Prof Sarah Hart

Overview
Overview
Highlights
My book "Once Upon a Prime", on the links between mathematics and literature, is published by Flatiron Books in the US and HarperCollins in the UK.
The New York Times profiled me and my work in an article by Siobhan Roberts here. The article was syndicated in The Independent.
I was also quoted in a 2023 NYT article "The Quest to find Rectangles in a Square" talking about what makes a good problem.
As Gresham Professor of Geometry (from 2020) I give six free public lectures each year. The most popular so far has been "Where do Mathematical Symbols Come From?", with over 100,000 YouTube views.
Ahab's Arithmetic: The mathematics of Moby Dick, my paper published in the Journal of Humanistic Mathematics in 2021, is my most downloaded paper with approx 4000 downloads as at April 2023.
I enjoyed being a guest on Steven Levitt's podcast People I (Mostly) Admire. Steven is an economist best known for his smash hit book Freakonomics. You can listen here (or wherever you get your podcasts).
I enjoyed chatting about maths and music with James Grime for MathsWorldUK in a video released last year.
Office hours
I don't have fixed office hours at the moment but am happy to see students via Teams or in person (pandemics permitting), just email to make an appointment.
Qualifications
 MA(Oxon) Mathematics, Balliol College, Oxford, 1996
 MSc Mathematics, University of Manchester, 1997
 PhD Mathematics, UMIST (University of Manchester Institute of Science and Technology), 2000
 Fellow of the Higher Education Academy, Higher Education Academy (now Advance HE), 2008
Web profiles
Visiting posts
 Gresham Professor of Geometry, Gresham College,
Professional activities
President of the British Society for the History of Mathematics
Member of the London Mathematical Society
Plus the usual community service including acting as external examiner for PhD vivas, refereeing papers for several journals, and serving as a member of the EPSRC peer review college. I was also a member of the LMS library committee from 20192022.
ORCID
0000000336120736 
Research
Research
Research interests
 Mathematics and culture
 "Solving equations in groups"
 Productfree and sumfree sets
 History of Mathematics
 Coxeter groups
 Commuting graphs
Research overview
Mathematics, culture and history
I am very interested in mathematics in its broader cultural context. This includes the history of mathematics and the people who have studied it, as well as the links between mathematics, music, art, fiction and other artistic activities. Mathematics fits firmly in with the arts in my philosophy. This of course is in line with the Ancient Greeks, who studied, the quadrivium, arithmetic, geometry, music, and astronomy. 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.
These interests are now the main focus of my work  mostly in the form of lectures or writing aimed at a general audience. My book "Once Upon a Prime: the wondrous links between mathematics and literature" is published in the US by Flatiron Books, and in the UK by HarperCollins.
In terms of academic research, I've been delighted with the amount of interest in my 2021 article "Ahab's Arithmetic" about the mathematics in Herman Melville's novel MobyDick, published in the Journal of Humanistic Mathematics. It's by far my most downloaded paper, which is very encouraging that more work in this area will be both rewarding for me personally but also of interest in the wider community.
Pure mathematics research
My PhD, and my published research for the first part of my academic career, were in the area of abstract algebra known as group theory, a beautiful mathematical tool for studying symmetry, in the widest interpretation of that word. You can look at my list of publications, but I've written lots of papers on Coxeter groups (a particularly nice kind of group if you're interested in symmetry and geometry), as well as commuting involution graphs in various groups, plus some work on sumfree and productfree sets, and most recently playing with the idea of solving equations in groups (starting with finding square roots and cube roots). For a lay introduction to sumfree sets see this blog, which also links to something I'm very proud of  having a theorem of mine (joint work with Michael Guidici) appearing as Theorem of the Day at theoremoftheday.org.

Supervision and teaching
Supervision and teaching
Supervision
Current and recently completed PhD students
 Dan McVeagh (current student)
 Precious Agigor (Commonwealth Scholar, 1 year visiting PhD fellowship 2022)
 Amal Sbeiti Clarke (completed 2018)
 Chimere Anabanti (completed 2017)
Unfortunately I have too many other work commitments to be able to take on any new PhD students for the forseeable future.
Teaching
Teaching modules
 Numbers, Proofs and Counting (BUEM096S4)
 Explorations in Mathematics (BUEM099S4)
 Algebra 3 (BUEM129H6)

Publications
Publications
Article
 Hart, Sarah and Rowley, Peter (2023) Lengths of Involutions in Finite Coxeter Groups. Journal of Pure and Applied Algebra 227 (2), pp. 107190. ISSN 00224049.
 Anabanti, Chimere and Hart, Sarah (2022) Groups with a given number of nonpower subgroups. Bulletin of the Australian Mathematical Society 106 (2), pp. 315319. ISSN 00049727.
 Hart, Sarah and Kelsey, V. and Rowley, P. (2021) Generating finite Coxeter groups with elements of the same order. Turkish Journal of Mathematics 45 (6), pp. 26232645. ISSN 13000098.
 Anabanti, Chimere and Aroh, A.B. and Hart, Sarah and Oodo, A.R. (2021) A question of Zhou, Shi and Duan on nonpower subgroups of finite groups. Quaestiones Mathematicae ISSN 16073606.
 Hart, Sarah (2021) Ahab's arithmetic; or, the mathematics of MobyDick. Journal of Humanistic Mathematics 11 (1), pp. 432. ISSN 21598118.
 Hart, Sarah and Mcveagh, Dan (2020) Groups with many roots. International Journal of Group Theory 9 (4), pp. 261276. ISSN 22517650.
 Hart, Sarah and Anabanti, Chimere (2020) A question of Mazurov on groups of exponent dividing 12. Communications in Algebra 48 (12), pp. 53725373. ISSN 00927872.
 Hart, Sarah and Sbeiti Clarke, Amal (2020) Commuting Involution Graphs in classical affine Weyl Groups. Communications in Algebra 48 (7), pp. 29412957. ISSN 00927872.
 Hart, Sarah and Rowley, P. (2018) Maximal length elements of excess zero in finite Coxeter Groups. Journal of Group Theory 21 (5), ISSN 14354446.
 Hart, Sarah and Sbeiti Clarke, Amal (2018) Commuting involution graphs for $\tilde C_n$. Communications in Algebra 46 (9), pp. 39653985. ISSN 00927872.
 Anabanti, C. and Erskine, G. and Hart, Sarah (2018) Groups whose locally maximal productfree sets are complete. Australasian Journal of Combinatorics 71 (3), pp. 544563. ISSN 22023518.
 Hart, Sarah (2017) How many elements of a Coxeter group have a unique reduced expression?. Journal of Group Theory 20 (5), pp. 903910. ISSN 14354446.
 Hart, Sarah and Anabanti, Chimere (2016) Groups containing small locally maximal productfree sets. International Journal of Combinatorics pp. 8939182. ISSN 16879163.
 Anabanti, C.S. and Hart, Sarah (2015) On a conjecture of Street and Whitehead on locally maximal productfree sets. Australasian Journal of Combinatorics 63, pp. 385398. ISSN 22023518.
 Hart, Sarah and Hedtke, I. and MuellerHannemann, M. and Murthy, S. (2015) A fast search algorithm for (m,m,m) triple product property triples and an application for 5 × 5 matrix multiplication. Groups Complexity Cryptology 7 (1), pp. 3146. ISSN 18696104.
 Hart, Sarah and Rowley, P.J. (2015) On excess in finite Coxeter groups. Journal of Pure and Applied Algebra 219 (5), pp. 16571669. ISSN 00224049.
 Hart, Sarah and Rowley, P.J. (2014) Corrigendum to "Involution products in Coxeter groups" [J. Group Theory 14 (2011), no. 2, 251–259]. Journal of Group Theory 17 (2), pp. 379380. ISSN 14354446.
 Hart, Sarah and Rowley, P.J. (2013) Xposets of certain Coxeter groups. Taiwanese Journal of Mathematics 17 (6), pp. 19011919. ISSN 10275487.
 Hart, Sarah and Rowley, P.J. (2012) Zero excess and minimal length in finite coxeter groups. Journal of Group Theory 15 (4), pp. 497512. ISSN 14354446.
 Hart, Sarah and Rowley, P.J. (2012) On cosets in coxeter groups. Turkish Journal of Mathematics 36 (1), pp. 7793. ISSN 13000098.
 Hart, Sarah and Rowley, P.J. (2012) Maximal length parabolic subgroups in finite Coxeter groups. JP Journal of Algebra, Number Theory and Applications 24 (2), pp. 185202. ISSN 09725555.
 Hart, Sarah and Rowley, P.J. (2011) Involution products in Coxeter groups. Journal of Group Theory 14 (2), pp. 251259. ISSN 14354446.
 Hart, Sarah and Rowley, P.J. (2011) Lengths of parabolic subgroups of finite coxeter groups. International Electronic Journal of Algebra 9, pp. 1037. ISSN 13066048.
 Hart, Sarah and Rowley, P.J. (2010) A note on maximal length elements in conjugacy classes of finite coxeter groups. Birkbeck Pure Mathematics Preprint Series 17,
 Hart, Sarah and Rowley, P.J. (2009) Poincaré series of cosets in Coxeter groups. Algebra Colloquium 16 (4), pp. 567574. ISSN 10053867.
 Guidici, M. and Hart, Sarah (2009) Small maximal sumfree sets. Electronic Journal of Combinatorics 16 (1), ISSN 10778926.
 Bundy, D. and Hart, Sarah (2009) The case of equality in the LivingstoneWagner Theorem. Journal of Algebraic Combinatorics 29 (2), pp. 215227. ISSN 09259899.
 Bates, C. and Bundy, D. and Hart, Sarah and Rowley, P.J. (2009) A note on commuting graphs for symmetric groups. Electronic Journal of Combinatrics 16 (1), ISSN 10778926.
 Bates, C. and Bundy, D. and Hart, Sarah and Rowley, P.J. (2007) Commuting involution graphs for sporadic simple groups. Journal of Algebra 316 (2), pp. 849  868. ISSN 00218693.
 Hart, Sarah and Rowley, P.J. (2007) Lengths of subsets in coxeter groups. Turkish Journal of Mathematics 31, pp. 6377. ISSN 13000098.
 Hart, Sarah and Rowley, P.J. and Bundy, D. and Bates, C. (2007) Primitive kfree permutation groups. Archiv der Mathematik 88 (3), pp. 193198. ISSN 0003889X.
 Hart, Sarah (2006) Commuting involution graphs for [(A)\tilde]n. Archiv der Mathematik 86 (1), pp. 1625. ISSN 0003889X.
 Bates, C. and Bundy, D. and Perkins, Sarah and Rowley, P. and Hart, Sarah (2005) Root differences for A n. Archiv der Mathematik 85 (4), pp. 313317. ISSN 0003889X.
Monograph
 Hart, Sarah and Sbeiti Clarke, Amal (2018) Commuting Involution Graphs in Classical Affine Weyl Groups. Birkbeck Mathematical Sciences Preprint Series London, UK: Birkbeck, University of London.
 Hart, Sarah and Sbeiti Clarke, A. (2018) A note on commuting Involution Graphs in Affine Coxeter Groups. Birkbeck Mathematical Sciences Preprint Series (43), London, UK: Birkbeck, University of London.
 Hart, Sarah and Clarke, A.S. (2018) Commuting Involution Graphs in Classical Affne Weyl Groups. London, UK: Birkbeck, University of London.
 Anabanti, Chimere and Erskine, G. and Hart, Sarah (2016) Groups whose locally maximal productfree sets are complete. London, UK: Birkbeck, University of London.
 Hart, Sarah (2016) How many elements of a Coxeter group have a unique reduced expression?. London, UK: Birkbeck, University of London.
 Anabanti, Chimere and Hart, Sarah (2015) On a conjecture of Street and Whitehead on locally maximal productfree sets. London, UK: Birkbeck, University of London.
 Hart, Sarah and Anabanti, Chimere (2015) A note on filled groups. Birkbeck Mathematics Preprint Series (17), London, UK: Birkbeck College, University of London.
 Hart, Sarah and Anabanti, Chimere (2015) Locally maximal productfree sets of size 3. Birkbeck Mathematics Preprint Series (10), London, UK: Birkbeck College, University of London.
 Hart, Sarah and Rowley, P. (2014) Maximal length elements of excess zero in Finite Coxeter Groups. Birkbeck Mathematics Preprint Series London, UK: Birkbeck College, University of London.
 Hart, Sarah and Rowley, P.J. (2014) Involution statistics in finite coxeter groups. Birkbeck Pure Mathematics Preprint Series 4, London, UK: Birkbeck College, University of London.
Other
 Hart, Sarah (2019) Mathematical Quotations in Melville’s MobyDick. unpublished.
External Repositories

Business and community
Business and community
Media
I am happy to receive enquiries from the media on the following topics:
 Mathematics
 Mathematics and Literature, Music, Art
 Women in Mathematics/Science
Outreach
I give frequent public lectures  in person, livestreamed and then freely available on YouTube  in my role as Gresham Professor of Geometry, the first woman to hold this role since its inception in 1597.
I am also regularly asked to speak in secondary schools  I can't accept all invitations, sadly, but do get in touch if you'd like me to give a talk at your school or college and I'll do what I can.
Media appearances have included guest appearances on podcasts such as Steven Levitt's Freakonomics radio podcast People I (Mostly) Admire (April 2023 and October 2021), the BookRiot podcast with Jeff O'Neal (April 2023), The Pulse (April 2023), celebrating Pi day on Radio 4's Today programme, chatting with Lauren Laverne on 6Music about Maths and Music (November 2020), explaining the maths of the Lottery on ITV News (2019), and being the mathematics expert on Channel 4's Child Genius programme (2019).
I also speak at Literary Festivals including York Literature Festival (March 2023), Marlborough Literary Festival (Sept/Oct 2023).