Alain Connes

Alain Connes (born 1 April 1947) is a French mathematician.

Alain Connes in 2012

Quotes

• There are two fundamental sources of ‘bare’ facts for the mathematician. These are, on the one hand the physical world which is the source of geometry, and on the other hand the arithmetic of numbers which is the source of number theory. Any theory concerning either of these subjects can be tested by performing experiments either in the physical world or with numbers. That is, there are some real things out there to which we can confront our understanding.
  • Connes, Alain (2000). "Noncommutative Geometry Year 2000". Visions in Mathematics. pp. 481–559. doi:10.1007/978-3-0346-0425-3_3. ISBN 978-3-0346-0424-6.  arXiv preprint

• ... string theory has uncovered beautiful relations between physics and different parts of mathematics, mostly differential geometry, enumerative algebraic geometry and complex analysis. In fact string theory started like this. At the very beginning when Veneziano and others were starting string theory motivated by the dual resonance model for strong interactions they found solutions to the duality equations for the scattering amplitudes in terms of Mandelstam parameters and these were nice mathematical functions like generalized beta functions which are very natural in terms of complex analysis. It was then realized, by Susskind and others, that these models could be understood geometrically from the propagation of strings. It is a very powerful idea to “test” a given complex space using the space of complex curves inside or of maps from Riemann surfaces to that target space. And physicists could use all the arsenal of conformal field theory which is quite powerful. This generated a very interesting group of people that do a kind of “physics motivated” mathematics which rejuvenated some parts of complex geometry. They adopt a rather free attitude towards mathematics, which is original and productive and had a very positive influence. It started as mathematics and had a very positive impact on mathematics up to now.
  • Interview with Alain Connes. conducted by G. B. Khosrovshahi & M. Khalkhli at 2005 Workshop on Noncommutative Geometry. IPM (Institute for Research in Theoretical Physics and Mathematics), Teheran, Iran (ipm.ac.ir). (quote from p. 6)

• I am not really motivated by confidence. Nor by curiosity. What I would say is, it’s more anxiety. I spend much more time being anxious than being confident or being curious. My mind sort of constantly worries. It’s not confidence — okay, I have of course some self-confidence, but it’s not a kind of overreaching confidence, by no means. I knew only one person who had overreaching confidence, that was Michael Atiyah. I really liked him a lot. He could jump to other topics. But I am not like him. I am much more motivated by the fact that when I do not understand something, it makes me suffer. It puts me into a state of misery. I am feeling bad until I understand. That’s exactly the motivating force.
  • quoted in: Jackson, Allyn (2021). Interview with Alain Connes. Celebratio Mathematica.

Quotes about Alain Connes

• Connes is one of the revolutionaries of the subject (Riemann hypothesis), a benign Robespierre of mathematics to Bombieri's Louis XVI.
  • Marcus du Sautoy (31 May 2012). The Music of the Primes: Why an unsolved problem in mathematics matters (Text Only). HarperCollins Publishers. pp. 3. ISBN 978-0-00-737587-5.