This biographical sketch is well-written, concise, and complete (or at least it appears to be). It includes many quotes and photos that I hadn’t seen before.<p>But I can imagine that some readers will be left wondering what was so remarkable about this guy’s work. Unfortunately, it’s hard to explain without some exposure to pure mathematics.<p>David Mumford, who pops up in this article, has a lengthy blog post[1] on this exact problem, stemming from his experience writing Grothendieck’s obituary for Nature. It’s an interesting read if you have some math background.<p>In any case, I think the New York Times obituary by Edward Frenkel[2] does a nice job of giving a taste of his work to a lay audience (by tackling the problem of defining Grothendieck’s schemes, just like Mumford did).<p>[1] <a href="http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html" rel="nofollow">http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie...</a><p>[2] <a href="https://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-grothendieck-a-mathematical-visionary.html" rel="nofollow">https://www.nytimes.com/2014/11/25/science/the-lives-of-alex...</a>
A few months ago, I stumbled upon an antique store in Paris where the owner had thousands of notes taken from Grothendieck's house after he died. Apparently he was in charge of appraising them. Which is pretty stunning since Grothendieck didn't publish anything for the last few decades of his life, so it's quite possible there's new math there.<p>Anyways the guy described how Grothendieck's house didn't have a roof and was pretty decrepit. Which made me pretty sad. One of the greatest mathematicians of the 20th century dying alone in a house with no roof. Part of me wonders if maybe, had he gotten proper mental health care, Grothendieck could have enjoyed a longer, more healthy career. Or career aside, could he have just had a better life? In the mathematical community it feels like there's a bit of an acceptance of idiosyncrasies bordering on potential mental health issues. Well I say acceptance but really it's bordering on willful ignorance. How many advisors give their doctoral students advice on mental health? How many advisors themselves received training on mental health? It's worth analyzing.
Quick point: His parents were Anarchists - in the workers'-movement, anti-Capitalist, revolutionary sense, Groethendieck wasn't. Or rather, his activities did not involve Anarchist organizing/politics.<p>Also, in the summary, where it says "discovered a proof of the Lebesgue measure" - that's obviously nonsensical, he (re-)developed the Lebesgue measure himself, without being aware of Lebesgue's work. Or so it says; I don't know whether he actually focused on non-Riemann-measurable sets etc.
You seem to have put quite an extensive amount of biographical research into this. I have never seen these photos in this high quality on the internet before.<p>As a maths person and a bit of a Grothendieck fan, thanks!
I read a few articles about Grothendieck when he died, but I still learned a lot from this one.<p>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:<p>> “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.”<p>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.<p>It also gets at just how much the culture of math education matters to math students, even ones like Grothendieck:<p>> [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.<p>And this was a guy whose internal mathematical drive was strong enough to independently discover measure theory as a teenager!<p>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.
An interesting, and sad story: that such a beautiful mind ended up with paranoia. It seems to be a real danger that many geniuses run, maybe in part (pardon the speculation) because they tend to work too hard: "Grothendieck was working on the foundations of algebraic geometry seven days a week, twelve hours a day, for ten years". That has to take a toll.
I recently enjoyed listening to this interview with someone who knew Grothendieck. It takes a while to get going, but some of the stories are quite gripping.<p><a href="https://youtu.be/L--9bJApz_A" rel="nofollow">https://youtu.be/L--9bJApz_A</a>