Mathematician and author
Director, International Centre for Mathematical Sciences, Edinburgh
Sir Edmund Whittaker Professor of Mathematical Sciences, Maxwell Institute Graduate School
Faculty Profile at the University of Edinburgh
I am a mathematician working primarily on arithmetic geometry, the study of spaces built out of finitely-generated systems of numbers. My main contribution to mathematics is the discovery of the non-abelian method of Chabauty, a theoretical framework for applying ideas of topology, especially homotopy theory, to the algorithmic resolution of Diophantine equations. I am also interested in mathematical physics, the mathematical structure of matter and spacetime in general, and topological quantum field theory in particular.
I have a keen interest in public engagement. I have given numerous presentations since 2010 at schools, teacher training workshops, and corporate training programmes, as well as 'talk concerts' on a wide range of topics in mathematics and its interface with other domains of inquiry, especially physics and economics. If you are interested in having me at such an event, do not hesitate to contact me. I have published nine books so far written for the general public. My interest in engagement is an important component of the way I've put together this site. I'm trying to make the material accessible and friendly to any curious person, even while providing standard information that might be useful for my colleagues in academia. I hope the style is not off-putting to the latter. However, I haven't anything like the energy and creativity that some of the serious communicators of science are able to put into their website. As a result, I fear that my modest effort here will look silly both to colleagues and to the general public.
I work at the International Centre for Mathematical Sciences, a gathering place for mathematical scientists from all over the world, located in the beautiful city of Edinburgh. The city is surrounded by nature, as rugged as can be in a major city, even while it's steeped in history, including intellectual history. It's a real privilege to trace the footsteps of inspiring figures like David Hume, Adam Smith, Mary Somerville, James Clerk Maxwell, and Michael Atiyah on a daily basis. I am also a distinguished professor at the Korea Institute for Advanced Study in the city of Seoul, itself a beautiful place in some similar and some different ways.
My main preoccupation at the moment is a new project of the ICMS with the name Mathematics for Humanity. It's main goal is to support mathematical activities around the world with potential for direct impact on the betterment of the human condition. A subsidiary goal is to provide a unifying umbrella for many things of this nature that mathematicians are already doing. By providing this unifying framework, I hope the value of such activity is better recognised and that the practioner can enjoy a greater sense of mission. Please look at the webpage linked above and submit proposals for activities. I hope especially to attract new ideas from young mathematicians.
The ICMS hosts regular public lectures including a series in honour of the Scottish scientist Mary Somerville. In the next instalment, 'The Poet and the Physicist', Rowena Kennedy-Epstein and I will try to come to terms with a difficult biography of the mathematical physicist Josiah Willard Gibbs (1839-1903) written by the poet and activist Muriel Rukeyser (1913-1980). We wish to understand the universalist vision of the world that led the poet to work with supreme dedication and passion on a subject in which she had no formal training.
I urge you to register and attend, in person or via zoom.
Edinburgh Cityscape from the film The Illusionist (2010)
Brief Professional Biography
I grew up in Seoul, Korea, studied mathematics at Seoul National University, then received my Ph.D. in Mathematics at Yale University under the direction of Igor Frenkel, Serge Lang, and Barry Mazur (Harvard). I moved on to faculty positions at MIT, Columbia University, the University of Arizona, Purdue University, the Korea Institute for Advanced Study, University College London, Pohang University of Science and Technology, Ewha Womans University, and the University of Oxford, where I was the head of the number theory research group. Most recently before moving to Edinburgh, I was Christopher Zeeman Professor of Algebra, Geometry, and Public Understanding of Mathematics at the University of Warwick.
It is perhaps not so well known that a mathematician's life involves a good deal of travel. In particular, I have held visiting professorships at numerous institutions including the University of Paris, University of Illinois, University of Kyoto, Seoul National University, ICTS Bangalore, and the University of Toronto.
What is Mathematics?
The part of physics where experiments are cheap. (V.I. Arnold)
It appears that mathematics as we know it arises from the nature of our brains and the embodied experience. (G. Lakoff and R. Nunez)
The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical. (D. Gale and L. Shapley)
If all mathematics disappeared today, physics would be set back exactly one week. (R.P. Feynman)
To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. (R.P. Feynman)
Its Applications (M. de Unamuno)