Earlier in the month, as I reported in ‘Who are your important living mathematicians?‘, The Times’ Eureka magazine celebrated science with a list of “the 100 most important people in British science and engineering”.

I asked the question: where are the mathematicians? Andrew Wiles is top, at #41. Simon Donaldson is #75. Marcus du Sautoy is #76. (Further details.)

So, I wondered, why so few mathematicians? Mark Henderson asked: Who are the mathematicians that are missing? And I asked you:

If you were asked for examples of “important” (set your own criteria) living UK mathematicians, who would you offer?

Well, here are the recommendations I got:

## Tim Gowers

Timothy Gowers FRS is Rouse Ball Professor of Mathematics at the University of Cambridge. He received the 1998 Fields Medal for research connecting functional analysis and combinatorics and was elected a Fellow of the Royal Society in 1999. He is known for his well read blog, Gowers’s Weblog, and for a post ‘Is massively collaborative mathematics possible?‘, which started the polymath project.

## Christopher Zeeman

Sir Christopher Zeeman FRS is Honorary Professor at the University of Warwick. Zeeman was elected a Fellow of the Royal Society in 1975. As well as work in research on geometric topology and singularity theory, Zeeman is well known in mathematics for presenting the Royal Institution Christmas Lectures in 1978. This was the first time the lectures were presented on mathematics and they are cited by many mathematicians as their childhood inspiration to study mathematics further and inspired the Royal Institution Mathematics Masterclasses, which reach around 3000 students across the UK annually. He is also known for founding the Mathematics Department at the University of Warwick. The Christopher Zeeman Medal for Communication of Mathematics was named in his honour and first awarded in 2008 to Ian Stewart.

## Michael Atiyah

Sir Michael Atiyah OM FRS FRSE is known for research in topology, geometry and analysis and, as a former President of the Royal Society (1990-5) and of the Royal Society of Edinburgh (2005-8), an influential figure in the mathematics community. Among many awards, he won a Fields Medal in 1966 and the Abel Prize for outstanding scientific work in the field of mathematics in 2004.

## Roger Penrose

Sir Roger Penrose OM FRS is Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford. A mathematical physicist, he is well known for work completed with Stephen Hawking, for series of popular books and within mathematics for a set of tiles for non-periodic tiling which carry his name.

Although The Times’ was a UK list, I also received recommendations for the following who are based outside of the UK:

## John Milnor

Described by @haggisthesheep as a god of topology, John Milnor is Professor of Mathematics and Co-Director of the Institute for Mathematical Sciences at Stony Brook University. He received the Fields Medal in 1962 for work in differential topology. Milnor is also recognised for work bringing mathematics to a wider audience with what his 2004 Leroy P. Steele Prize for Mathematical Exposition citation called “sublime elegance”.

## Terence Tao

Terence Tao FRS is Professor of mathematics at the __Department of Mathematics__, __UCLA__. Tao has wide ranging interests – his webpage describes his work as “primarily in”: harmonic analysis, PDE, geometric combinatorics, arithmetic combinatorics, analytic number theory, compressed sensing, and algebraic combinatorics. An Australian, he was elected a Fellow of the Royal Society in 2007. He keeps a well read blog, ‘What’s new‘, on which he discusses his research as well as open problems and other topics in mathematics, and is an administrator of The Polymath Blog, a massively collaborative mathematics initiative.

## John Conway

John Conway is an English mathematician living and working in America as von Neumann Professor at Princeton University. Conway works in game theory, geometry, topology, group theory and provocative work in theoretical physics on free will. He has contributed to many branches of recreational mathematics, particularly through interaction with Martin Gardner, and is noted as the inventor of the Game of Life. Conway was elected a Fellow of the Royal Society in 1981 and, as author of several books, was awarded the 2000 Leroy P. Steele Prize for Mathematical Exposition, the citation for which notes: “his joy in mathematics is clearly evident in all that he writes”.

## John Baez

John Baez is a Professor of mathematics at the University of California, Riverside, where his work is in the mathematics of fundamental physics. Currently he is spending two years at the Centre for Quantum Technologies in Singapore where, his website explains, he will “think about technology and the global ecological crisis.” From 1993 to 2010 he wrote a well read column “This Week’s Finds in Mathematical Physics” and now writes the successor, Azimuth, on which he says he plans to talk about topcis from “math to physics to earth science and biology, computer science and the technologies of today and tomorrow – but in general, centered around the theme of what scientists can do to help save a planet in crisis.”

## Donald Knuth

Described by this biography as the “Leonard Euler of computer science”, Donald Knuth is a researcher in mathematical techniques for analysis of algorithms, Professor Emeritus of the Art of Computer Programming at Stanford University, creator of the TeX typesetting system and author of the multi-volume work in progress The Art of Computer Programming.

Thanks to @haggismaths, @Gelada and @Tony_Mann for suggestions.