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.

Reduce, remove, refreeze: Repairing the Earth's climate

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.

 

Bye bye 23, hello 24!

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.
 

Can we build a low carbon energy network

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

The travelling salesman

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.

The universal machine: Putting Alan Turing on the stage

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.

A disappearing number

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.

Victoria Gould: Combining mathematics and acting

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.

Have physicists discovered a fifth force of nature?

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.

How many dimensions are there?

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.

Telescope topology

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.
 

From clicks to chords

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.

How does human noise impact whales?

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.

Living Proof: The irrational diary of Clara Valentine

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.
 

Mathematical summer fun

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.

Gravitational waves reveal cosmic hum

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.

Sarah Hart: Once upon a prime

"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.

A very old problem turns 30!

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.

Chocolate and mayonnaise

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.

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