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

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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).

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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.

 

 

 

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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.

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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.

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Tue, 28 Jun 2022

The Mathematical Genius of Bach - James Sparks to Open Spitalfields Music Festival

Spitalfields Music Festival banner

J.S. Bach is sometimes described as the mathematician's musician. But why is that?

James Sparks is a professional mathematician here in Oxford; but he was also an organ scholar as an undergraduate in Cambridge and he is fascinated by the mathematical aspect of Bach's work.

On June 30th James will open the Spitalfields Music Festival 2022 with a talk on the 'Mathematical Genius of Bach'. He will be followed by the City of London Sinfonia playing the Goldberg Variations where that genius reaches its apogee.

More details here

 

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Mon, 27 Jun 2022

All we ever wanted was everything / 24.02.22 (for Ukraine)

Image of sculpture

On June 27th, in the Reception area of the Mathematical Institute, Oxford artist Andy Bullock unveiled his most ambitious knot sculpture to date, a large floor-based work titled ‘All we ever wanted was everything / 24.02.22 (for Ukraine)’ constructed using 70 metres of metal trunking. As with all his knot sculptures they often reference issues of complexity with situations and people, the personal and interpersonal; focusing on what it means to be human.

In a first for the artist, Bullock will be inviting members of the recently arrived Ukrainian refugee community to contribute to the artwork by incorporating items of personal relevance. Bullock is reaching out to Oxfordshire’s Ukrainian community in a collaboration with Yulia Astasheva, a recent arrival herself from the Dnipropetrovsk region, where she still has close family living only miles from the Russian-occupied region.

The idea for the work came initially from a commission from Oxford Mathematics for Bullock to create an exhibition of his maths-related painting, photography and sculpture to be open to the public this summer. The core of his fine art master’s degree show last year was a creative examination and exploration of the topological subject of knot theory, and in particular the work of Clifford Hugh Dowker (1912-82), an eminent mathematician whose work is still studied today. “I find a poetic beauty in the mathematics I researched even though my understanding of the subject is virtually nil” said Bullock. “My final dissertation for my master’s degree examined the similarities in thought of mathematicians working in these areas and that of artists working in a more conceptual arena”.

In the lower ground floor space of the building there is an exhibition of some of Andy Bullock’s ‘knot variation’ paintings and photographs and a display of original handwritten manuscripts from Dowker’s personal archive alongside Andy's own sketchbooks, allowing an insight into the respective processes of mathematician and artist.

The exhibition will run until 22 July.

For further information:

Andy Bullock - @email - 07582 526957 - www.bullockstudio.com

Yulia Astasheva - @email

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Thu, 16 Jun 2022

3 Minute Thesis Competition

Image of Benedikt Stock giving his talk; and his slide which features David Hilbert, Yuri Matiyasevich and a cartoon of Benedikt himself.

For 4 years our DPhil (PhD) students go deep into their area of research. Then we suggest they sum it all up in 1 slide and 3 minutes.

6 of them have done just that in our 3 Minute Thesis Competition. Easy-peasy.

Alexander Van-Brunt - PDE theory and the energy storage problem
Sophie Abrahams - How bubbles affect kidney stones
Benedikt Stock - (Un)Decidability in Number Theory
Matthew Cotton - Curvature inducing membrane-bound proteins
Michael Negus - Making an impact with droplet modelling
Jared Duker Lichtman - The Erdos primitive set conjecture

The competition is organised by the Oxford Mathematics SIAM-IMA Student Chapter.

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Mon, 13 Jun 2022

Jagoda Kaszowska-Mojsa wins Excellence in Artificial Intelligence Award

Image of Jagoda with the prize

Oxford Mathematician Jagoda Kaszowska-Mojsa has won the Excellence in Artificial Intelligence Award for her MACROPRU project at the Perspektywy Women in Tech Summit in Warsaw, Poland.

Jagoda's goal is to investigate how new macroprudential policies can influence financial stability without contributing to inequality in society. In her project she is applying cutting-edge, agent-based simulation, big data and AI techniques to uncover the redistributive effects of public policies and to examine the optimal combination of macroprudential tools from a social welfare perspective.

Jagoda developed an agent-based simulation with an AI component. In other words, she simulated the behaviour of the economy as if we were modelling a virtual reality in which entities make informed decisions, learn and create the reality in which they coexist. This is a major shift in the modelling approach in economics and finance that could spark a paradigm shift.

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Mon, 06 Jun 2022

Oxford graduate student proves decades old Erdős conjecture on primes

Photo of Jared

Oxford Mathematician Jared Duker Lichtman explains his fascination and frustration with a conjecture that has puzzled mathematicians for years.

"The Erdős Primitive Set Conjecture centres around one key definition. A set of positive integers $A\subset \mathbb{Z}_{>1}$ is called primitive if no number in $A$ divides another. For example, the primes form a primitive set. More generally, for any $k\geq 1$ the set of numbers with exactly $k$ prime factors (counted with repetition) is also primitive.

The definition of primitivity is quite simple, so it forms a very broad class of sets and it is easy to construct many examples. An example of particular significance historically is the set of perfect numbers. Since Ancient Greece we say a number is perfect if it equals the sum of its proper divisors. For instance 6 is perfect since its proper divisors 1,2,3 sum to 6 itself. Perfect numbers have fascinated mathematicians for millennia, and it is a nontrivial fact that they form a primitive set.

We number theorists often think of the set of primes as a precious gem like a rare diamond. Similarly, we may think of the broader class of primitive sets like a larger treasure trove of jewels, including emeralds, rubies, and sapphires. Each primitive set has its own special properties, just as each gem has its own unique characteristics, like brilliance, colour, and rarity.

We know that the primes become quite rare further out along the number line. Technically speaking, the primes have density zero.

In 1935, the great mathematician Paul Erdős generalized this result considerably. He proved that every primitive set has (lower) density zero. In fact, he showed the stronger result

Theorem (Erdős, 1935):  We have uniformly for all primitive $A$,

$$f(A)=\sum_{a\in A}\frac{1}{a\log a} < \infty.$$

His proof also interpreted these series $f(A)$ as encoding the size of density zero objects $A$. Rather, $f(A)$ roughly measures the density of the multiples generated by $A$.

Once we know these series converge, it is natural to ask for a maximum. In 1988, Erdős famously asked if the primes $\mathcal P$ are maximal among all primitive sets.

Erdős Primitive Set Conjecture (1988):  We have  $f(A) \leq f(\mathcal P)$ for all primitive $A$.

I immediately fell in love with the problem when I first heard it, and had been thinking about it ever since. Usually it can be difficult to say exactly why we feel the way we do about those dear to us. But in this case, the conjecture articulates precisely how the primes are special in a broader context.

For four years, I was wrestling with the conjecture and tried several approaches. After a while I revisited Erdős' original argument from 1935. Roughly speaking, it was very efficient with sets of numbers that were either prime themselves or had only small prime factors, and one could prove the conjecture in this special case. But if any composite numbers had a large prime factor, the Erdős argument became much cruder.

But then in the winter during lockdown, I realized one could leverage ideas from probability theory: morally, I proved that a primitive set cannot contain too many composite numbers with a large prime factor. Thus we can actually avoid many of the crude cases, thereby exploiting extra efficiency from the Erdős argument. From this key connection to probability, a solution finally emerged.

Theorem (L., 2022):  The Erdős Primitive Set Conjecture is true.

After all is said and done, we now see another reason why the prime numbers are indeed special."

You can read Jared's proof here and watch him introduce the Conjecture in the short film below. You can also read a feature on Jared in Quanta magazine and a longer explanation of the work on Numberphile.

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