What are groups and what are they good for?

Maths on the Move

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The Final Flight of Captain Forrester

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The Final Flight of Captain Forrester | 1. The Mystery of Tiny 05 38:05

לפני 11 ימים38:05

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לייק

אהבתי

38:05

In late 1972, U.S. Marine Captain Ron Forrester disappeared on a bombing run into North Vietnam. Back home in Texas, his family could only wait and hope. Audio subscribers to Texas Monthly can get early access to episodes of the series, plus exclusive interviews and audio. Visit texasmonthly.com/audio to join. Go to HelloFresh.com/FLIGHT10FM to get 10 Free Meals with a Free Item For Life.…

לפני שנה 25:14

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Over the summer we've been incredibly lucky to have been working with Justin Chen, a maths student at the University of Cambridge who is about to start his Masters. Justin has done some great work on how to explain the concept of a mathematical group, and group theory as a whole, to non-mathematicians. In this episode of Maths on the move he tells us how groups are collection of actions, akin to walking around on a field, and why group theory is often called the study of symmetry. He also marvels at the power of abstraction mathematics affords us, tells us about what it was like diving into the world of maths communication, and what his plans are for the future.

You can find out more about groups in the following two collections Justin has produced:

You might also want to read Justin's article Explaining AI with the help of philosophy mentioned at the beginning of the podcast. It is based on an interview with Hana Chockler, a professor at King's College London, conducted at a recent event organised by the Newton Gateway to Mathematics and the Alan Turing Institute.

This article 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.

100 פרקים

#Science #Math #plus.maths.org #Podcasting Education #Living Proof

Maths on the Move

What are groups and what are they good for?

Maths on the Move

published לפני שנה

שתפו

MP3•בית הפרקים

You can find out more about groups in the following two collections Justin has produced:

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

100 פרקים

#Science #Math #plus.maths.org #Podcasting Education #Living Proof

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Maths on the Move

1
Living proof: A conversation with Sarah Hart 24:39

לפני 18 ימים24:39

24:39

Sarah Hart is a mathematician who is interested, not just in the maths itself, but also its connections to other areas of culture and art. She's done an amazing number of things throughout her career — from research in pure mathematics and heading up a maths department, to being the first woman Gresham Professor of Geometry and President of the British Society for the History of Mathematics . Sarah has also written a fascinating book, called Once upon a time: The wondrous connections between mathematics and literature , and she gave a talk at this year's Cambridge Festival , with the intriguing title Life in Lilliput – The Mathematics of Fictional Realms. The talk was the contribution to the Festival of the Isaac Newton Institute for Mathematical Sciences (INI). Sarah also participates in the Modern History of Mathematics research programme that is currently taking place at the INI. In this episode of Living proof , produced in collaboration with the INI, Sarah tells us about the many things she has done and how they all fit together, and gives some advice for budding mathematicians of all ages: keep pursuing all the things you love doing, and one day it may turn out that they all fit together. To find out more about some of the things mentioned in this podcast see the fllowing links: Sarah Hart: Once upon a prime — In this episode of our Maths on the Move podcast Sarah talks about her book and the connections between maths and literature. Maths in three minutes: Groups — This article gives a brief introduction to Sarah's research area. Life in Lilliput – The Mathematics of Fictional Realms — Click this link to watch a recording of Sarah's Cambridge Festival talk at the INI. Sarah Hart at Gresham College — Click this link to watch Sarah's Gresham College public lectures. This podcast forms 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.…

Maths on the Move

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Rob Eastaway: Shakespeare's mathematical life and times 23:57

לפני 25 ימים23:57

23:57

One thing we all have in common is that we did maths at school. Those of us from the English speaking world most likely also did Shakespeare at school. Do these two things have anything in common? It turns out that they do! Our friend Rob Eastaway , author and Director of the amazing Maths Inspiration project, has written a book called Much Ado About Numbers: Shakespeare's mathematical life and times . In this episode of Maths on the Move , Rob tells us about some of the many instances of maths appearing in Shakespeare's work. He also tells us about the mathematical climate that Shakespeare lived in. Among other things, it included a mathematical revolution, saw music as a subfield of maths, and gave rise to the word "trivial" so much beloved by mathematicians. The book is out in paperback now. To find out more about some of the topics mentioned in this episode, see the following links: The fabulous positional system is an article exploring the nature of our number system. Rob's Gresham College lecture explores some of the topics mentioned in this podcast and in his book. Maths Inspiration runs inspiring and interactive maths shows for teenagers. Finally, here are reviews of some of Rob's books: The hidden mathematics of sport (with John Haigh) Maths for mums and dads (with Mike Askew) More maths for mums and dads (with Mike Askew) How long is a piece of string? (with Jeremy Wyndham) Mindbenders and brain teasers (with David Wells) How to take a penalty (with John Haigh) How many socks make a pair ?…

Maths on the Move

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Living proof: Diving into maths with Emmy Noether 29:02

לפני 5 weeks29:02

29:02

Every now and again, and more often than you'd think, the work of mathematics overlaps with the world of theatre and film. This happened again recently when the Isaac Newton Institute for Mathematical Sciences (INI) organised a staging of the play Diving into math with Emmy Noether. Noether was a pure mathematician whose results made waves far beyond her field. Albert Einstein called her a "creative mathematical genius". The play is produced by Portrait Theater Vienna in co-operation with Freie Universität Berlin, directed by Sandra Schueddekopf, and features Anita Zieher as Emmy Noether. It was put on as part of the Modern History of Mathematics research programme that is currently taking place at the INI and the Inclusivity in the Mathematical Sciences workshop that was organised by the Newton Gateway to Mathematics in March 2025. In this episode of Maths on the move we talk to historian of mathematics David E. Rowe , who provided scientific advice for the play, about the life and work of Emmy Noether, and about what it's like putting mathematics on stage. You might also want to read our article Emmy Noether: A creative mathematical genius . 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 .…

Maths on the Move

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The Abel Prize 2025 29:47

לפני 6 weeks29:47

29:47

Last Wednesday, March 26, 2025, this year's Abel Prize was awarded to the Japanese mathematician Masaki Kashiwara. The Abel Prize is one of the most prestigious honours in mathematics. It is awarded every year by the Norwegian Academy of Science and Letters and comes with a prize money of over £550,000. In this episode of Maths on the Move we talk to Helge Holden , Chair of the Abel Prize Committee. Helge tells us about this year's winner, the history and purpose of the Prize, and how the winners are chosen. He also tells us why good mathematicians are needed in all sectors of science and beyond, and talks about the tragic story of the mathematician Niels Henrik Abel, after whom the Prize is named. To find out more about some of the topics mentioned in this episode, see: The Abel Prize 2025: Masaki Kashiwara - An accessible look at some of Kashiwara's mathematics. The Chern Medal 2018: Masaki Kashiwara - Another look at Kashiwara's work written on the occasion of his winning the Chern Medal in 2018. What are groups and what are they good for? - An episode of the Maths on the Move podcast which explores group theory. Stubborn equations and the study of symmetry - An article which touches one of Niels Henrik Abel's most famous results. Journal für die reine und angewandte Mathematik - Also known as Crelle's journal, this publication is mentioned in the podcast.…

Maths on the Move

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Evidence week: Shaping the future of AI 24:49

לפני 7 weeks24:49

24:49

The UK government has recently pledged to put around £14 billion into supporting the development of artificial intelligence over the next few years. But because AI comes with perils as well as promises, careful policy decision are going to be crucial. In order to make such decision in an informed way, politicians need to interact with the mathematicians and scientist who develop AI. In this episode of Maths on the Move we talk to mathematician Chris Budd who recently went to Parliament for something called Evidence Week , where he and other AI researchers talked with MPs and Peers from the House of Lords. Chris tells us about the discussions he had with politicians — about the worrying issue of bias in AI, its promising applications, for example in the medical arena, and also about the fact that AI is built on mathematics. A strong maths education, starting at primary school, is therefore essential if we're going to make the best of AI in the future. Chris is Professor of Applied Mathematics at the University of Bath, co-lead of the research project Maths4DL , and Director of Knowledge Exchange for the Bath Institute for Mathematical Innovation . He attended Evidence week with a team of researchers which included Yolanne Lee, a Maths4DL PhD student who recently featured in another Maths on the Move episode . The image above shows, from left to right, Dáire O’Kane (Maths4DL), Jenny Power (IMI), Yolanne Lee (Maths4DL), and Alexandra Freeman, Baroness Freeman of Steventon. To find out more about some of the topics discussed in this episode see AI be the judge: The use of algorithms in the criminal justice system Can AI help with breast cancer screening? Maths4DL AI policy brief: Black boxes of AI - watch maths open them This podcast was produced as part of our collaboration with the Mathematics for Deep Learning (Maths4DL) research programme. Maths4DL brings together researchers from the universities of Bath and Cambridge, and University College London and 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 .…

Maths on the Move

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Living proof: Communicating mathematics with the INI and Hannah Fry 28:40

לפני 8 weeks28:40

28:40

We kick off our latest series of podcasts with an episode of Living proof , produced jointly with the Isaac Newton Institute for Mathematical Sciences (INI). This episode is all about the communication of mathematics to the wider world, which is becoming ever more recognised as a priority within the maths community. We talk to Sara Khan, Communications Manager at the INI, about how this renowned research institute supports mathematics communication. And we revisit our interview with Hannah Fry who has just taken up her new role as Professor of the Public Understanding of Mathematics here at the University of Cambridge As Hannah puts it, "It's really important that people feel that [mathematics] is being done with them, not to them." We also find out about Hannah's own research in her previous role as Professor for the Mathematics of Cities at University College London, and hear about her favourite mathematical moment. To find out more about organisations and events in support of mathematics communication mentioned in this episode, see the following links: The Mathsci-comm network is funded by an INI Network grant and 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 run by the Editors of plus.maths.org, Marianne Freiberger and Rachel Thomas, together with Maha Kaouri from the Newton Gateway to Mathematics Communicating mathematical and data sciences — what does success look like? was a workshop organised by the Mathsci-comm network, which took place at the INI in November 2024. Hannah Fry announced her move to Cambridge at this event. The Graduate training workshop for the Mathematical Sciences , organised by the Newton Gateway to Mathematics , took place at the INI in February 2025 and comprised a significant component dedicated to communication, delivered by the Editors of plus.maths.org, Marianne Freiberger and Rachel Thomas, together with Alison Kiddle and Katie Steckles . This followed a pilot event which took place in October 2024. Talking maths in public (TMiP) is a conference which runs in the UK every two years, for people who work in, or otherwise participate in, communicating mathematics to the public. TMiP 2025 will take place at the University of Warwick on 28th - 30th August 2025, with the option to participate online. 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 .…

Maths on the Move

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Euromaths: Reinhard Siegmund-Schultze 15:30

לפני 20 weeks15:30

15:30

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 .…

Maths on the Move

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Playing with VisualPDE 29:59

לפני 21 weeks29:59

29:59

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? Play with the simulation! 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…

Maths on the Move

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Solve for X and the Martingale Foundation 25:30

לפני 22 weeks25:30

25:30

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. Alexandra Sorinca Malachy Reynolds Chloe Slevin…

Maths on the Move

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Yolanne Lee: Cats, dogs and AI 23:42

לפני 23 weeks23:42

23:42

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 .…

Maths on the Move

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Hannah Fry: Mathematics for the people 26:00

לפני 24 weeks26:00

26:00

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 .…

Maths on the Move

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Euromaths: Heather Harrington 28:21

לפני 25 weeks28:21

28:21

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 r 0, the circles are small enough to not overlap (left). Once the radius exceeds r 0, but is smaller than r 1, the circles overlap and together form a ring-like structure (middle). One the radius is larger than r 1 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 < r 0 there are 20 red lines indicating there are twenty connected components without holes. For r 0 < r < r 1 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 > r 1 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 .…

Maths on the Move

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Euromaths: Giovanni Forni 26:08

לפני 26 weeks26:08

26:08

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 .…

Maths on the Move

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Euromaths: Jessica Fintzen 14:16

לפני 27 weeks14:16

14:16

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 .…

Maths on the Move

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Euromaths: Richard Montgomery 16:40

לפני 28 weeks16:40

16:40

The world is full of networks. We're part of them, our infrastructure is full of them, and there are even networks within our bodies (e.g. made from neurons). This summer the mathematician Richard Montgomery won a prestigious EMS Prize at the European Congress of Mathematics (ECM) for his work on the pure maths of networks, also known as graph theory . In this episode of Maths on the move Richard tells us about an amazing result he helped to prove to great acclaim, known as Ringel's conjecture , and why it's interesting to take graphs to the extreme. You might also want to read this article about Richard's work. To find out more about the event at the Isaac Newton Institute in honour of Tim Gowers, which is mentioned in the podcast, see here . This content was produced with kind support from the London Mathematical Society .…

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