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.
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.
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.
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).
And for the more nonlay audience, Grothendieck's real pull is the persistence with which he applied category theoretic techniques successfully. Usually one would qualify this to algebraic geometry, but I think his approach can be followed in any of the many extensive fields in mathematics.
I would contrast this to what often happens in the physics community, albeit not in a condescending manner, where techniques diverge rather than converge. In fact, I would guess this is the role that Einstein played a hundred years ago: to encourage sensible connections between researchers' work.
rough translation (it's kinda tricky to preserve the tone. Question marks are words I'm not sure the translation works):
> Riemann-Roch theorem: the last trend(?): the diagram(?) <formula> is commutative!
To give this statement over f:x->y an approximative sense I had try the patience of the listeners for almost 2 hours. Black-on-white (in Springer's Lecture Notes) its about 400, 500 pages. A fitting example how our drive to knowledge and discovery more and more realizes itself in a far-from-life logical delirium, while the life itself is ruined in a thousand ways - and is threatened by total destruction. High time to change our path!
I wonder if he means what I think he means, which is that a concept that is for some field all-encompassing in your mind takes 400 pages to write down in a way that translates your ideas. University group theory is like that, when the real objective may just be to show that you can't circle the square.
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.
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.
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).
[1] http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie...
[2] https://www.nytimes.com/2014/11/25/science/the-lives-of-alex...