisiting interviews with Fields Medallists who previously won an EMS prize. This week we hear from Maryna Viazovska who won a Fields Medal in 2022 and an EMS prize in 2020, talking about the theory of optimal transport and how it applies to a wide range of things, from crystals to clouds.

You can read about Maryna's work in this article. To listen to previous episodes of Euromaths click here.

This content was originally produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2022 International Congress of Mathematicians here.

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;
• You can find out more about the Enigma code and how it was cracked in Exploring the Enigma;
• You can read about morphogenesis in How the leopard got its spots;
• And there is more on Turing and his work in Alan Turing: ahead of his time and What computers can't do. These two articles also look at the halting problem which is related to the Entscheidungsproblem mentioned in the podcast.

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.

Victoria Gould has always known she would be an actor, and went straight from studying arts at school to running her own theatre company. But she eventually had to come clean about her guilty secret - she loves maths - and has since managed to combine a career as a research mathematician and teacher with a successful acting career on television and in theatre. For this episode of Maths on the move, which was recorded in 2008, Victoria told us what it's like being an actor and a mathematician and how those two, at first sight very different, areas overlap.

You can also read the article accompanying this podcast, and find out more about the play A disappearing number here.

We were inspired to revisit this episode when we met mathematical film maker Ekaterina Eremenko at this year's Heidelberg Laureate Forum. Eremenko's latest film, Solving the Bonnet problem, really gets across that mathematics is a dynamic, and sometimes dramatic, pursuit that can be well suited for the stage and screen. You can watch the trailer here.

How many dimensions are there? We might not be aware, but we are actually used to living in a curved, multidimensional Universe. In this episode theoretical physicist David Berman explains how, and he also dives into the world of string theory which predicts that the Universe has ten dimensions, some of which are hidden from our view. We first published this episode back in 2012, as part of our Science fiction, science fact project.

David Berman

You can also read the articles that accompany this podcast: Kaluza, Klein and their story of a fifth dimension and The ten dimensions of string theory.

n this podcast we bring you breaking news from the world of topology! Four mathematicians, all in earlier stages of their career, have resolved the long-standing telescope conjecture which explores holes in spheres – of any dimension!

The result was announced this summer at a conference organised by Isaac Newton Institute for Mathematical Sciences in Cambridge (INI).

We talk to two of these mathematicians, Tomer Schlank and Jeremy Hahn, to get a gist of this high-powered result in pure mathematics, which is nevertheless wonderfully intuitive. So fasten your seatbelt and join us on a trip into the wonderful world of homotopy theory!

Jeremy Hahn                  Tomer Schlank

To read an article exploring the telescope conjecture and for some background reading, see here.

This content was produced as 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.

How is mathematics related to frequency related to pitch? We found out from our favourite music correspondent, Oli Freke! In this podcast you can hear how the music we love emerges from pure mathematical beats.

This podcast was originally released earlier this year when musician Ed Sheeran was in the news  as he was being sued for similarities between his song Thinking out loud from 2014, and Marvin Gaye's song Get it on from 1973. But, given the way we write music to fit into specific genres, is it possible to write unique music with the limited quantity of notes and chords available?

After first answering this question in this podcast, Oli has now written a brilliant article, From clicks to chords, where you can see some of the connections between maths and music come to life.   

You can find out more about the maths in music in Oli's articles other – How many melodies are there? and Sine language. And you can find more of Oli's music, and his book "Synthesizer Evolution", here!

The music in this podcast comes from, of course, Oli Freke! The track is called Funk Off.

We humans have many rules and regulations surrounding noise — because we recognise that noise disruption is annoying, stressful, and ultimately robs us of our health.

Spare a thought for whales then, who have to put up with the constant noise caused by shipping and the construction of oil rigs and wind farms in the oceans. There are concerns that the noise pollution we cause bothers and confused the whales so much, it may even disrupt their ability to go on their annual migrations.

In this episode we talk to Stuart Johnston of the University of Melbourne in Australia who uses mathematics to understand the migration of whales and how it might be impacted by human generated noise. The ultimate aim is to figure out what we can do to mitigate the disruption we cause.

We met Stuart at a workshop on collective behaviour, which took place at the Newton Institute for Mathematical Sciences (INI) in Cambridge in August 2023. The workshop was part of a 6-month research programme on the mathematics of movement which is currently taking place at the INI.

This content was produced as 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.

This week we co-host a fascinating episode of the Isaac Newton Institute's Living Proof podcast. In the episode Dan Aspel speaks to Coralie Colmez, author of the young adult novel The irrational diary of Clara Valentine, recently chosen as one of Chalkdust magazine's books of the year. Coralie’s ambition was to write a story rich in both mathematics and mystery, with the Chalkdust review highlighting that "the explanations of the solutions to these puzzles are blended into the story expertly". In this interview, Coralie explains further about the books origins, its intentions and what comes next.

Find out more about Coralie's writing, download a free PDF of the book, and find links to other online sellers here.

This podcast is 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.

Did you do anything fun on your summer holidays? The mathematicians in this podcast spent some of their summer helping to create the perfect smoothie, getting the most sugar out of sugar cane, and attacking other important real-world problems.

They did all this attending the Graduate Modelling Camp, which is organised every year by the Newton Gateway to Mathematics in Cambridge. The camp gives early career mathematicians a chance to experience life as a mathematical modeller by challenging them to solve problems posed by industry.

We talk to Chris Breward, who has been helping to run the modelling camp for many years, to PhD students Emily Cook, Julian Glover, and Michael Smah, who attended this year's camp, and to Ashleigh Hutchinson who took part as a mentor. They all enjoyed the camp immensely — find out why in this podcast!

This content was produced as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics. The INI is an international research centre in Cambridge which attracts leading mathematicians from all over the world. The Newton Gateway is the impact initiative of the INI, which engages with users of mathematics. You can find all the content from the collaboration here.

We're very excited to be going to this year's European Congress of Mathematics (ECM), which will take place in Seville, Spain, in July! We noticed that mathematicians who win one of the prizes awarded at the ECM by the European Mathematical Society quite often go on to win a Fields Medal, one of the highest honours in mathematics.

So to celebrate the run-up to the ECM we've launched Euromaths, a miniseries of podcasts revisiting interviews with Fields Medallists who previously won an EMS prize. This week we hear from Artur Avila who won a Fields Medal in 2014 and an EMS prize in 2012, talking about the theory of optimal transport and how it applies to a wide range of things, from crystals to clouds.

You can read about Artur's work in this article. To listen to previous episodes of Euromaths click here.

This content was originally produced as part of our collaboration with the London Mathematical Society. You can find all our content on the 2014 International Congress of Mathematicians here.

There's been some huge news in the world of cosmology: for the first time scientists have detected a low frequency hum of gravitational waves. The new results were published by the North American Nanohertz Observatory for Gravitational Waves, NANOGrav for short. The NANOGrav team were not alone — they coordinated with collaborations in Europe, India, Australia, and China, which released similar findings at the same time.

In this podcast we find out what these new results mean, and why they're so exciting, with Michalis Agathos, Amelia Drew, and Ulrich Sperhake of the Stephen Hawking Centre for Theoretical Cosmology at the University of Cambridge. Join us on this fascinating, and slightly mind-bending, cosmic ride!

To find out more about the topics discussed in this podcast see:

• Maths in a minute: Gravitational waves
• Maths in a minute: Black holes
• Maths in a minute: Einstein's general theory of relativity

You might also want to listen to our recent podcast A new map of dark matter.

The illustration above is an artist's rendering of black hole binaries emitting gravitational waves, produced by Olena Shmahalo for NANOGrav and reproduced here under CC BY 4.0.

People don't usually think about maths and literature as related subjects, but it turns out that there are plenty of connections between the two. In this podcast we talk to mathematician Sarah Hart about her brilliant book Once upon a time: The wondrous connections between mathematics and literature.

Sarah tells us about the links between poetry and mathematical proof, the maths of Moby dick and the The luminaries, and why mathematical patterns and references can enhance your enjoyment of a book even when you're not aware of them.

To find out more about the problem of squaring the circle, which is mentioned in this podcast, see Mathematical mysteries: Transcendental meditation. To find out more about conic sections, see here.

"I think I'll stop here." This is how, on 23rd June 1993, Andrew Wiles ended his series of lectures at the Isaac Newton Institute (INI), our neighbour here at the Centre for Mathematical Sciences. The applause, so witnesses report, was thunderous. Wiles had just announced a proof that had eluded mathematicians for over 350 years: the proof of Fermat's Last Theorem.

Wiles' announcement, 30 years ago today, was a thrilling moment in mathematical history. But Fermat's Last Theorem is not just the story of one person. Jack Thorne, who works on new mathematics that builds on Wiles' proof, told us that it is actually a story of people talking to each other over a period of centuries.

To celebrate 30 years since that exciting moment, we were lucky enough to speak with Andrew Wiles and Jack Thorne, and also to Tom Körner, who was there the day Wiles announced the proof.

This is a special joint episode with the INI's Living Proof podcast, made in collaboration with our friend Dan Aspel, from the INI.

You can find out more about Fermat's Last Theorem in the article that accompanies this podcast, and in this collection of further reading.

This podcast 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.

Chocolate and mayonnaise are two of our all time favourite foods, so we were very happy to get the chance to talk to Valerie Pinfield, Professor of Engineering at Loughborough University, who has used maths to work on both chocolate and mayonnaise.

We talked to Valerie at the Isaac Newton Institute for Mathematical Sciences in Cambridge where Valerie is currently co-organising a research programme on the mathematical theory and applications of multiple wave scattering. As we will find out, this has a huge range of applications, from understanding mayonnaise to making invisibility cloaks.

While Valerie is a professor at the University of Loughborough now, her career path has also involved work in industry and time out for kids, so we also asked her for some advice for women mathematicians and scientists wondering how to build their career.

This podcast 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.

You might have heard in the news recently that musician Ed Sheeran was being sued for similarities between his song Thinking out loud from 2014, and Marvin Gaye's song Get it on from 1973. But, given the way we write music to fit into specific genres, is it possible to write unique music with the limited quantity of notes and chords available? In this podcast Oli Freke, our favourite music correspondent, answers this question and plays us real examples of the connections between maths and music.

You can find out more about the maths in music in Oli's articles – How many melodies are there? and Sine language. And you can find more of Oli's music, and his book "Synthesizer Evolution", here!

The music in this podcast comes from, of course, Oli Freke! The track is called Funk Off.

Did you know that we don't know what 85% of the stuff in our Universe is made of? This mysterious 85% is known as dark matter. We can't see it because it doesn't emit or reflect light, but we know it's there because it exerts a gravitational pull on stars and galaxies, and also bends the path of light.

In this podcast we talk to Blake Sherwin about a brand new map of dark matter that has been produced by a consortium of scientists using data from the Atacama Cosmology Telescope which sits high up in the Chilean Andes. Sherwin is part of that consortium, and he is also Professor of Cosmology and Astrophysics the University of Cambridge and a member of the Stephen Hawking Centre for Theoretical Cosmology at Cambridge.

Sherwin tells us how you go about producing a map of something you can't see, in how far the new map solves the so-called crisis of cosmology, and whether we will ever find out what dark matter is made of.

To find out more about dark matter, read Maths in a minute: Dark matter and What is dark matter? And you can find all the details about the research by Blake, his PhD student Frank Qu, and their colleagues in their series of papers here, here and here.

The music in this podcast is by eusa and the track is called Plankton. you can find their music on Soundcloud.

Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues Ed Hill and Laura Guzmán-Rincón from SBIDER about some of the COVID models that fed into public policy.----more----

Matt Keeling

----more----We're very pleased to host this episode of SBIDER Presents, one of the podcasts produced by the Zeeman Institute for Systems Biology & Infectious Disease Epidemiology Research (SBIDER). You can find out more about the work Matt Keeling is discussing in this podcast in our article Shining a light on COVID modelling. And you can hear more from Ed and Laura in our previous podcasts On the mathematical frontline: Ed Hill and Climate change and ready meals: Challenges for epidemiologists.

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.

In a tank in an underground laboratory in Cambridge a little green alga is executing a powerful breaststroke. It belongs to a group of algae called volvocales and it doesn't have a brain. So how can it coordinate its tiny little "arms" to perform motions worthy of an Olympic swimmer?

Algae going through their paces.  (Movies: Kirsty Wan and Raymond E. Goldstein, for more information see this paper)

In 2019 we visited Ray Goldstein, Schlumberger Professor of Complex Physical Systems at Cambridge, and he explained how algae manage to synchronise their so-called flagella, what this means for human physiology, and how it sheds light on the evolution of multi-cellular organisms from single-celled ones.

You can also read our article on Goldstein's work with volvocales, or watch an interview with Goldstein in this video.

Sound effects in this podcast are from Robinhood76 and 16HPanskaKanclirova_Victoria on freesound.org.

This podcast was partially funded by the European Mathematical Society.

What is infinity? What is infinity plus 100? What is infinity plus infinity?

Today's podcast was inspired by questions sent in by our friend Ash. To answer Ash's questions we take a trip to our favourite hotel, and we revisit our 2012 interview with our late boss, John D. Barrow, when we asked him – does infinity exist? Listen to the podcast to find out how infinity can corrupt the youth, why subtracting infinities can give you the right answer, and the weirdness that might be lurking out there in the cosmos...

Image created by FAVIO.

You can read more about infinity on plus.maths.org. And if you have a question about life, the universe and everything you'd like us to answer – email us as plus@maths.cam.ac.uk or contact us on twitter.

During the pandemic we all learnt to value the work of epidemiologists, whose mathematical models are essential in giving us an idea of where an epidemic might be heading. But just as there's a wide range of infectious diseases apart from COVID, so there's also a wide range of research questions epidemiologists ask.

In this podcast we talk to researchers Helena Stage and Laura Guzmán-Rincón about two such questions. One concerns the fact that a warming climate allows disease-carrying mosquitoes to live in places they previously found too cold. The other asks how you might detect a hidden outbreak of food poisoning coming, for example, from ready meals having been contaminated way back in the production chain. Both require clever mathematical ideas and ingenious detective work.      

Helena and Laura are members of the JUNIPER modelling consortium. We met them at a JUNIPER research meeting which took place at the University of Warwick in March 2023.

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

We're very excited to be going to this year's European Congress of Mathematics (ECM), which will take place in Seville, Spain, in July! We noticed that mathematicians who win one the prizes awarded at the ECM by the European Mathematical Society quite often go on to win a Fields Medal, one of the highest honours in mathematics.

So to celebrate the run-up to the ECM we've launched Euromaths, a miniseries of podcasts revisiting interviews with Fields Medallists who previously won an EMS prize. This week we hear from Alessio Figalli who won a Fields Medal in 2018 and an EMS prize in 2012, talking about the theory of optimal transport and how it applies to a wide range of things, from crystals to clouds.

You can read about Alessio's work in this article. To listen to previous episodes of Euromaths click here.

This content was originally produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2018 International Congress of Mathematicians here.

"What's a statistician's favourite sandwich filling?..."

Timandra Harkness – presenter, writer, comedian and Fellow of the Royal Statistical Society – told our friends Dan Aspel and Maha Kaouri her favourite maths joke in this episode of the Living Proof podcast from the Isaac Newton Institute for Mathematical Sciences.

Timandra Harkness

Timandra brilliantly chaired several sessions of the Communicating mathematics for the public event at the Newton Gateway to Mathematics. In this podcast Timandra spoke about how to make maths funny, and how she came to fall in love with mathematics from an arts and humanities background.

Oh and the punchline to Timandra's favourite joke? You'll have to listen to the podcast to find out!

00:00 – Introduction 00:44 – Welcome, discussing Communicating mathematics for the public 03:38 – Origins of Timandra's interest in maths, understanding "enough to ask the right questions" 07:50 – Discussing Timandra's book Big Data – Does Size Matter? 11:10 – Other current projects and shows, writing another book about "why everything is personalised" 13:13 – Mingling an arts background with a mathematics focus, "coming out as a closet mathematician" 17:10 – How do you make maths funny as a comedian? … "What's a statistician's favourite sandwich filling?" 21:10 – Future projects

This podcast was inspired by the Communicating mathematics for the public event at the Newton Gateway to Mathematics in January 2023.

(If that joke tickles your funny bone – try this one!)

This podcast is 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.

Having empathy with your audience – with all your audiences – is the first step for making your content accessible. Hannah Thomas of the Government Analysis Function explained this in her brilliant talk at the Communicating mathematics for the public event at the Newton Gateway to Mathematics. Hannah's talk was full of insights and practical ideas on how to make all content published online easy to access and use for all users, regardless of impairment, medical condition or disability.

Our friends Dan Aspel and Maha Kaouri spoke to Hannah for this episode of the Living Proof podcast from the Isaac Newton Institute for Mathematical Sciences. Hannah told them about her work helping to make government data more accessible, the common pitfalls of data accessibility and tips and tricks that can help. They also find our why more people used to get married at the end of the tax year...

Hannah Thomas speaking at the Communicating mathematics for the public event

00:00 – Introduction 00:44 – Welcome, discussing “Communicating Mathematics for the Public” (“as entertaining as Disneyland Paris and definitely more inspiring”) 04:20 – All about Government Analysis Function, a love of data journalism, career history 13:35 – Visualising data and making digital information accessible 21:40 – Common accessibility pitfalls 24:20 – Plans for the future… e-learning resources

This podcast was inspired by the Communicating mathematics for the public event at the Newton Gateway to Mathematics in January 2023. For more information we strongly recommend you watch Hannah's talk from that event, Data Visualisation and Digital Accessibility: What We Can Do to Help.

This podcast is 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.

We are very happy to work closely with our neighbours, the Isaac Newton Institute for Mathematical Sciences (INI), to help explain, celebrate and publicise the research that happens at the Institute. But what challenges does that present? And why should it happen in the first place?

Following on from the Communicating mathematics for the public event at the Newton Gateway to Mathematics we spoke to the INI's Dan Aspel about our work in this episode of the Living Proof podcast. You can find all the content from our collaboration here.

Communicating from the mathematical frontiers - from plotting a path to the highest peak to exploring the hidden depths.

00:00 – Introduction 00:44 – Welcome, discussing Communicating Mathematics for the Public, the importance of trustworthiness 05:30 – Who you're speaking to vs what you're saying 07:38 – Making higher mathematics accessible to audiences: "any bit of mathematics either comes from somewhere, or is going somewhere, or both" 14:20 – Are there incommunicable subjects? 16:55 – The rarity of maths "headlines" 19:25 – The partnership between INI and Plus magazine – why is it important? 23:25 – Are some topics inherently more interesting? 25:26 – What is the end goal of maths communication? "I would love it if people could see how maths is everywhere… that maths is a language of rhythms and patterns" 30:00 – Looking to the future

This podcast was inspired by the Communicating mathematics for the public event at the Newton Gateway to Mathematics in January 2023. You can watch our talk from that event, Trust, time and truth, that was about our collaboration with JUNIPER modelling consortium.

This podcast is 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.

Here at Plus, we were very grateful for Tom Irving's work during the COVID-19 pandemic. He was the Co-Head of the secretariat of the Scientific Pandemic Influenza Modelling group (otherwise known as SPI-M). One of his responsibilities was writing the consensus statements that came out of SPI-M, summarising current understanding of the mathematical advice to the UK government. We found these incredibly useful when reporting on the pandemic.

We finally met Tom when we were both speaking at the Communicating mathematics for the public event in January 2023 at the Newton Gateway to Mathematics in Cambridge. In this podcast Tom tells us about providing a bridge between policy and mathematics, the importance of transparency, and the joy of the R number being discussed at the hairdressers.

This episode is part of On the mathematical frontline, a special series of the Plus podcast which explores the work of mathematicians grappling with the unprecedented challenge of studying a live pandemic unfolding in front of their eyes. In this series we interview our colleagues in the JUNIPER modelling consortium, whose research and insights have fed into SPI-M and SAGE - the Scientific Advisory Group for Emergencies, both of whom advise the UK government on the scientific aspects of the COVID-19 pandemic.

You can watch Tom's talk on the Challenges in Communicating the Results of SAGE's Covid Modelling, and you can find all our work covering COVID-19 here.

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

If you've ever been lucky enough to meet David Spiegelhalter, or hear him talk in person or on TV or radio, you'll know he tells a great story. And the stories he told in his 2015 book Sex by numbers were fascinating and highly entertaining, as well giving us the tools to critically assess the statistics we read every day in the news. And sex is back in the news as the National Survey of Sexual Attitudes and Lifestyles that featured in his book is being conducted again this year. Who knows what stories will come out of the next survey?

We were very happy to start 2023 with catching up with David (the first time in person since the pandemic!) at the Communicating mathematics for the public event that we were both speaking at in the Newton Gateway to Mathematics in Cambridge. We hope you enjoy this interview with him from 2015, where he gives us some of his favourite snippets from the book, and some easy ways you can think more critically about statistics. (You can also watch our interview as a video or read the associated article.)

The world needs to move to renewable energy sources, such as solar or wind. The problem with those is that they're intermittent. That's because the Sun doesn't always shine and the wind doesn't always blow. What we need, then, are efficient ways of storing energy: efficient batteries. Currently lithium ion batteries are being used but there are issues around their cost, how long they last, and their safety.

Donald Sadoway

Hope is on the horizon in the form of liquid metal batteries. At a recent event organised by the Newton Gateway to Mathematics in Cambridge we met Donald Sadoway who played a very important role in pioneering these batteries. In this podcast he talks to us what they are and why they are better, when they'll be commercially available, and why sometimes it's best to ignore the experts.

To watch a talk given by Sadoway at the Newton Gateway event go to the Newton Gateway website. And to find out more about magnetohydrodynamics, a theory that has been used to describe liquid metal batteries, go here.

Will climate change leave the region you live in hotter and drier, or wetter and stormier? It's a question of utmost importance in many areas of the world, yet it's one that climate scientists can't answer. This is why world-leading climate scientist Tim Palmer is calling for a high-performance supercomputing centre dedicated entirely to climate change.

Tim Palmer.

We were lucky enough to meet Palmer at a recent event organised by the Newton Gateway to Mathematics In Cambridge. In this podcast we talk to Palmer about this call for a "CERN for climate change" and why climate forecasting requires so much computing power in the first place. Palmer also tells us about a technique for dealing with uncertainty called ensemble forecasting, and what his work has taught him about uncertainty more generally, as it crops up in many areas of life and nature.

Tim Palmer's new book on the science of uncertainty, The primacy of doubt, is published by Oxford University Press. To learn more about climate models see this article. To learn about weather forecasting see this article, and to read about uncertainty more general click here.

This podcast 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.

There are some numbers you can rely on. The speed of light, c, is 299,792,458 ms-1. The gravitational constant, G, is 6.674 x 10-11m3kg-1s-2. These are examples of what are often called the constants of nature – fundamental physical quantities that seem to be the same everywhere, and unchanging over time.

Or are they? Today would have been our wonderful boss, John D. Barrow's, 70th birthday. And to celebrate him and his work we look at the answer to this question in today's podcast.

John D. Barrow (Image credit: Tom Powell)

Over time, since these constants were discovered, people had hoped to find a theory, a great theory of everything, that would explain why these particular values had arisen. However, as John explains in this podcast, developments in recent decades, in areas such as string theory, have shown that these constants could take any value. And this provided the motivation for studying whether such constants might be changing in value.

John, together with the astronomer John Webb, initiated an observational programme looking at the light produced by quasars in the distant Universe. They developed new techniques to analyse the light to test if certain constants had the same value near a quasar as they did in laboratories here on Earth.

You can find out more about this aspect of John’s work in this podcast, and read more in his accompanying article: Are the constants of nature really constant? And you can find out more about some of John's other work and interests in his many Plus articles.

This interview was recorded in 2009 as part of our celebration of the International Year of Astronomy 2009, where we tried to answer the questions everyone wanted to ask about the Universe

Amid much controversy, the 2022 World Cup has begun and the action has now moved onto the football pitches inside the many newly built stadiums in Qatar. But how are these stadiums turned from architectural sketches into real buildings?

For this week's episode we delve back far into our archive to hear from Paul Shepherd from the University of Bath, an expert in building football stadiums such as the famous Emirates stadium in London. In this interview, first recorded back in 2007, he tells us about what kind of things are important in building a stadium, how maths is an integral part of the design process, and why his work required him to listen to Belgian techno.

The Emirates Stadium, home of the Arsenal football club. (Photo Arne Müseler – CC BY-SA 3.0 DE)

You can hear more about the maths behind famous sporting buildings in our recent podcast How the velodrome found its form. And you can find out much more about the maths behind football and sports, and behind engineering and architecture here on Plus.

Yuriy Semenov was forced to leave Ukraine, and his work at the Institute of Hydromechanics at the National Academy of Sciences, due to the Russian invasion of February 2022. He found sanctuary in Britain at the University of East Anglia. In part this was thanks to the Solidarity for mathematicians programme ran by the Isaac Newton Institute for Mathematical Sciences (INI).

In this podcast Yuriy speaks to the INI's Dan Aspel and shares his experience of the Russian invasion of Ukraine, and why the work of a mathematicians is always possible.

We are very pleased to host this episode of the Living Proof podcast as part of our collaboration with the wonderful INI.

We're very excited to be going to this year's European Congress of Mathematics (ECM), which will take place in Seville, Spain, in July! And we noticed that mathematicians who win one the prizes awarded at the ECM by the European Mathematical Society quite often go on to win a Fields Medal, one of the highest honours in mathematics.

So to celebrate the run-up to the ECM we've launched Euromaths, a miniseries of podcasts revisiting interviews with Fields Medallists who previously won an EMS prize. This week we hear from James Maynard who won a Fields Medal in 2022 and an EMS prize in 2016, talking about is work on the fabled twin prime conjecture.

You can read about James's work in this short introduction and this in-depth article.

Click here to listen to last week's episode of Euromaths featuring Fields Medallist Hugo Duminil-Copin.

This content was originally produced as part of our collaborations with the London Mathematical Society and the Isaac Newton Institute for Mathematical Sciences. You can find all our content on the 2022 International Congress of Mathematicians here.

Professor Nataliya Vaisfel'd was until recently a mathematician at Odesa I. I. Mechnykov National University. Forced to flee Ukraine after the Russian invasion of her home country in February of this year, Nataliya has since travelled across Europe with her wheelchair-bound mother and their dogs, eventually finding sanctuary in Britain. In part this was thanks to the Solidarity for mathematicians programme ran by the Isaac Newton Institute for Mathematical Sciences. She is now a Senior Lecturer at King’s College London. 

In this podcast Nataliya tells her story in conversation with the INI's Dan Aspel.

We are very pleased to host this episode of the Living Proof podcast as part of our collaboration with the wonderful INI.

This podcast 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.

Over the summer we were lucky enough to meet some young female mathematicians who were just finishing up their summer research projects with the Philippa Fawcett Internship Programme and the Cambridge Mathematics Placements programme.

On our way to the writing workshops we were running with these women, we walked past six inspiring portraits of female mathematicians from Cambridge. These form part of the Women of Mathematics photo exhibition, which celebrates female mathematicians from institutions throughout Europe. It's been a great pleasure revisiting our our 2017 Women of Mathematics interviews with these mathematicians about their work and their mathematical lives in this special series of podcasts.

Today's podcast is the final one of this series, and we are very pleased to revisit our interview with Carola-Bibiane Schönlieb, now professor of applied mathematics and a very good friend of us here at plus.maths.org. Carola works on the interface between machine learning and the mathematics of image analysis.

You can read more about some of Carola's recent work, including how artificial intelligence can support medical doctors in their work, and the INTEGRAL project, a collaboration with Indian researchers on how machine learning can make sense of the vast amounts of remote sensing data that is available to help conserve forests and improve life in cities.

To find a transcript and video of this interview, meet the other female mathematicians, and find out more about the exhibition, see here.

In this podcast we are very happy to revisit our 2017 interview with Holly Krieger, one of the six Cambridge mathematicians whose portrait is included in the Women of Mathematics photo exhibition. Krieger works in dynamical systems theory, particularly on chaotic systems. In this interview she told us about the joys of learning and conversations with colleagues.

Holly Krieger (Photograph by Henry Kenyon)

You can find more about Krieger's prize winning work in Dynamic numbers and you see her talk about complex numbers and dynamical systems in our collection Complex numbers: Why do we love them?

To find a transcript and video of this interview, meet the other female mathematicians, and find out more about the exhibition, see here.

In this podcast we are very happy to revist our 2017 interview with Julia Gog - Professor of Mathematical Biology and a very good friend of us here at plus.maths.org. Over the last two years we've been working closely with Gog and her colleagues at the JUNIPER modelling consortium, communicating their work on the mathematical front-line of the COVID-19 pandemic.

In this interview, first recorded to celebrate the addition of six portraits of Cambridge mathematicians to the Women of Mathematics photo exhibition, Gog told us about the buzz of mathematical research, and how maths can help you do good in the world.

To find a transcript and video of this interview, meet the other female mathematicians, and find out more about the exhibition, see here. And you can read more about the work of Gog and her JUNIPER colleagues here.