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I have tried to expand a bit the text at the beginning of the category:people entry Alexander Grothendieck, mention more of what his work was about, add more hyperlinks. It could still be much improved, but right now it reads as follows:
The french mathematician Alexandre Grothendieck, (in English usually Alexander Grothendieck), has created a work whose influence has shown him to be the greatest pure mathematician of the 20th century; and his ideas continue to be developed in this century.
Initially working on topological vector spaces and analysis, Grothendieck then made revolutionary advances in algebraic geometry by developing sheaf and topos theory and abelian sheaf cohomology and formulating algebraic geometry in these terms (locally ringed spaces, schemes). Later topos theory further developed independently and today serves as the foundation also for other kinds of geometry. Notably its homotopy theoretic refinement to higher topos theory serves as the foundation for modern derived algebraic geometry.
Grothendieck’s work is documented in texts known as EGA (with Dieudonné), an early account FGA, and the many volume account SGA of the seminars at l’IHÉS, Bures-sur-Yvette, where he was based at the time. (See the wikipedia article for some indication of the story from there until the early 1980s.)
By the way, in view of the recent objection to referring to people as “famous” in category:people entries: the lead-in sentence here is not due to me, it has been this way all along. One might feel that it should be rephrased, but I leave that to those who feel strongly about it.
I for one feel it should be rephrased. Surely “greatest pure mathematician of the 20th century” is a matter of debate. (This obsession with linearly ordering intelligence, creativity, etc. When will people ever learn that intelligences are not linearly ordered, and maybe not even partially ordered?) Also, I would capitalize French (the lower case makes me think it was written by a Francophone).
How about this:
The French mathematician Alexandre Grothendieck, (in English usually Alexander Grothendieck), has created a very influential body of work foundational for (algebraic) geometry but also for modern mathematics more generally. He is widely regarded as a singularly important figure of 20th century mathematics and his ideas continue to be flourishing in the 21st century.
Great!
@Todd: of course, although I agree about linearly ordering people which is very silly (and annoying), he could be the top element in a poset which was not linearly ordered. :-)
(In other words, it is thinking that the order makes sense that is the bother not the fact that it is linear.)
Initially working on topological vector spaces and analysis,
Not only working – his work on the topic of tensor products of topological vector spaces is the most important work on that topic.
By the way, Popescu’s 1973 book calls Yoneda lemma Yoneda-Grothendieck lemma. Anybody knows a bit on this part of the history ?
Could be… although the case of Erdős (as just one example) makes me think that the debate is hopelessly apples-to-oranges, as well as invidious and basically fruitless. Agree with your second sentence I think.
This on tvs is from the previous version of the entry the way it used to be all along. Please split it off as a paragraph and expand.
Thanks for the pointer to that story by Lawvere. I had seen that before, but forgotten about it. Have added it now here.
Also I didn’t know the story about the Yonda lemma originating at Gare du Nord. That’s a neat bit of information. Hopefully somebody finds the time to chase down that catlist post!
(Finally regarding the comment on “singularly important”. I don’t get what you mean. I checked to see if I am making some stupid mistake, but it seems I didn’t. For a change.)
Not sure what compromise you mean. Notice that it’s not just me who does the authorial work, it’s a bunch of people and on this entry I just made a minor addition and an attempt at rephrasing one sentence. On texts that I edit alone, I have a lot less discussion overhead! :-)
Thanks for the date of the catlist discussion. If nobody else adds it to the entry, maybe I’ll do it some other day.
I will add the link (tomorrow). Meanwhile, it is here: http://www.mta.ca/~cat-dist/catlist/1999/yoneda.
I've rephrased to imply that ‘Alexander’ is the preferred spelling.
Wikipedia (English) describes Grothendieck as ‘stateless’ (without citation), so I wonder if it would be better to describe him as ‘francophone’ rather than ‘French’. But I don't know what's behind that (did he renounce his French citizenship? did he never have any citizenship? or what?)
What about ’European’? He had parents from two European countries, and lived and worked (and probably still lives) in France, which is a third. ‘Stateless’ is a term that went out of current language use sometime in the 1960s when most of the people who had been refugees after the second world war, began to be absorbed into their countries of adoption. (Its use may need to be reborn in the current political climate!) I believe Alexander never became a French citizen, but I may be wrong.
There were two good articles in the Notices AMS. in 2004 I have added links to them.
I have incorporated the ’European’ and made minor changes.
According to Cartier (p. 9), Grothendieck obtained French citizenship in the 1980s.
Have added this quote (and am adding it to the top of K-theory):
The way I first visualized a K-group was as a group of “classes of objects” of an abelian (or more generally, additive) category, such as coherent sheaves on an algebraic variety, or vector bundles, etc. I would presumably have called this group $C(X)$ ($X$ being a variety or any other kind of “space”), $C$ the initial letter of ’class’, but my past in functional analysis may have prevented this, as $C(X)$ designates also the space of continuous functions on $X$ (when $X$ is a topological space). Thus, I reverted to $K$ instead of $C$, since my mother tongue is German, Class = Klasse (in German), and the sounds corresponding to $C$ and $K$ are the same.
According to Courtney’s notes a source for this quote is:
but I haven’t actually seen that text, or any other authorative source for the quote. If anyone knows a better citation, let’s add it.
In that editorial (DOI 10.1007/BF00533984, accessable for me via Sci-Hub), Bak introduces that quote with the following sentence
Concerning his group and the choice of the letter K, Grothendieck says in his letter of 9 February 1985 to Bruce Magurn:
No further information provided.
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