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Michael Atiyah Collected Works, Volume 7: 2002-2013

Michael Atiyah
Oxford University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Fernando Q. Gouvêa
, on

When volumes of collected papers are published while their author is still alive, it is not surprising when supplementary volumes eventually need to be published. I suspect, however, that it is quite uncommon that two supplementary volumes are needed. That is what we have here: Atiyah’s collected papers were originally published in five volumes in 1988, when Sir Michael was about 60 years old. The sixth volume appeared in 2004. And here is the seventh, published as Sir Michael reaches his 85th year. It starts with paper number 174 and ends with 206. Not bad at all!

The material included here is quite varied. Most of the more technical papers are “on the frontier between mathematics and physics,” where Atiyah’s work has made a significant mark. There are also several survey papers, ranging from an autobiographical essay written for the first Abel Prize volume to accounts of mathematics as “art and science.” Atiyah has had a significant institutional role and that is reflected here as well, for example with a piece written for the opening of the Andrew Wiles Building at the Oxford Mathematical Institute. There are also, inevitably, a couple of essays in memory of other mathematicians.

Many of the papers are reproduced photographically, with the usual results: readability depends directly on the match or mismatch between the format of the original and of this book. Articles published in larger-format journals, such as PLOS One or the Notices of the American Mathematical Society, come out very hard to read, especially when the original font was a light sans-serif.

Those whose research is in the kind of mathematical physics Atiyah has worked on don’t need to be told that this volume is important for them, but I would argue that it will also be of great interest to historians. Atiyah is one of the most significant figures in the mathematics of the late twentieth century, as witnessed by his Abel Prize in 2004. Anyone interested in the period will find valuable source material in the survey essays in this volume.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME. 

174. (with Paul Sutcliffe) Skyrmions, Instantons, Mass and Curvature, Physics Letters B (605) pp.106-114 (2005)
175. (with G.B. Segal) Twisted K-theory & Cohomology in Inspired by S.S. Chern: A Memorial Volume in Honor of a Great Mathematician vol: 11, Publisher: World Scientific Pub. Col. Ltd.(2007)
176. (with R. Dijkgraaf & N. Hitchin) Geometry and Physics. Philos. Trans. R. Soc. London, Ser A Math. Phys. Eng. Sci. 368, no. 1914, pp.913-926. (2010)
177. (with Gregory W. Moore) A Shifted View of Fundamental Physics in Singer 85, Journal of Differential Geometry, Survey in Differential Geometry Vol. 15 (2011)
178. (with Nicholas Manton & Bernd Schroers) Geometric Models of Matter , Proc. of Roy.Soc.A. (to appear)
179. (with Claude LeBrun) Curvature, Cones and Characteristic Numbers, Math. Proc. Camb. Phil. Soc. Vol. 155, Issue 01, 13-37.
180. (with S. Zeki, O.J. Hulme, B. Roulston) The Encoding of Temporally Irregular and Regular Visual Patterns in the Human Brain. PLoS ONE 3(5): e2180 (2008)
181. The impact of Thom's cobordism theory. Bulletin of the American Mathematical Society, Volume 41, Number 3, pp.337-340 (2004)
182. Einstein and geometry. The legacy of Albert Einstein, 15-23, World Sci. Publ. Hackensack, NJ, pp.83-03(53-03), (2007)
183. Riemann's Inuence in Geometry, Analysis and Number Theory, Conferencies FME (Fac- ultat de Mathematiques i Estadistica, Universitat Politecnica de Catalunya), Vol. 15, 2008
184. Duality in Mathematics and Physics, Conferencies FME, Centre de Recerca Matematica (CRM), Institut de Matematica de la Universitat de Barcelona (IMUB), Vol. 15 2008
185. Some personal reminiscences, Oxford Figures: Eight Centuries of the Mathematical Sciences (editors: J. Fauvel, R. Flood and R.J. Wilson), pp. 325-334, OUP (2013)
186. Mathematics : Art and Science, Bulletin of the American Mathematical Society, Vol.43, pp.87-88 (2005)
187. Geometry and Physics of the 20th Century. In : KOUNEIHER Joseph, FLAMENT Do- minique, NABONNAND Philippe, dir., et al. Gomtrie au XXe sicle, 1930-2000. Histoire et horizons. Paris : Hermann, 2005. p. 4-9.
188. The art of mathematics. Notices Amer. Math. Soc. 57, no.1, p.8 (2010)
189. Mind, matter and mathematics, Berlin-Brandenberg Academy of Sciences, Berichte un Abhandlungen, 14: pp.151-161 (2008)
190. Introduction. Genie individuel ou environnement culturel, La Mathematique les lieux et le temps, Vol.1 p1-10, (2009) (English version)
191. The Athens Dialogues: Science & Ethics, The Spirit of Mathematics, (unpublished) (2011)
192. The Elements, Festival Milanesiana Lecture, July 2008
193. Lessons from the Scottish Enlightenment, Biennial Lecture of the Faculty of Actuaries, British Actuarial Journal & Institute and Faculty of Actuaries, Vol. 16, Part 1, pp.1-14 (2011)
194. Eighty Years On. A Community of Scholars: Impressions of the Institute for Advanced Study, Institute for Advanced Study, 2011
195. Science and the Military, Science and Technology Ethics edited by Raymond Spier, Routledge London, pp.207-219 (2002)
196. Science, Society and Side Effects, Science & Public Affairs, British Science Association, pp.22-23 (2002)
197. Benjamin Franklin and the Edinburgh Enlightenment, Proc. American Philosophical Society, 150 (4), pp.591-606 (December 2006)
198. Advice to a young mathematician in The Princeton Companion To Mathematics (T. Gowers, J. Barrow-Green, I. Leader (ed)) pp.1000-1010 (2006)
199. Raoul Bott, Biographical Memoirs of Fellows of the Royal Society, Vol.53, pp.63-76 (2007)
200. Jo Rotblat - Man with a Cause in Joseph Rotblat: Visionary for Peace, Wiley VCH, p.99-101 (May 2007)
201. Working with Raoul Bott: from geometry to physics. A celebration of the mathematical legacy of Raoul Bott, pp.51-61, CRM Proceedings Lecture Notes, 50, American Mathematical Society, Providence, RI (2010)
202. Autobiography in The Abel Prize 2003-2007, Springer (2010)
203. Mathematical work of Nigel Hitchin. The many facets of geometry, pp.11-16, Oxford University Press (2010)
204. Book reviews on Bourbaki: A Secret Society of Mathematicians and The Artist and the Mathematician, Notices of the American Mathematical Society, Vol.54, No.9 (2007)
205. Book Review, Thoughts of a Mathematician, Brain, Volume 131, Number 4 pp.1156-1160 Oxford University Press, (2008)