A mad day's work: from Grothendieck to Connes and Kontsevich. The evolution of concepts of space and symmetry (Q2750960)

This very dense and well-documented article focusses (somewhat at variance with its title) on Grothendieck's contribution to the mathematical conceptualization of space and symmetry, which came from his purely mathematical work and constituted -- according to Cartier -- an ``unexpected marriage'' of mathematics and physics. Grothendieck extended the notion of a point using sheaf theory, where he and Deligne ``spoke interchangeably of point and fiber functor'' (400). Further contributions were in noncommutative geometry and on the question of internal symmetries, which is acute in particle physics (403). Cartier finally discusses Grothendieck's only partly developed theory of ``motives'', which would in particular unify Galois theory and topology. NEWLINENEWLINENEWLINEThe paper begins with a brief biography of Alexander Grothendieck (born 1928 in Germany and still alive), who had a turbulent political life as well, even after he survived as a Jew in occupied France. The article was written on the occasion of the 40th anniversary of the French mathematical research institute IHES, at which Grothendieck spent the last 12 years of his life as a mathematician which found an abrupt end in 1970.