Last summer we were lucky enough to attend the European Congress of Mathematics (ECM) in Seville, Spain. The Congress sees the award of several prestigious prizes, including the Otto Neugebauer Prize for the History of Mathematics.

In this episode of Maths on the Move we talk to this year's winner of the Otto Neugebauer Prize, Reinhard Siegmund-Schultze, who has worked on and written about mathematicians who fled Nazi Germany. Reinhard tells us about the motivation for his work, how the Nazi regime impacted mathematics and mathematicians, and what future historians might say about the mathematics of today.

This content was produced with kind support from the London Mathematical Society.

What is as hypnotising as a beautiful goldfish circling its bowl, but can help you understand the way a virus can spread? The answer is one of the beautiful interactive simulations produced by VisualPDE !

In this podcast we talk to Benjamin Walker from University College London, and to Adam Townsend and Andrew Krause from Durham University, who together created this online solver of partial differential equations. Such equations describe how quantities change over space and time and therefore used throughout science to describe processes that play out in the real world — from the transmission of airborne viruses to the flow of water during a flood. Ben, Andrew and Adam tell us about their motivation for building VisualPDE and what they can do with it.

We met Ben, Andrew and Adam through the Mathsci-comm network for people who communicate maths and data science to non-expert audiences. As you can see by playing with the simulation below, VisualPDE is a great tool for communicating maths research to non-experts, as well as allowing mathematicians to quickly simulate what their mathematical models can tell them.

Adam is also part of the team behind the brilliant Chalkdust, a magazine for the mathematically curious. Why not order the latest issue for a Christmas gift?

Suppose that lots of people are sitting in a sealed room and one of them is infectious. We'll assume that the infectious person is constantly producing virus-laden particles that spread out around them and lose their potency over time. The simulation below shows what this might look like. The colour corresponds to the concentration or amount of the virus in the air.

With VisualPDE, we're not just limited to watching a simulation: we can interact with it too. Clicking in the room will introduce some viral particles to the air, as if someone with an infection had coughed (coughing is actually a lot more complicated and is the focus of lots of research). Try clicking to see what difference a cough can make.

Though each cough introduces some virus to the room, it looks like it quickly decays away until we can't even tell it was there. So, does this mean we shouldn't be worried about a cough?

To explore this further, let's look at the probability (or chance) of getting an infection, which is related but not equal to the virus concentration. Specifically, we'll look at the chance of catching the virus assuming that you'd been in the same location for the duration of the simulation. With VisualPDE, we can do this by switching to the Probability View by pressing and choosing "Probability".

Now for the goldfish. People don't always stay still in the middle of rooms. Unsurprisingly, the movement of an infected individual can have a big impact on the spread of a virus. The next simulation is set up so that the source of the infection moves around the room, as if they were a waiter going between tables in a restaurant, perhaps. The air conditioner is turned off, so that the air in the room is still.

The Probability View shows the build-up of a ring of likely infections as the infectious person circles the room. A quick look at the Concentration View shows their circular path, leaving a trail of viral particles behind them.

To find out more about this simulation and how to explore it, go to the VisualPDE site.

The two scientific papers mentioned in the podcast are:

• Predicting the spatio-temporal infection risk in indoor spaces using an efficient airborne transmission model by Zechariah Lau, Ian M. Griffiths, Aaron English and Katerina Kaouri

• Turing Instabilities are Not Enough to Ensure Pattern Formation by Andrew L. Krause, Eamonn A. Gaffney, Thomas Jun Jewell, Václav Klika and Benjamin J. Walker

Are you thinking of doing a Masters or PhD in maths or another STEM subject but are worried about funding? Then the Martingale Foundation might be for you. The Foundation's mission is "to enable and nurture talented individuals from low-socioeconomic backgrounds to thrive within world-leading postgraduate study and become STEM leaders" by providing full scholarships as well as a development programme.

In this episode of Maths on the Move we talk to two current Martingale scholars, Alexandra Sorinca and Malachy Reynolds, who have both just started their PhD at King's College London. We met them this summer at Solve for X, a mathematical modelling retreat delivered by the Martingale Foundation in partnership with the Newton Gateway to Mathematics and the Isaac Newton Institute for Mathematical Sciences (INI), which challenged teams of students to solve real-life maths problems posed by industry. Solve for X is one of the activities the Martingale Foundation provides for its scholars. Alexandra and Malachy tell us about their challenges and also about what it's like being a Martingale scholar.

We also talk to Chloe Slevin, the Martingale Foundation's Communications Manager, who explains the Foundation's aims and gives useful advice for new applicants.

As a PhD student working with the Maths4DL research project, Yolanne Lee works on the mathematics that powers artificial intelligence. In this podcast she tells us about what she thinks AI will be able to do in the near future, what it has to do with cats and dogs, and how music provided her first experience of science. We also get to hear her play the piano!

To find out more about the topics discussed in this podcast 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 very excited that Hannah Fry is coming to join us in Cambridge in January 2025. Fry is a brilliant mathematician, best-selling author, award winning science presenter and host of popular podcasts and television shows. She'll be Cambridge's first Professor for the Public Understanding of Mathematics.

In this episode of Maths on the Move Hannah explains how her interest in public engagement grew directly out of her work as a mathematician, talks about how she got into maths in the first place, and shares one of her favourite mathematical moments.

We were very proud that Hannah announced the news at an event we organised together with the Newton Gateway to Mathematics. It was called Communicating Mathematical and Data Sciences – What does Success Look Like? and took place at the Newton Institute for Mathematical Sciences (INI) on November 21, 2024. The event was part of the mathsci-comm network which aims to connect those working in, and with a stake in, communicating complex mathematics and data science to a variety of non-expert audiences. The network is supported by the INI — find out more here.

Image above: Lloyd Mann.

This content was produced as part of our collaborations with the Isaac Newton Institute for Mathematical Sciences (INI) and the Newton Gateway to Mathematics.

The INI is an international research centre and our neighbour here on the University of Cambridge's maths campus. 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 all know what data is: bits of information of which in this age of Big Data we have lots of. You might also know what topology is: the study of shapes that considers two shapes to be the same if you can deform one into the other without tearing them or gluing things together.

But what is topological data analysis? And how might it help to understand proteins or diseases such as cancer? We find out with Heather Harrington a mathematician we met at the European Congress of Mathematics (ECM) this summer. Heather tells us how topological data analysis can produce a so-called barcode for a given data set which gives deep insights into its structure. Below are a couple of images illustrating a barcode to illustrate what we talk about in the podcast.

We attended the ECM with kind support of the London Mathematical Society (LMS). Heather gave the LMS lecture at the ECM.

You might also want to listen to more episodes of our Euromaths series which reports on the ECM.

Circles drawn around 20 points in the plane. If the radius r is less than r0, the circles are small enough to not overlap (left). Once the radius exceeds r0, but is smaller than r1, the circles overlap and together form a ring-like structure (middle). One the radius is larger than r1 the circles join up in the centre of this ring-like structure. What you see now is a single blob without a hole.

The barcode captures this information. For r < r0 there are 20 red lines indicating there are twenty connected components without holes. For r0 < r < r1 there is one green line indicating there is one connected component with one hole (the colours red and green differentiate between no hole and one hole). For r > r1 there is one red line indicating there is one connected component without a hole.

This content was produced with kind support from the London Mathematical Society.

We love a game of billiards — or at least the mathematical version of it. It's a dynamical system that's just about basic enough to study but still poses lots of open questions. In this episode of Maths on the Move we talk to Giovanni Forni about chaos, periodicity and the many things we still hope to learn about billiards.

We met Giovanni at the European Congress of Mathematics (ECM) in summer this year, which we attended with kind support of the London Mathematical Society. See here for more episodes of our Euromaths series which reports on the ECM.

To find out more about mathematical billiards on Plus see

• Chaos on the billiards table
• Playing billiards on doughnuts
• Playing billiards on strange tables

Here are a couple of academic papers by Forni and his collaborators:

• Weakly Mixing Billiards, J. Chaika, G. Forni
• Weak Mixing in rational billiards, F. Arana-Herrera, J. Chaika, G. Forni.

This content was produced with kind support from the London Mathematical Society.

As the days in the UK get shorter and darker we continue remembering the brilliant time we had in Seville last summer at the European Congress of Mathematics (ECM). In this episode of Maths on the move we talk to one of the mathematicians we met at the ECM, Jessica Fintzen, who won a prestigious EMS Prize at the Congress.

Jessica tells us how to capture infinitely many snowflakes at the same time, the maths of symmetry and her work on representation theory, and why she likes doing handstands.

To find out a little more about Jessica's mathematics, as well as her gymnastics, see this video.

You might also like to look the following content relevant to topics discussed in the podcast:

• Groups: the basics
• Maths in a minute: Representing groups

This content was produced with kind support from the London Mathematical Society.