hello, Alexander Grothendieck was a member of Bourbaki for years. From 1957 to 1962 at the least. reference : http://en.wikipedia.org/wiki/Fondements_de_la_G%C3%A9ometrie_Alg%C3%A9brique and here : http://www.numdam.org/numdam-bin/search?h=aur&aur=Grothendieck,+Alexander&fo... for example this document : http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_1963__17_/PMIHES_1963__17__5... which is from 1963, from what I can see this is the purest Bourbaki style of mathematics. ... A.G. is a great master of higher mathematics. 2 things could happen, in 200 years this will look like trivial or something else will come out in a complete different direction ? What will prevail is the principle of l'économie de pensée, i.e. the shortest and simplest way to explain things. Maybe that guy was 400 years ahead of his time ? Well, this was 50 years ago and as far as I can tell, there is no simplification that came out. I had a personal friend (Pierre Bouchard) in Montréal, recently deceased, he was a specialist of Grothendieck's work, we (some friends and I) asked him many times, how come this is interesting ?, tell us! please!, He could hardly give any example. We all stumbled on the first books of Bourbaki (he had them all). That example of the definition of the empty set was a subject of discussion, lots of it, nothing came out of all this. Maybe as they say in the 'le monde' article that the subconscious of mathematicians is haunted by that guy and what he did, I am not certain of this. This is my personal opinion. Best regards, Simon Plouffe