The Fourier transform is a piece of maths that is, almost single-handedly, responsible for the digital revolution. We asked Chris Budd what the Fourier
transform does, and how it does it. This podcast accompanies the Plus
article Saving lives: The mathematics of tomography.

Plus Advent Calendar Door #5: Catching waves

Maths on the Move, the podcast from plus.maths.org, will bring you the latest news from the world of maths, plus interviews and discussions with leading mathematicians and scientists about the maths that is changing our lives. Hosted by Plus editors Rachel Thomas and Marianne Freiberger.

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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.

Ramanujan: Dream of the possible

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.

You can listen to the podcast using the player above, and you can listen and subscribe to our podcast through Apple Podcasts, Spotify and through most other podcast providers via podbean.

Celebrating spring with new shoots of mathematics

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.

How physics can help AI learn about the real world

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.

The force awakens: Quantum collisions

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.

Plus Advent Calendar Door #5: Catching waves

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