Thu, 22 Sep 2022

James Maynard awarded a New Horizons Prize for Early-Career Achievements in Mathematics

Photo of James

Oxford Mathematician James Maynard has been awarded a 2023 New Horizons Prize for Early-Career Achievements in Mathematics in recognition of his multiple contributions to analytic number theory, and in particular to the distribution of prime numbers. 

James, who recently won the Fields Medal for his work, is recognised as one of the leading figures in the field of number theory. Much of his career has focused on the study of general questions on the distribution of prime numbers and his achievements include settling a long-standing conjecture of Paul Erdős on large gaps between primes and showing the existence of infinitely many primes missing any given digit (for example, 7).

More recently, in joint work with D. Koukoulopoulos he settled the Duffin-Schaeffer conjecture and dramatically improved upon the work of Schmidt concerning simultaneous approximation by rationals with square denominator. Most recently, he published a monumental series of works on the distribution of primes in residue classes which goes beyond what follows from the Generalised Riemann Hypothesis.

James Maynard did his undergraduate studies at Queens' College, Cambridge before moving to Oxford to do a DPhil under the supervision of Roger Heath-Brown where he has spent much of his career to date. He is now a Professor of Number Theory in Oxford and a Supernumerary Fellow at St John's College.

The New Horizons Prize is part of the Breakthrough Prizesthe world’s largest science awards founded by Sergey Brin, Priscilla Chan and Mark Zuckerberg, Julia and Yuri Milner, and Anne Wojcicki. The prizes recognise the top scientists in the fields of Life Sciences, Fundamental Physics, and Mathematics.

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Tue, 13 Sep 2022

Cascading Principles - a major mathematically inspired exhibition by Conrad Shawcross

Photo of exhibit with someone walking past

Oxford Mathematics is delighted to be hosting one of the largest exhibitions by the artist Conrad Shawcross in the UK. The exhibition, Cascading Principles: Expansions within Geometry, Philosophy, and Interference, brings together almost 40 sculptures realised by the artist over the last seventeen years. The artworks are placed in public and private areas, forming a web of relationships which emerge as the viewer moves through the building.

Conrad Shawcross models scientific thought and reasoning within his practice. Drawn to mathematics, physics, and philosophy from the early stages of his artistic career, Shawcross combines these disciplines in his work. He places a strong emphasis on the nature of matter, and on the relativity of gravity, entropy, and the nature of time itself. Like a scientist working in a laboratory, he conceives each work as an experiment. Modularity is key to his process and many works are built from a single essential unit or building block. If an atom or electron is a basic unit for physicists, his unit is the tetrahedron.

Unlike other shapes, a tetrahedron cannot tessellate with itself. It cannot cover or form a surface through its repetition - one tetrahedron is unable to fit together with others of its kind. Whilst other shapes can sit alongside one another without creating gaps or overlapping, tetrahedrons cannot resolve in this way. Shawcross’ Schisms are a perfect demonstration of this failure to tessellate. They bring twenty tetrahedrons together to form a sphere, which results in a deep crack and ruptures that permeate its surface. This failure of its geometry means that it cannot succeed as a scientific model, but it is this very failure that allows it to succeed as an art work, the cracks full of broad and potent implications.

The show includes all Conrad's manifold geometric and philosophical investigations into this curious, four-surfaced, triangular prism to date. These include the Paradigms, the Lattice Cubes, the Fractures, the Schisms, and The Dappled Light of the Sun. The latter was first shown in the courtyard of the Royal Academy and subsequently travelled all across the world, from east to west, China to America.

The show also contains the four Beacons. Activated like a stained-glass window by the light of the sun, they are composed of two coloured, perforated disks moving in counter rotation to one another, patterning the light through the non-repeating pattern of holes, and conveying a message using semaphoric language. These works are studies for the Ramsgate Beacons commission in Kent, as part of Pioneering Places East Kent.

Cascading Principles: Expansions within Geometry, Philosophy, and Interference will be accompanied by a four-part symposium, with events taking place throughout the year of the exhibition. Researchers from Oxford Mathematics will be paired with artists and philosophers for talks that will foster cross-fertilisation of thought and creativity. The symposium series is organised in partnership with Modern Art Oxford and Ruskin School of Art, evoking the collaborative ethos of Conrad's artistic practice.

The exhibition Cascading Principles: Expansions within Geometry, Philosophy, and Interference is curated by Fatoş Üstek, and is organised in collaboration with Oxford Mathematics.

The exhibition is open 9 am-5 pm, Monday to Friday. Some of the works are in the private part of the building and we shall be arranging regular tours of that area. If you wish to join a tour please email @email

The exhibition runs until 8 October 2023.

Cascading Principles is generously supported by our longstanding partner XTX Markets.

Please contact us for feedback and comments about this page. Created on 13 Sep 2022 - 09:34.
Thu, 08 Sep 2022
Tue, 06 Sep 2022

Oxford Mathematics Public Lecture: A mathematical journey through scales - Martin Hairer

Banner for lecture

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.

Please email @email to register.

The lecture will be available on our Oxford Mathematics YouTube Channel on 22 September at 5 pm.

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

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Wed, 24 Aug 2022

Roger Heath-Brown awarded the Sylvester Medal

Photo of Roger Heath-Brown

Oxford Mathematician Roger Heath-Brown has been awarded the Sylvester Medal by the Royal Society "for his many important contributions to the study of prime numbers and solutions to equations in integers". The Sylvester Medal is awarded annually by the Royal Society for an outstanding researcher in the field of mathematics. The award was created in memory of the mathematician James Joseph Sylvester who was Savilian Professor of Geometry at the University of Oxford in the 1880s.

Roger Heath-Brown is one of the foremost analytic number theorists of his generation. His important works on prime numbers and related topics include, among many others:

- "Heath-Brown's identity", an important way of decomposing the primes into multilinear pieces, used in many other works such as Zhang's work on bounded gaps between primes

- There are infinitely many primes of the form x^3 + 2y^3 (currently the sparsest natural sequence where one can find primes)

- if a is coprime to q, there is always a prime a (mod q) of size < q to the power 5.5

- at least one of 2,3,5 is a primitive root modulo infinitely many primes.

His contributions to solving equations in integers and rationals include, for instance:

- every nonsingular cubic form in 10 variables has a rational point (and 10 is best possible)

- every cubic form in 14 variables has a rational point

- development of "the determinant method"

- breakthrough quantitative results on the number of rational points up to a given height

Roger Heath-Brown was educated at Cambridge (a student of Alan Baker) and moved to Oxford in 1979. He was made FRS in 1993, and was twice a speaker at the International Congress of Mathematicians. He remained at Oxford throughout his career, first at Magdalen College and then, upon being promoted to a personal statutory professorship in 1999, at Worcester College. He retired in 2016. Among his many graduate students was James Maynard, who was awarded the Fields Medal in 2022.

You can watch an interview with Roger by Ben Green on occasion of his retirement (a loose term for a mathematician) .

Please contact us for feedback and comments about this page. Created on 24 Aug 2022 - 00:01.
Fri, 19 Aug 2022

Imagining AI - exhibitions and workshop

Sketch of Babbage's Difference Engine

You can't move (or read) for mention of artificial intelligence. And while we may only have a vague idea of what AI is, we know for sure that it is revolutionary and that it is new.

Except it isn't. Think Mary Shelley's creation in ‘Frankenstein’, and how it challenged ideas of what it meant to be human. How about Victorian Charles Babbage's 'Difference Engine' (pictured), feted as the forerunner of the computer. Babbage’s collaborator Ada Lovelace understood how it might weave patterns and compose music, as well as crunch numbers.

Or look at Stanley Jevons's remarkable mechanical 'logic piano' from the 1860s, which seemed to reduce the operations of the brain to wood and wire (pictured below).

'Imagining AI' places artificial intelligence in its historical context via displays, lectures and demonstrations. See AI in the making with manuscripts from Babbage, Lovelace, Shelley, and Turing's collaborator Christopher Strachey. Look at Jevons' 'logic piano', and components of Babbage’s machines. 

And meet Ai-Da, a thought-provoking contemporary robot artist providing inspiration to pupils of Cheney school. You are all welcome to join us in Oxford in the Bodleian's Weston Library, and the History of Science Museum.

9th September
Workshop in the Blackwell Hall, Weston Library. A day's talks and discussions, from Mary Shelley and Ada Lovelace in the 19th century to Christopher Strachey and Alan Turing in the 20th. Sign up to the workshop

The workshop will be accompanied by a free Exhibition opening in the Weston Library and History of Science Museum featuring the work of Shelley, Lovelace, Jevons and many others.

10th September
Imagining AI demonstrations, including Ai-Da, the world’s first ultra-realistic robot artist (booking required), and a 3-D print of Babbage's Difference Engine.

More information on all the exhibitions here

Stanley Jevons's piano

Please contact us for feedback and comments about this page. Created on 19 Aug 2022 - 09:54.
Fri, 05 Aug 2022

MAT Livestream 2022 up and running - watch episode 1 now

Image of MAT question

"Somehow, two hours of maths has become complete chaos."

"This is genuinely fun."

"How likely is it that we’ll be allowed to bring in a Samsung smart fridge to the MAT?"

Just some of the feedback from the first episode of our MAT (Mathematics Admissions Test) 2022 Livestream with MC James Munro.

You can watch the first episode (below) any time and subsequent episodes live on Thursdays at 5 pm UK (and any time after). And you'll get the answer to the MAT question in the image as well as joining in the poll asking, "do you start your sequences a_n with a_0 or with a_1?" (it was a close run thing).

Please contact us for feedback and comments about this page. Created on 05 Aug 2022 - 14:38.
Tue, 19 Jul 2022

Me and My Maths - Episode 2

Image of Ghita

With 'Me and My Maths' we are showing the sort of people who do maths round here, the sort of maths they do and what they get out of it. 

In Episode 2 we meet Jason who is a geometer working in multiple dimensions, Wojciech (with Delta) who is a mathematicial logician and Ghita who looks at financial modelling. The films are one-minute each though as someone pointed out the whole length of the film is 3.14 minutes. Deliberate of course.

PS: 'Me and My Math' if you are outside the UK. Or 'My Maths and I' as a purist might prefer.

 

 

 

Please contact us for feedback and comments about this page. Created on 19 Jul 2022 - 11:36.
Tue, 05 Jul 2022

James Maynard awarded the Fields Medal

Photo of James Maynard

The Fields Medal is widely regarded as the highest honour a young mathematician can attain and is especially hard to win because the medals are only awarded every four years to mathematicians under the age of forty. This year Oxford Mathematician James Maynard is one of four recipients for his "contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation."

James is recognised as one of the leading figures in the field of number theory. Much of his career has focused on the study of general questions on the distribution of prime numbers. His early research was on sieve methods and gaps between prime numbers and as a postdoctoral researcher in Montreal he developed a new sieve method for detecting primes in bounded length intervals, and settled a long-standing conjecture of Paul Erdős on large gaps between primes. Subsequently he showed the existence of infinitely many primes missing any given digit (for example, 7).

More recently, James has developed a growing interest in questions about Diophantine approximation, and in joint work with D. Koukoulopoulos he settled the Duffin-Schaeffer conjecture and dramatically improved upon the work of Schmidt concerning simultaneous approximation by rationals with square denominator. Most recently, improving on classical work of Bombieri, Friedlander and Iwaniec, he published a monumental series of works on the distribution of primes in residue classes which goes beyond what follows from the Generalised Riemann Hypothesis.  

James Maynard grew up in Chelmsford, Essex and attended the local grammar school (King Edward VI Grammar School). He did his undergraduate studies at Queens' College, Cambridge before moving to Oxford to do a DPhil under the supervision of Roger Heath-Brown where he has spent much of his career to date. After graduation, he was a CRM-ISM fellow in Montreal, a Junior Research Fellow at Magdalen College, Oxford and a Clay Research Fellow based in Oxford. He is now a Professor of Number Theory in Oxford and a Supernumerary Fellow at St John's College.

For his research in number theory, James has been awarded the SASTRA Ramanujan prize, the LMS Junior Whitehead prize, an EMS Prize, the Compositio prize and the AMS Cole Prize. His research was the focus of an AMS current events bulletin and a séminaire Bourbaki, and he was an invited speaker at the 2018 ICM.

The other three winners of the 2022 Fields medals are Hugo Duminil-Copin from the Université de Genève, June Huh from Princeton University (also a former Clay Research Fellow) and Maryna Viazovska from École Polytechnique Fédérale de Lausanne (EPFL).

Watch James discuss the award, his work and where he gets his inspiration in this short interview.

Please contact us for feedback and comments about this page. Created on 05 Jul 2022 - 02:00.
Fri, 01 Jul 2022

Oxford Mathematicians win London Mathematical Society Prizes

Image of John, Ian and Dawid

Three Oxford Mathematicians, John Ball, Ian Griffiths and Dawid Kielak have won prizes from the London Mathematical Society (LMS).

John Ball (also of Heriot-Watt University) is awarded the De Morgan Medal for his multi-faceted and deep contributions to mathematical research and the mathematical community over many years, in particular by his seminal work on nonlinear elasticity, fusing two communities: the community of rational mechanics and materials science on the one hand, and the community of the calculus of variations and nonlinear elliptic systems on the other.  In the words of the citation "John Ball is a true role model for a mathematician".  Read the full citation here.

Ian Griffiths is awarded a Whitehead Prize for his many contributions and insights to a wide range of challenging questions in applied and industrial mathematics, which he has achieved using a combination of asymptotic analysis and numerical simulations, supplemented by outstanding physical understanding. Read the full citation here.

Dawid Kielak is awarded a Whitehead Prize for his striking, original and fundamental contributions to the fields of geometric group theory and low-dimensional topology, and in particular for his work on automorphism groups of discrete groups and fibrings of manifolds and groups. Read the full citation here.

Please contact us for feedback and comments about this page. Created on 01 Jul 2022 - 18:02.