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Oration

Today, it is my great honour to welcome Professor Sarah B. Hart to a College Fellowship at ����logo���, University of London.

My favourite mathematics anecdote comes from C. P. Snow’s 1959 Rede Lecture entitled ‘The Two Cultures’. The historian A. L. Smith was sitting at High Table, engaging in his usual ‘cheerful Oxonian chit-chat’ with the man opposite – who simply grunted a reply. Smith then turned to the man of his right-hand side, only to get another grunt. The two grunters looked at each other, and one said, ‘Do you know what he’s talking about?’. ‘I haven’t the least idea’, the other man responded. At this point, the Vice-Master interrupted the awkward exchanging, reassuring Smith with the words: ‘Oh, those are mathematicians! We never talk to them!’

This anecdote, drawing on the ‘two cultures’ of the sciences versus the arts, could never be applied to Sarah Hart. She is as comfortable talking about pure mathematics (especially group theory) as she is in expounding on music, art, and fiction. I highly recommend her thoughts on Tolstoy, Melville, Poe, Joyce, Swift, Tolkien, George Eliot, Arthur Conan Doyle, and Dan Brown. As Sarah explains her philosophy,

Arithmetic is number; geometry is number in space, music is number in time, and astronomy is number in space and time. Of course, since mathematics is the language of the universe, it is an indispensable tool in science, but I've always viewed it as a creative art and doing mathematics as more akin to making art, music or poetry.

A mathematician, like a painter or a poet, is a maker of patterns.

The entire ����logo��� community has been invigorated by such a philosophy. Sarah has been at the heart of Mathematics at ����logo��� for nineteen years, and Professor for ten of those years. Indeed, when she was promoted to a full professorship at ����logo���, in 2013, she was the first female Professor of Mathematics and one of only five female mathematics professors under the age of forty in the UK. Equally impressive, she was appointed the Gresham Professor of Geometry, the first women to hold this Professorship since it was established in 1597.

The love of mathematics was instilled in Sarah from her youth. Both of her parents were schoolteachers with mathematics degrees. It is no surprise to learn that, while still in secondary school, Sarah was publishing in the field. In 1993, she published an exploration into extending Euler’s polyhedral formula to four dimensions. As the young Sarah Hart (then, Perkins) wrote in an article entitled ‘Investigating Four Dimensional Figures’,

Euler's theorem for three dimensional solids states that V+ F= E+ 2, where V is the number of vertices, F the number of faces and E the number of edges. When my sister, Mary, and I were thinking about this theorem, we wondered if perhaps there could be something similar in four dimensions, so we looked at a four dimensional hypercube.

She went on to complete an MA in Mathematics at Balliol College, Oxford, and then a M.Sc. in Pure Mathematics at the University of Manchester. This degree included a semester at the University of Bordeaux where she wooed everyone by her fluent command of French. From 1997 and 2000, she could be found at the University of Manchester’s Institute of Science and Technology. Her PhD thesis was entitled Coxeter Groups, Conjugacy Classes and Relative Dominance. Two postdoctoral research posts followed, funded by the Leverhulme Trust and the Engineering and Physical Sciences Research Council. The Institute provided her with valuable teaching experience, until she was appointed as Lecturer at ����logo��� in 2004. She quickly moved up the ranks. Indeed, she was promoted every two or three years: from Lecturer to Senior Lecturer to Reader and then Professor.

It was a meteoric rise, based on her research expertise. According to my count (which is incomplete), she has published a book, 10 monographs, and at least 34 articles in the highest-ranking mathematical journals, including Journal of Pure and Applied Algebra, Journal of Humanistic Mathematics, International Journal of Group Theory, Communications in Algebra, International Journal of Combinatorics, Groups Complexity Cryptology, Journal of Algebra, Number Theory, and Applications, and Journal of Algebraic Combinatorics. Alongside these achievements, Sarah is a ‘good citizen’, playing key roles in the Department, including Assistant Dean and Head of Department. She is President of the British Society for the History of Mathematics, member of the London Mathematical Society, Fellow of the Higher Education Academy, and Member of the Advisory Board of the Greenwich Mathematics Centre.

She is also an inspiration. She has fought for gender equality and been instrumental in supporting the College work for an Athena Swan. There is nothing elitist about her – everything she does is inclusive and engaging.

Her reputation as a communicator of mathematics is unrivalled in the world. She knows how to ‘pitch’ her stories – whether it is to schoolchildren or fellow-professors. It surprised no-one when 900 people turned up to hear her speak on ‘How to Prove Absolutely Anything’. Her remarkable listening numbers at Gresham College is evidence of her ability to draw people into her mathematical web. When she unravels all stereotypes about mathematicians (as discussed by Snow in his famous Rede Lecture), she is hilarious. She rails against

the beguiling fantasy that scientists, and especially mathematicians, are driven by pure reasons, that cleverness can get you out of any fix, and that everything can finally make sense if you can just ramify the ninth-dimensional asymptotes over a tangential vector field.
Sadly, you can’t, first, because life isn’t like that, and second, because I’ve just made up all those phrases, so they are meaningless.

I have loved reading her reflections on mathematics and literature. Her analysis of Michael Creighton’s novel Jurassic Park helped me understand fractals. Moby-Dick is one of her favourite books. It turns out that Moby-Dick is packed with witty mathematic references. Ishmael (the narrator) praises a sperm whale for the ‘mathematical symmetry’ of its head, giving it a ‘pervading dignity”. When he complains about the parsimony of a landlord, he wittily contends that:

Abominable are the tumblers into which he pours his poison. Though true cylinders without – within, the villainous green goggling glasses deceitfully tapered downwards to a cheating bottom. Parallel meridians rudely pecked into the glass, surround these footpads’ goblets.

As Sarah explains, in the novel, mathematics is ‘a talismanic protection against chaos’.

Sarah’s recent book, wittily called Once Upon a Prime, is simply a brilliant read. I laughed aloud on many occasions. In it, Sarah sets out to convinced readers that mathematics and literature are ‘complementary parts of the same quest to understand human life and our place in the universe’. Indeed, she tells us, poetry is ‘simply the continuation of mathematics by other means’.

Sarah wants her readers to enjoy both mathematics and literature, believing that an understanding of both will enhance our lives. Let me give you one example. In 2013, Sarah was reading The Luminaries by Eleanor Catton (it went on to win the 2013 Booker Prize). It didn’t talk long before she realised that there was ‘something mathematical going on: The chapters displayed a geometric progression, halving in length one to the next’. According to Sarah, this was compelling: ‘It’s refining and refining and refining, gradually waning down, until it’s quite poignant at the end….. It’s a feeling of inevitability, closing in the kernel of the love story at the centre of the entire novel’.

What about the person? She lives in Walthamstow, East London. Her two daughters and her spent lockdown taking lessons in origami, etymology, Latin, palindromic numbers, code cracking, and geometric patterns. Sarah also plays the piano – extremely well. She told a journalist for the New York Times: ‘Was it Paul Klee who talked about ‘taking a line for a walk’? I like to take an idea for a walk’. Reading is a passion. Every year, she reads the short-list for the Booker Prize.

Everyone wanted to speak to me about Sarah. She is funny, but also ‘always kind and helpful and very much one of those colleagues you can be completely honest with when it all feels a bit overwhelming’. Her colleagues tell me that they ‘could not have asked for a more supportive person’. She is generous in sharing her teaching notes and experiences, and in mentoring colleagues. Her PhD students attest to the way she is ‘unswervingly encouraging’ and ‘always there to help me do the mathematical equivalent of climbing out of a hole I’ve fallen into’. Another told me that she is ‘hands down, the best lecturer I’ve ever had: friendly, encouraging, enthusiastic’, as well as being ‘extremely kind both with her time and expertise’.

Finally, Sarah is a ����logo���ian. She is passionate about ensuring everyone has opportunities to learn and develop their skills to the highest level. We have all learnt so much from her. These are just some of the reasons we are thrilled to welcome her to a College Fellowship.