I read a few articles about Grothendieck when he died, but I still learned a lot from this one. Those articles usually skipped over his early years as some ver

I read a few articles about Grothendieck when he died, but I still learned a lot from this one. Those articles usually skipped over his early years as some version of anarchy. This one better fills in those gaps. For example, I didn't realize how haphazard Grothendieck's early professional progress was, or that it depended on an interview with a French education official who recognized unorthodox talent: > “Instead of a meeting of twenty minutes, he went on for two hours explaining to me how he had reconstructed, ‘with the tools available’, theories that had taken decades to construct. He showed an extraordinary sagacity.” It reminds me of Ramanujan, another exceptionally gifted and devoted mathematician who acquired most of his education on his own, and was very nearly lost to history but for the efforts of a few well-connected officials who could see his potential. Conversely, what a bummer it is to think of similar talents who didn't get so lucky. It also gets at just how much the culture of math education matters to math students, even ones like Grothendieck: > [Grothendieck] felt free to ask questions, but also found himself “struggling to learn things that those around him seemed to grasp instantly […] like they had known them from the cradle”. The contrast lead Grothendieck to eventually leave Paris, in October of 1949 on the advice of Cartan and Weil who recommended he instead travel to Nancy to work with Schwartz and Dieudonné on functional analysis. And this was a guy whose internal mathematical drive was strong enough to independently discover measure theory as a teenager! Then there are all the other "failures" absent from a short biographical blurb: he finished his PhD "with few prospects for employment after his graduation in 1953", then "planned to write a book on topological vector spaces, but it never materialized", spent a year failing to solve the "approximation problem", despaired that the field of his thesis was "dead", pivoted away from analysis, rest is history, etc.