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.

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

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.