Oxford Mathematics
Proving the Erdős Primitive Set Conjecture
updated
Starring: Jessica, Terry, Lena and Zoe who tell us what doing maths means for them.
Me and My Maths. Short films about people who also do maths.
14-inch pizza or 12? Which is the best value?
Oxford Mathematician James Munro on making the best use of our dough.
Yes, mathematicians.
Starring Chris Thorogood, Derek Moulton, Hadrien Oliveri and Alain Goriely (in the case-study below).
You can read the full research case-study here:
maths.ox.ac.uk/node/64967
Episode 12 of 'When did you know it was Maths?' Oxford Mathematicians telling tales in school.
#shorts
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
Andrew Wiles, for example.
The latest episode of 'When did you know it was Maths?'
#shorts
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
Let Charlotte explain in the latest episode of 'When did you know it was Maths?'
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
The latest episode of 'When did you know it was Maths?' Oxford Mathematicians explaining why it's maths for them.
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
James Munro on the mathematical cunning of shrinkflation.
In this panel discussion two scientists and one artist, all leaders in their field, will try to provide an answer. They have more in common than you would think.
Nobel-prize winning scientist Roger Penrose is Emeritus Rouse Ball Professor in Oxford. Carlo Rovelli is a Professor in the Centre de Physique Théorique de Luminy of Aix-Marseille Université and the author of several popular science books including 'Seven Brief Lesson on Physics'. Conrad Shawcross is an artist specialising in mechanical sculptures based on philosophical and scientific ideas. His exhibition, 'Cascading Principles', is currently showing in the Mathematical Institute.
The discussion is chaired by curator and writer Fatos Ustek who is the curator of the 'Cascading Principles' exhibition.
The Oxford Mathematics Public Lectures and the Conrad Shawcross Exhibition are generously supported by XTX Markets.
The latest episode of our summer series 'When did you know it was Maths?'
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
#shorts
Chaim Goodman-Strauss, one of the authors of the paper describing the new work, will give an overview. This will be followed by a panel discussion with Chaim, fellow author Craig Kaplan, mathematician Marjorie Senechal and Nobel Laureate Roger Penrose. The discussion is chaired by Henna Koivusalo.
@OxfordMathematics
To celebrate, here is his contribution to our 'When did you know it was Maths?' films in which he explains how he was very nearly lost to medicine.
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
Our latest "When did you know it was Maths?' film. Stories of why mathematicians are mathematicians.
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
#shorts
But, as Petra explains, sometimes it takes a lot longer.
Episode 5 of 'When did you know it was Maths?'
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
Mathematics as indisputable truth. Manchester's finest, Georgia Brennan, describes what made her a mathematician.
Episode 4 of 'When did you know it was Maths?' Stories of epiphanies and gradual dawns.
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
The location: Rainey Endowed School, Magherafelt, Northern Ireland
The action: a maths lesson
The talent: a young Philip Maini
The story so far: a long explanation of an oscillating pendulum...
Episode 3 of our summer series 'When did you know it was Maths?'
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
Not every mathematical epiphany, the moment when you decide you love maths, happens when you are young. In our second 'When did you know it was Maths' film, Kate Wenqi describes how she left maths for a career in finance, only to return when the stress was becoming too much.
With apologies to Joni Mitchell from whose song 'Big Yellow Taxi' the quote comes. True about a lot of things.
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
Introducing our new summer series: 'When did you know it was Maths?'
Starring: Oxford Mathematicians
The plot: students, researchers & professors reveal the moment when they knew that it was maths for them.
Episode 1: Alicia
You can watch all the films in the series here: youtube.com/playlist?list=PL4d5ZtfQonW0Fr0y-DatepvEKBQTWiXjw
#shorts
Starring:
Arkady Wey - Mathematical models of filtration
Patrick Nairne - Diaries, memory & embeddings of metric spaces
Nivedita Nivedita - Axiomatic approaches to field theory (algebraic and functional)
Xu'an Dou - Blow-up time dilation: generalized solution for a Fokker-Planck equation in neuroscience
Torin Fastnedge - Fighting the fuzz
Yue Liu - Parameter identifiability and experimental design for PDE models of cell invasion
So, take a sheet of paper. . .
Tadashi Tokieda is a professor of mathematics at Stanford. He grew up as a painter in Japan, became a classical philologist (not to be confused with philosopher) in France and, having earned a PhD in pure mathematics from Princeton, has been an applied mathematician in England and the US; all in all, he has lived in eight countries so far. Tadashi is very active in mathematical outreach, notably with the African Institute for Mathematical Sciences.
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
In this Oxford Mathematics Public Lecture he explains the fascinations and frustrations of the primes before sitting down with Hannah Fry to discuss his work and his life.
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
Tim Harford has some ideas.
This talk, to an audience of 9-13 year-olds and their families, was part of the 2023 Oxford Maths Festival. The advice works for all ages.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Starring: Adam, Sofia, Edwina and Yixuan talking about their mathematical lives (and the Oxford Mathematics Fast Hat).
Me and My Maths. Short films about people who also do maths.
This version was performed in early March 2023 by Oxford Mathematics students and fellow students from across the University. The venue was a lecture theatre in the Andrew Wiles Building, home to Oxford Mathematics and named after the mathematician who is the subject of the story.
Subtitles available via the subtitles icon.
Filmed and edited by Steve Pierce at Oxford Film Shed.
Students are then shown how they can use the theory of Fourier series, taught in the preceding lectures, to solve the initial value problem. The behaviour of the solutions is discussed mathematically and in the context of physical applications.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
In this fascinating discussion artist Conrad Shawcross and mathematicians Martin Bridson and James Sparks explore connections between mathematics and art. An exhibition of Conrad's mathematically inspired work, curated by Fatos Ustek, chair of this discussion, is showing in the Andrew Wiles Building, home to Oxford Mathematics, until October 2023.
You can read more about the exhibition via this link: maths.ox.ac.uk/node/61184
The Oxford Mathematics Public Lectures and the Conrad Shawcross exhibition are generously supported by XTX Markets.
Students are then shown how they can use the theory of Fourier series, taught in the preceding lectures, to solve the initial value problem. The behaviour of the solutions is discussed mathematically and in the context of physical applications.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Students are then shown how they can use the theory of Fourier series, taught in the preceding lectures, to solve the initial value problem. The behaviour of the solutions is discussed mathematically and in the context of physical applications.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Students are then shown how they can use the theory of Fourier series, taught in the preceding lectures, to solve the initial value problem. The behaviour of the solutions is discussed mathematically and in the context of physical applications.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Starring: Kylie and Chloe, Andrea, Doyne, and Kate Wenqi.
Me and My Maths. Short films about people who also do maths.
Marieke van Beest - Non-perturbative Quantum Field Theories (case study below)
maths.ox.ac.uk/node/41103
Ian Griffiths - COVID-19 modelling: rapidly predicting the spatially varying infection risk indoors from airborne transmission
maths.ox.ac.uk/node/41517
Ross Zhang - Understanding Navier-Stokes
Solveig van der Vegt - Mathematical modelling of autoimmune myocarditis
maths.ox.ac.uk/node/60777
Jagoda Kaszowska-Mojsa - Assessing the COVID-19 prevention and control schemes
maths.ox.ac.uk/node/41122
Much of the context will be familiar from high school but the way we think and write about it, and construct arguments and proofs, will be more rigorous.
In summary it is a recap and a pointer to what is to come for our students. We are showing the whole course over eight lectures. This is the eighth and final lecture in which Ian is problem solving.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Much of the context will be familiar from high school but the way we think and write about it, and construct arguments and proofs, will be more rigorous.
In summary it is a recap and a pointer to what is to come for our students. We are showing the whole course over eight lectures. This is Lecture 7 and looks at constructing statements and proofs.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Helen Wilson is Head of the Department of Mathematics at UCL. She is best known for her work on the chocolate fountain (which features in this lecture) but does do serious mathematical modelling as well.
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
Probably a bit of both. At our Postgraduate Open Day you can hear from students & faculty with talks on:
Why do a doctorate?
Life as a PhD/DPhil student
Choosing a field of study
The statement of purpose
The interview process
Overview of our MSc programmes
If you want to know more about postgraduate study at Oxford follow this link: maths.ox.ac.uk/study-here/postgraduate-study
Much of the context will be familiar from high school but the way we think and write about it, and construct arguments and proofs, will be more rigorous.
In summary it is a recap and a pointer to what is to come for our students. We are showing the whole course over eight lectures. This is Lecture 6 and looks at logical notation and quantifiers.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Much of the context will be familiar from high school but the way we think and write about it, and construct arguments and proofs, will be more rigorous.
In summary it is a recap and a pointer to what is to come for our students. We are showing the whole course over eight lectures. This is Lecture 5 and looks at functions.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Joshua Bull is a mathematical modeller. He was also the winner of the 2020 Fantasy Football competition from over eight million entrants. So when it came to the Oxford Mathematics 2022 World Cup predictor, Josh fitted the bill perfectly. Honing in on the data, applying his modelling skills, and adding a pinch of the assumptions that inform modelling (disclaimer: he is an Ipswich Town fan), Josh has come up with the answers - or rather, likely outcomes. See what you think.
PS: some people have commented that Josh has got the last 16 wrong because those combinations cannot come out of the groups. However, he explicitly says in the video that this is an overall prediction not a specific one. For a specific one and more forecasts and thoughts, please go to our social media pages via this link: maths.ox.ac.uk for links).
Much of the context will be familiar from high school but the way we think and write about it, and construct arguments and proofs, will be more rigorous.
In summary it is a recap and a pointer to what is to come for our students. We are showing the whole course over eight lectures. This is Lecture 4 and looks at relations and equivalence relations.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Our lives start, progress in complex ways, and are finally complete. So do tasks executed on a computer. Multimodal streams are a pervasive “type”, and even without fixing the context, have a rich structure. Developing this structure leads to wide-ranging tools that have had award-winning impact on methodology in health care, finance, and computer technology.
Terry Lyons is Professor of Mathematics in Oxford and a Fellow of St Anne's College. His research is supported through the DataSig and Cimda-Oxford programmes.
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
Much of the context will be familiar from high school but the way we think and write about it, and construct arguments and proofs, will be more rigorous.
In summary it is a recap and a pointer to what is to come for our students. We are showing the whole course over eight lectures. This is Lecture 3 and continues the previous lecture's look at sets, and specifically algebra of sets, truth tables and cardinality.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Correction: in Q6 (iii) the binary tree that's drawn on screen is missing an influencer in the top-right. This has been corrected in the thumbnail of the video. And don't worry, we've told James that he made a mistake.
More MAT resources at http://www.maths.ox.ac.uk/r/mat
The MAT is used by Oxford Mathematics to help us decide which candidates to invite for interview.
More like this on our second channel:
youtube.com/c/OxfordMathematicsPlus
Much of the context will be familiar from high school but the way we think and write about it, and construct arguments and proofs, will be more rigorous.
In summary it is a recap and a pointer to what is to come for our students. We are showing the whole course over eight lectures. This is Lecture 2 and focuses on the binomial theorem and sets.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
Much of the context will be familiar from high school but the way we think and write about it, and construct arguments and proofs, will be more rigorous.
In summary it is a recap and a pointer to what is to come for our students. We are showing the whole course over eight lectures. This is Lecture 1 and focuses on the natural numbers and induction.
All first and second year lectures are followed by tutorials where students meet their tutor to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.
In 1936, Alan Turing proved the startling result that not all mathematical problems can be solved algorithmically. For those which can be, we still do not always know when there's a clever technique which could give us the answer quickly. In particular, the famous "P = NP" question asks whether, for problems where the correct solution has a proof which can easily be checked, in fact there's a quick way to find the answer.
Many difficult problems become easier if they have symmetries: finding the shortest route to deliver many parcels would be easy if all the houses were neatly arranged in a circle. This lecture explores the interactions between symmetry and complexity.
Colva Roney-Dougal is Professor of Pure Mathematics at the University of St Andrews and Director of the Centre for Interdisciplinary Research in Computational Algebra.
The Oxford Mathematics Public Lectures are generously supported by XTX Markets.
To find out, we filmed a supervision. Introducing Professor Jason Lotay & graduate student Izar Alonso Lorenzo as they discuss geometry in seven dimensions related to special holonomy, gauge theory and heterotic String Theory.
The tiny world of particles and atoms and the gigantic world of the entire universe are separated by about forty orders of magnitude. As we move from one to the other, the laws of nature can behave in drastically different ways, sometimes obeying quantum physics, general relativity, or Newton’s classical mechanics, not to mention other intermediate theories.
Understanding the transformations that take place from one scale to another is one of the great classical questions in mathematics and theoretical physics, one that still hasn't been fully resolved. In this lecture, we will explore how these questions still inform and motivate interesting problems in probability theory and why so-called toy models, despite their superficially playful character, can sometimes lead to certain quantitative predictions.
Professor Martin Hairer is Professor of Pure Mathematics at Imperial College London. He was awarded the Fields Medal in 2014.
Check out the two other episodes via our playlists, and watch Jared talking about his brilliant proof, earlier this year, of the Erdős primitive set conjecture in this video: youtube.com/watch?v=c81ilGlIH1I