# Talk:Alexander Grothendieck

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## Untitled

(See old discussion atTalk:Alexander_Grothendieck/Major_topics)

Well, let's write now all these articles about his (and other people's) work :)

## Alexandre versus Alexander

Does he spell his name "Alexandre" instead of "Alexander"? In the letter circulating around the French mathematical community this last month, he signs his name "Alexandre". http://sbseminar.wordpress.com/2010/02/09/grothendiecks-letter/

Yes he writes himself Alexandre in all his correspondence that I have seen --helohe (talk) 13:05, 30 December 2011 (UTC)
On the other hand his published mathematical works are fairly equally divided between just the initial A., and the spelling "Alexander," with many fewer "Alexandre." Colin McLarty (talk) 02:13, 14 November 2014 (UTC)

## Thanks

Thank you, Charles Matthews for your great article and comments. Still, I think claiming that Grothendieck's work is of axiomatic kind is precise only when referring to certain period. There is nothing about axioms is Esquisse. It's normal that style changes with time and I think it would be right if you corected this.

You wrote: The style of the mathematics is very distant from Kronecker's, though. It is axiomatic, and claims descent from David Hilbert's approach; as interpreted by Nicolas Bourbaki. Its influence spilled over...

I can't correct this because there is some error with this sentence. What means 'the mathematics'? Did you mean 'his mathematics of that period' which is OK for me or 'his mathematics' (which I consider as factual error) --Ilya 18:13, 15 Dec 2003 (UTC)

It's a fair comment: it is what Jean Dieudonné always said about him, but I know that it isn't really the whole story. So I have made some changes.

Charles Matthews 19:11, 15 Dec 2003 (UTC)

In what sense is Grothendieck's work "scarcely credible"? This needs some elaboration and appears to be personal opinion. - Gauge 04:44, 12 Mar 2005 (UTC)

The achievement is scarcely credible, if you simply look at how much mathematics came out of IHES in the period 1960-1967, say. The SGA series is a vast enterprise. Charles Matthews 08:04, 12 Mar 2005 (UTC)

## 20th century is over ...

Permanently, as far as I know. So changing 'was' to 'is' breaks the line of thought. Charles Matthews 08:31, 28 January 2006 (UTC)

## Incorrect edit about death by User:Orz

Orz, in his last edit, deleted some content about Grothendieck's disappareance and added a comment saying he is said to have died in 1993. I think we would definitely require a citation for this kind of comment. Grothendieck legally transferred rights over his papers to Malgoire in 1995 and other mathematicians say they spoke to him in the mid 1990s (see AMS Notices articles cited). --C S (Talk) 10:17, 2 April 2006 (UTC)

morover, a famous mathematician who is very often visiting ihes (let me not specify his name), told myself that "i have talked to grothendieck middle of 2004" and he added "he is enjoying very good health" but no more detail. ma. 26may2006.

## 87 letter

I stubled upon an interesting letter [1], which charts some of grothendieck retreat from mathematics. Not sure if its worth including. --Salix alba (talk) 18:46, 2 August 2006 (UTC)

Les Annettes July 8, 1987.

Dear Piotr Blass,

Thanks for your letter and MS. I am not going even to glance through the manuscript, as I have completely given up mathematics and mathematical involvements. If you complete your book, you may mention on the cover that it is based on my EGA IV (sic) notes, but you are to be the author and find your own title.

I have a foreboding that we'll contact again before very long, but in relation to more inspiring tasks and vistas than mathematical ones.

With my very best wishes

Alexander Grothendieck

## Grothendieck's parentage

jinfo [2] gives the following information, from which it is clear that his father was Jewish and that the most reliable source, Grothendieck's friend Pierre Cartier, says that his mother was Jewish too. Note that even if his mother was not Jewish, he should be placed in the category Jewish mathematicians, as this includes people of Jewish descent.

According to a recent memoir in the Bulletin of the American Mathematical Society (Vol. 38, No. 4, 2001, pp. 389-408: http://modular.fas.harvard.edu/sga/from_grothendieck.pdf) written by the prominent mathematician Pierre Cartier, Grothendieck's father was a Russian Jew surnamed Shapiro and his mother a German Jewish women named Hanka Grothendieck. Cartier, a close acquaintance of Grothendieck, states: "what I know of his life comes from Grothendieck himself." Thomas Drucker's earlier account in Notable Twentieth-Century Scientists, edited by Emily McMurray (Gale Research, Detroit, 1995, pp. 821-823) states that Grothendieck's father was a Russian Jew named Morris Shapiro and that the name "Grothendieck" was not that of his mother, but rather that of a governess who cared for him in Germany between 1929 and 1939. The source of this account is the mathematician and Grothendieck biographer Colin McLarty, who has described it as "one version that Grothendieck has given." The most recent account, by Allyn Jackson in Notices of the American Mathematical Society (Vol. 51, No. 9, 2004, pp. 1039-1040: http://www.ams.org/notices/200409/fea-grothendieck-part1.pdf), states that Grothendieck's father was a Russian Jew whose original name may have been Alexander Shapiro, but who later assumed the name Alexander (Sascha) Tanaroff, and that his mother was Johanna (Hanka) Grothendieck, a German Lutheran from Hamburg. This information is attributed to another Grothendieck biographer, Winfried Scharlau of the Universität Münster. As Jackson notes: "many of the details about Grothendieck's family background and early life are sketchy or unknown." According to all three accounts, however, Grothendieck's father was Jewish, and was deported and murdered at Auschwitz, and Grothendieck himself was sheltered (along with several thousand other Jews) in the French Protestant village of Le Chambon-sur-Lignon in southern France.

--Brownlee 16:17, 13 August 2006 (UTC)

The most authoritative resource for information on Grothendieck's life is the Grothendieck Circle at http://www.grothendieckcircle.org/. This contains primary sources from Grothendieck's parents and also points out the fact that Cartier's article has biographical inaccuracies. All sources except for Cartier's article identify Hanka Grothendieck as Lutheran. Allyn Jackson's article uses her autobiography Eine Frau as a source. In any case, the previous revert destroyed a lot of grammatical edits which should have stayed anyway. 128.148.123.6 10:19, 14 August 2006 (UTC)
The most authoritative resource for information on Grothendieck's ancestry is Cartier's article, which is why jinfo.org accepts it. If any grammatical erors remain, please fix them.--Newport 19:48, 14 August 2006 (UTC)
This is wrong. See post and website above. It is absurd to state that jinfo.org is a more authoritative source on Grothendieck's ancestry than the Grothendieck Circle. Also, do not use reverts indiscriminately, unless you intend to fix the grammar yourself. 128.148.123.4 08:10, 15 August 2006 (UTC)

The point is that Jinfo regards Cartier as the most reliable source. It violates WP:NOR to assert that the Grothendieck Circle is more reliable without providing a source that says so.--Newport 19:48, 15 August 2006 (UTC)

There is no reason to favor the claims of jinfo over the Grothendieck Circle. jinfo is a less reliable source than that of Grothendieck Circle for it provides no contact information other than email nor the names of any individual who operates the webpage. It is impossible to gauge the credentials of jinfo for this reason. Quoting WP:V: Self-published sources (online and paper)
Anyone can create a website or pay to have a book published, and then claim to be an expert in a certain field. For that reason, self-published books, personal websites, and blogs are largely not acceptable as sources. Exceptions may be when a well-known, professional researcher in a relevant field, or a well-known professional journalist has produced self-published material. In some cases, these may be acceptable as sources, so long as their work has been previously published by credible, third-party news organizations or publications. However, exercise caution: if the information on a professional researcher's blog is really worth reporting, someone else is likely to have done so.
Jinfo does not list any professional researcher nor journalist. If you feel that Jinfo does not fall under the given criterion for being a dubious source, please explain why. 128.148.123.43 22:19, 15 August 2006 (UTC)
128 is totally right. Per WP:RS jinfo is a self-published website which lists, comparatively, very scarce sources for its claim. It cannot be used as a source any more than jew watch can be. Think about it, Jew Watch has a clear anti-jewish bias and concurrently Jinfo has a clear pro-jewish bias. Any site of the like would.
Furthermore, no wikipedia user can make up their own definition for who counts as a "German Jew" or "Jewish mathematician." You can't say "Oh, a German Jew is anybody who is Jewish by religion, culture, self-association, or who has anything up to a Jewish great-grandparent." It's not our place to define how people identify or are identified. Simply because Grothendieck had a Jewish father doesn't automatically define him as a "Jewish mathematician" anymore than Marconi would be an Irish inventer because his mother was Irish. 72.144.60.231 04:35, 16 August 2006 (UTC)
I checked the above mentioned texts and none of them convinced me. I propose mentioning in the article that his mother was Jewish according to some, and Lutherian according to others (as does jinfo, by the way). With cited sources, of course. Hopefully one day a more reliable source (or maybe a future biographer) will settle the point. Lenthe 06:58, 16 August 2006 (UTC)

Note 2 on Grothendieck's page still marks the origin of his mother as "uncertain". In view of the new book by Winfried Scharlau, this needs to be removed. The book contains detailed information on Hanka as well as on his family. Her ancestery is not uncertain by any means. And there are no Jewish parents.

http://www.scharlau-online.de/DOKS/Anarchist.pdf —Preceding unsigned comment added by 130.149.12.163 (talk) 11:07, 28 November 2007 (UTC)

Just in case somebody has not noticed: the user Newport was banned a long time ago for his infractions against Wikipedia rules. Feketekave (talk) 14:26, 16 June 2008 (UTC)

Jinfo lists several sources and concludes that Grothendieck's friend is the most reliable. Jinfo thus asserts that Grothendieck is Jewish. It is original research to assert that another source is more reliable than Grothendieck's friend without a source to verify this.--Brownlee 14:59, 16 August 2006 (UTC)

You appear to have missed the discussion directly above your post. Please check there for details. 128.148.123.7 15:24, 16 August 2006 (UTC)

What Lenthe thinks is original research. Wikipedia should just quote what sources say.--Brownlee 15:29, 16 August 2006 (UTC)

Unfortunately, your revert is not doing that. It seems you are placing too much weight on a source (Jinfo) that is not even considered reliable. 128.148.123.7 15:35, 16 August 2006 (UTC)

Most editors who have looked at Jinfo consider it reliable. In any case, for Grothendieck it quotes three sources, so we can rely on those.

Don't forget to sign your name. Sure. Of those three sources, one states that his mother was Jewish, another states that his mother was Lutheran, and the third does not discuss his mother at all. Clearly not enough to make the assertion that his mother was Jewish. 128.148.123.7 15:44, 16 August 2006 (UTC)

The edit by User:128.148.123.7 removing a source is not acceptable. You have to add sources, to give a proper survey of the evidence. Charles Matthews 16:01, 16 August 2006 (UTC)

Sources have been added. The conflicts are mentioned. 128.148.123.7 16:09, 16 August 2006 (UTC)

I haven't yet looked deeply into this, but the German Wikipedia version is interesting, and the Scharlau material it links to. Charles Matthews 16:22, 16 August 2006 (UTC)

## Was he Jewish?

It seems this issue is being forced on this page. I find it distasteful, but we have rules for dealing with contentious matters. It is common ground that his father was a Russian or Ukrainian Jew. Apart from that, what do we have to go on? I have never heard that he was religious in any way.

I suppose the point should be made that he may well have been stateless; the French Wikipedia says so, and I heard this long ago also. We say he is a French mathematician and a German mathematician, even so. Therefore it might be considered that his paternal Jewish background is of at least as important a status. This is something to discuss.

Charles Matthews 15:52, 17 August 2006 (UTC)

Religiousness is nothing to do with being Jewish. Einstein was not religious in any conventional Jewish sense, but was incontestably Jewish. The Wikipedia rule is that if a source says someone is or was Jewish, we are entitled to say so. I am extremely grateful to Mr Matthews for his comments.--Newport 16:12, 17 August 2006 (UTC)
To be correct, the Wikipedia rule says that a Jewish person is a person who has either converted or has a Jewish mother. In any case, the source claiming such facts must be reliable. I would say that it would be appropriate to not list him as a French or German mathematician either. Officially, Grothendieck was stateless except for his early life (The AMS article states this). One could say that he has as much a claim to being Russian through his father as he does being French or German. Certainly Grothendieck himself would have rejected being categorized into any such groups; it is mentioned in Allyn Jackson's article that he preferred jail to recognizing the sovereignty of a national government. His distrust for governments was well-known. 128.148.123.1 16:52, 17 August 2006 (UTC)

Just so everyone here realizes, a person can be referred to as Jewish or half Jewish on Wikipedia only if a reputable source refers to them as that (same thing for anything else, athiest, Irish-American, Welsh, etc.). Regardless of their mother's, father's, whatever's background. You may not list a person with a Jewish mother as "Jewish" unless you have a source that explicitly calls that person "Jewish" themselves and likewise a person with a Jewish father or even paternal grandfather will absolutely be listed as Jewish if a reliable source refers to them that way. Don't bring up "Who is a Jew", because, aside from the fact that you may not mix-and-match definitions to decide who is a what (see the WP:NOR example of deciding who is or is not a plagiarist), the page presents several ways in which a person can be "Jewish", of which Charles Matthews has picked one, which he may not do. This is not up for discussion, negotiation - Wikipedia editors simply can not decide who is Jewish based on their favorite definition of the term (nor may they decide who is, again, Italian-American, etc.). This is the "standard" used for every and any Wikipedia article and it is the standard used for every X-American or X-whatever list. Now, regardless of the background of either his father or mother, the questions here seem to be A. Since JInfo refers to Grodenchick as Jewish, is JInfo a reliable soure? What is their source? Or B. Is there any other source out there that refers to him as Jewish? Mad Jack 17:09, 18 August 2006 (UTC)

he was born to a jewish family(father). so what? it is totally non-sense rule of wikipedia. marhahs 24sep2006.
He was clearly not jewish. It is mentioned in the article of Winfried Scharlau http://www.scharlau-online.de/ that Grothendieck turned to Christian mysticism somewhere later in his life. --helohe (talk) 00:03, 30 December 2011 (UTC)

## FGA

i am going to add to the section "EGA and SGA" something about FGA without which, i think, something serious will be missing in this article. marhahs 24sep2006.

## Living or disappeared?

I don't think people are supposed to be in both the Living People and Disappeared people categories. If someone has really disappeared, we can't be sure if he's still alive. Which is more appropriate?--Runcorn 10:14, 28 December 2006 (UTC)

## Dolbeault-Grothendieck lemma ?

What is the Dolbeault-Grothendieck lemma? DFH 20:20, 26 January 2007 (UTC)

I suspect it is the so-called Grothendieck lemma mentioned [3] in the Springer EoM s.v. differential form, for the Dolbeault complex. Charles Matthews 16:34, 16 June 2007 (UTC)

## Photos

There are several famous photographs of Grothendieck available on the web, but I have not been able to find any information about their copyright status. It would be nice to be able to upload one or more of them for use in this article. File:Grothendieck.jpg was deleted 22/4/2007 under CSD I4 (no copyright information). Geometry guy 16:30, 16 June 2007 (UTC)

I've emailed Leila Schneps about the pictures on www.grothendieckcircle.org. We'll see what she says. Ryan Reich 16:46, 16 June 2007 (UTC)
Thanks! Geometry guy 18:23, 16 June 2007 (UTC)
Say hi to Leila from me. Charles Matthews 19:11, 16 June 2007 (UTC)
Did the same on 7 May, with no reply yet. I hope you shall get a faster response. Stca74 17:24, 17 June 2007 (UTC)
Nothing so far, but it's not yet during the week. Ryan Reich 01:27, 18 June 2007 (UTC)
```Hello,
I have to admit I don't know what the legal status of the photographs
on the Grothendieck circle site are.  I found them in various places,
some were already on the web, others in private photo albums belonging
to friends and family members of the Grothendieck family.  Let me
be clear, I didn't ask for anyone's permission to put them there, for
all I know I behaved illegally, but nobody has protested so far, although
Grothendieck's ex-wife did make a remark that maybe I shouldn't do that,
but she didn't ask me to take them off.  You are welcome to use them
if you wish, under these circumstances.

Best
Leila Schneps
```
I also took a look and found that the 2-part Grothendieck article in the AMS Notices (vol. 51, nos. 9-10) uses some of these photos, attributed to Hirzebruch and Karin Tate (1st part), Michael Artin and Karin Tate (2nd part), and www.grothendieckcircle.org. One could perhaps argue that the AMS believes the website's images to be public domain, but if any of them are copyrighted then that copyright has certainly not expired. I think that, perfectly honestly, we can only claim that the pictures of unknown status are orphaned works, and there isn't a policy on those yet. It's a shame, since the article could use a picture. However, the MacTutor biography page has a standard boilerplate attached to two well-known images of him which states that it believes them to be public domain. As does Leila Scheps and, apparently, the AMS. Although this rationale is given more or less explicitly in Wikipedia:Fair use#Examples of unacceptable use as invalid for fair use claims, aside from our ignorance of the actual copyright holder (or creator) of these images we do satisfy the ten criteria given on that page. Ryan Reich 15:53, 19 June 2007 (UTC)
Before resorting to stretching the fair use policy (and practically inviting reverts, I'm afraid), I would suggest two possibilities: (i) check the Gorthendieck Festschrift (Birkhäuser) for an attribution in the photo in the first volume, and try to get admission from the copyright holder directly or perhaps through Birkhäuser/Springer; or (ii) contact Mike Artin or other identified apparent copyright holders of other photos for permission. Stca74 16:29, 19 June 2007 (UTC)
I looked at the Festschrift, which has a single photo of Grothendieck at the front of Volume 1 (it's a cropped version of this photo which omits the other people). Absolutely no indication of copyright is given; the page simply says "Alexander Grothendieck", and the only mention of any kind of copyright is the usual boilerplate on the copyright page of the book, which doesn't explicitly mention the photograph and simply says that permission must be obtained from the owner in order to reproduce. I will email Birkhauser but I can't say I expect a speedy reply. Ryan Reich 18:44, 19 June 2007 (UTC)
Thanks for looking into this Ryan. I think we have no chance with an image whose copyright status is unknown. The boilerplate at MacTutor is useless because it only states that they believe that most of the images on their entire website are public domain.
So far, we have not found any images which we are sure are in the public domains, so our best hope is fair use (preferably with permission). My understanding is that photographs are the copyright of the photographer unless they explicitly release them into the public domain. The use of the phrase "courtesy of" by the AMS indicates that it does not hold the copyright for these images, and in the cases of the named individuals (Hirzebruch, Tate and Artin), it seems to me that this implies that they hold the copyright. In particular, Hirzebruch almost certainly is the copyright holder for the photograph of Grothendieck at his home. I think this meets the verifiability criterion (an interested party could contact the AMS or Hirzebruch himself). Similarly, if Leila could identify which friend or family member supplied a particular photograph, then we would have copyright information for that.
It seems to me that the only remaining stumbling blook would then be fair use criterion #1 (No free equivalent), as amplified by the unacceptable use #8 (An image of a living person that merely shows what s/he looks like. The rationale is that this is potentially replaceable with a freshly produced free photograph.). We would have to argue that in this case the rationale is invalid, because it would be virtually impossible to obtain a fresh photo of a recluse like Grothendieck. Comments? Geometry guy 16:50, 19 June 2007 (UTC)
PS. Note, even {{Withpermission}}, I think the fair use criteria must still be satisfied. Geometry guy 16:55, 19 June 2007 (UTC)
Under Wikipedia's fair use policy, we are obligated to use non-free material minimally. Therefore, we should use only one picture, since none of the photos on www.grothendieckcircle.org really provide biographical or historical value above that of the sentimental. Since the Festschrift uses without attribution this photo I mentioned above, there's a good chance it's free, and it's a nice picture of him. I will pursue the status of this one's copyright; if we ultimately don't need to claim fair use, all the better.
As for the fair use criteria, I had drafted a point-by-point response to the fair-use criteria in my above post with Leila's letter, but I omitted it since it seemed premature; I mention this only to say that I think we can satisfy the criteria. Essentially, I agree that we satisfy criterion #1 and avoid exclusion #8 by virtue of Grothendieck being dead for photographic purposes. Ryan Reich 18:44, 19 June 2007 (UTC)
I agree entirely. I only mentioned multiple photos to give us as many options as possible for what that one photo should be. The Montreal photo is perhaps the most iconic, so I am glad you are pursuing it. Good luck, or should I say, bon courage! Geometry guy 19:18, 19 June 2007 (UTC)

By chance, I discovered that the Montreal photo was taken by Konrad Jacobs, and so the copyright is held by Oberwolfach. I've uploaded it with a fair use rationale. Geometry guy 17:38, 5 July 2007 (UTC)

Great! I wasn't getting anywhere with Birkhauser; they forwarded my letter and I haven't received any response in more than a week. Ryan Reich 20:14, 5 July 2007 (UTC)
But shouldn't you also link the photo into the article? Ryan Reich 20:44, 5 July 2007 (UTC)
There is no harm in doing that, although I was going to wait until the copyright patrollers had time to check the upload. If you want to add it, the image is Image:Grothendieck.png. Geometry guy 21:12, 5 July 2007 (UTC)

I've done that now: it seems my fair use rationale is sufficiently robust. Lets hope! I guess I should probably remove the experimental persondata page, although I am also tempted to roll it out more widely, since it seems to work quite well. Any comments here? Geometry guy 23:49, 6 July 2007 (UTC)

Just fyi the experimental persondata page is still there: Talk:Alexander_Grothendieck/Persondata. —Msmarmalade (talk) 09:22, 25 October 2014 (UTC)

## Far gone

Is this another case of a brilliant person who produced valuable work and then had a mental breakdown? After such an irreversible brain change, such people are usually no longer able to produce anything of general value.Lestrade (talk) 01:16, 18 February 2008 (UTC)Lestrade

Does this question have a point? Ryan Reich (talk) 01:27, 18 February 2008 (UTC)

Not really. It only concerns a Wikipedia article about an important mathematician whose life interests changed fundamentally and radically. Small potatoes.Lestrade (talk) 01:37, 18 February 2008 (UTC)Lestrade

It's about the subject of the article, but it's not about the article. It's not even about anything that might conceivably go in the article. I mean, everyone who's ever heard of Grothendieck finds him a fascinating, enigmatic character, but the question is, did you mean to suggest some kind of improvement to the article with your question about this? This isn't a newsgroup or message board or comments on a blog or whatnot; if you want to talk about the guy, you can just wander into a random mathematics department. Ryan Reich (talk) 01:44, 18 February 2008 (UTC)

I was wondering if his mental alteration resulted in his inability to produce the kind of work that he had previously produced. Did he experience a qualitative change? Is he the same mathematician that he was previously? Is his mind now so altered that it is impossible for him to think topologically? Is his current long autobiographical writing evidence of a total, absolute, complete change in his mind? Is this similar to Grigory Perelman's situation? Lestrade (talk) 02:16, 18 February 2008 (UTC)Lestrade

Okay, well, let's take this to my talk page. I'm generally happy to BS about Grothendieck, but this is (as I said) not the right forum. Satisfying though it may be to try to understand the mind of this genius, nothing we decide is going to be "encyclopedic" enough for his article. Ryan Reich (talk) 05:24, 18 February 2008 (UTC)

## One of the greatest ever?

Any citations on this? I'm a mathematician and never heard of him, until recently. Looks like the article is written from category theorists' POV, who assume their theory is the most important thing in mathematics, when it clearly isn't.  Grue  04:46, 11 May 2008 (UTC)

Not sure what kind of cite would satisfy you. 2061 citations on MathSciNet? (Hilbert has only 826, and most of Grothendieck's production either wasn't in citable form or is so foundational there's no need to cite.) Fields Medal and Crafoord Prize? Two-part biography in the Notices? I think it's indisputable that Grothendieck was one of the greatest mathematicians ever to work in algebraic geometry, commutative algebra, non-commutative algebra, topology, differential geometry, complex analysis, functional analysis or number theory, not to mention category theory. And then there's mathematical physics, and so on. He didn't just do good work in these fields, he changed how they were done. That you've never heard of him doesn't mean he's not a giant. Gleuschk (talk) 13:21, 11 May 2008 (UTC)
I don't know where you received your title of "mathematician", but it's probably some pretty lousy place (although I suspect my mere saying so will prompt you to make up some well-known name to artificially strengthen your credentials). I am a mathematician (a PDE analyst, to be precise). My research is quite remote from the far-reaching results of Grothendieck. And yet, naturally, I have known of him since my early years in the business. Granted, I'm French, but I was trained in the US. Anyhow. I just can't fathom there would be any (serious) mathematician out there who wouldn't have heard of Grothendieck. Then again, maybe I've been too fortunate to study and work in top places... Have you ever heard of Cauchy? Hilbert? Riemann? J.-P. Serre? P.-L. Lions? Terry Tao? —Preceding unsigned comment added by 84.72.93.5 (talk) 16:50, 15 May 2008 (UTC)
In your critique, you commit the following logical fallacies:
• That because you are a mathematician, you know of and can objectively rate all other mathematicians, or at least the most famous. However, I'm pretty sure you can't do this with "all academics" instead of "all other mathematicians", even though you yourself are a member of academia. You probably couldn't do "all scientists" either, and it would be amazing if you could even do it with people at your particular university. So if generalizing up doesn't work, why should generalizing down? A number theorist probably has no idea who the great PDE researchers are, a combinatorialist is likely in the dark about the leaders in the field of symplectic geometry. Analysis is so big that God (and other analysts) only know who the greats are there. Even if you knew their names, could you say why they were revered? If Terry Tao hadn't proved his theorem with Ben Green, number theorists might know of him only as an unusually prolific analyst.
• That because you are a mathematician, you can understand and evaluate all kinds of math. Therefore, you easily identified the subject of this article as a "category theorist", when in fact, he was not. Would you also agree that John Forbes Nash was a game theorist, that H.S.M. Coxeter was a finite group theorist, and that Serge Lang was a textbook writer? Of course, they all did these things, and their contributions there are central to their legacies as mathematicians...but these are not their categories.
• That since category theory isn't universal in math, it must not be very important at all. Technically, you don't say this, but if it were very important, why would you be denying that a great category theorist is a great mathematician? It's possible you're just being modest about your own field, but I'm guessing from your tone that you don't use much category theory yourself. As in the first point, this disqualifies you from saying whether it is important to anyone else, or indeed, everyone else (I don't know what you do, but then, you don't know how many people who don't do that, do use category theory all the time).
• Is that a touch of asperity in your tone? If you don't like category theorists because of their arrogant self-promoting claims, trying to tear down Grothendieck on a Wikipedia talk page is a petty way of expressing this.
The article is extensively referenced with citations to his work and also to biographical writings, like that two-part Notices article. This is Wikipedia: the point of such an article is to bring together all this data so that people can learn from it. Now, it's virtually impossible for me to comprehend how anyone could fail to appreciate the huge significance of Grothendieck in half a dozen areas of math, but there isn't an article on that phenomenon. You, however, are in luck. Ryan Reich (talk) 16:27, 11 May 2008 (UTC)
The part that says that he is one of the greatest is not cited. It is pure POV. His list of achievements doesn't look all that significant, if you consider that most of them are in some obscure part of mathematics. Half of his "major archievements" don't even have a Wikipedia article. The more I look at it, the more it looks like some sort of fraud, or an instance of extreme fanboyism, exactly what Wikipedia is trying to prevent.  Grue  19:13, 12 May 2008 (UTC)
Did you actually read the Allyn Jackson article? It says on page 1211 (the conclusion): "The stature of Grothendieck can be compared to that of, for example, Albert Einstein." Albert Einstein is among the greatest physicists by general acclaim (a claim acknowledged in the introduction to his article); ergo, Grothendieck is among the greatest mathematicians. If it would soothe your sensibilities, I will place a reference to this sentence in the article. As for your other claims:
• That in your opinion his achievements don't "look all that significant" means nothing. You have already acknowledged that you have no idea what he did or have any appreciation for the context in which he did it.
• That you consider most of them to have affected "some obscure part of mathematics" reveals more about your own limitations than his.
• Granted that Grothendieck does attract a following of fanboys and obsessive admirers, the sentiments expressed in the article are nonetheless real and supported by numerous testimonials from real mathematicians and a thoroughly researched biographical piece published in a magazine of the main professional society of American mathematicians.
You appear to be some kind of idiot. Ryan Reich (talk) 20:20, 12 May 2008 (UTC)
Who is Allyn Jackson again? I dare you, name me one well-known mathematician who said that Grothendieck is one of the greatest ever. Nice to see you're resorting to personal attacks instead of trying to answer my question. In my experience, that's the primary characteristic of a POV-pusher.  Grue  00:58, 13 May 2008 (UTC)
I think Ryan's last sentence, though provoked, might be, umm, rethought. Off the top of my head, another person who compared AG's work to Einstein's is AG himself in Recoltes. :-) What's funny about this is that this is an exception to the rule that this is a sign of crankhood. In the introduction to the 3-volume Festschrift, with scads of very prominent contributors, I think there are laudatory statements to the effect that Grothendieck changed the way mathematicians think, something very few do, and that much of his work is for future generations to explore. Look at the number of Field's medalists who work in (parts of) Grothendieck's mathematical universal kingdom, or someone like Alain Connes who philosophically view their own work as extending its borders, or trying to do what he did in a new context. Again IIRC Robert Thomason in his Festschrift paper says that he and several others compare him to Newton, and it didn't appear to be coming from a dead friend who appeared to him in a dream. :-). For early approbation, look at Atiyah-Singer's statement in their greatest hit, that they attempted to model it after the approach of Grothendieck's RR theorem, with incomplete success in their opinion. That AG belongs in the alltime greats should be pretty easy to cite. David Ruelle's recent book might say something like that. As to his achievements being not too significant, Grue, tell that to my back i.e. don't try putting them in a box and then walk down an (illegally) steep staircase, owww - (let alone drop them on your head.) This mass times the pathbreaking quality of the ideas and insight, plus the liberality which he gave ideas to others in the 60's and later are what makes him considered by all knowledgeable people a giant. Again iirc, Jacob Murre in a biographical article, the kind of person that makes people say "we will not see his like again."John Z (talk) 01:54, 13 May 2008 (UTC)
You are being willfully obtuse. You are also being malicious and unhelpful by advancing your own ignorance as proof of Grothendieck's non-notability, creating an artificial debate on a topic no one except you contends, basing your criticisms on a singularly exclusionary point of view, and then accusing me of being a "POV-pusher" when I call you on it, in addition failing to actually substantiate your claims when asked but simply throwing up more straw men, such as by dismissing the reliability of any positive evaluation of Grothendieck made in the most detailed existing biographical work on him because it was made by someone who was not a well-known mathematician (despite the variety of superlative testimony given by many leading mathematicians in the article). The article is a reliable source by any standard other than yours, it supports the claim in "question", and no further discussion on this point can be productive. Ryan Reich (talk) 04:21, 13 May 2008 (UTC)

Grue, why don't you tell us who you consider big cheeses in central areas of mathematics, and we'll see if we can find praise from them. Could be a fun game.John Z (talk) 01:54, 13 May 2008 (UTC)

I'm trying to remember who called him the "pope of mathematics" in the 60's Dieudonné?, Cartier? Concerning the article, perhaps Grothendieck's imho accurate evaluation in Recoltes that motifs are his deepest work, while the theory of topoi is the one of broadest importance is worth mentioning.John Z (talk)

I, personally, think really well of Grothendieck; that being said, i would posit that "greatest" / "worst" / "mediocre" / etc., when it comes to character and achievement, can never find a universally acceptable metric and is therefore a [non-neutral] POV. Grothendieck has achieved a lot; this should be documented in the article and from that the individual reader can draw their own conclusion as to his greatness, or lack of it. Quaeler (talk) 06:59, 13 May 2008 (UTC)

I note that Britannica calls Grothendieck "one of the most influential mathematicians of the 20th century". You know, this whole discussion reminds me of the time a physicist complained that calling David Hilbert "one of the most influential" was unsubstantiated POV. He even said he had asked some mathematician friends and they had never heard of the guy. [4] He later retracted his comments. --C S (talk) 17:22, 18 May 2008 (UTC)

I am still amazed that there is any sort of discussion on this matter. I have met people who don't like some of the stylistic effects of Grothendieck's work, but I have never met anybody who takes issue with his occupying a place in the mathematical community of the second half of the twentieth century roughly comparable to that of Hilbert's at the beginning of the century. (Hilbert probably worked in more areas, but he lived at an earlier time.) Feketekave (talk) 14:23, 16 June 2008 (UTC)

It is self–evident that Groth is simply the greatest who ever walked this earth. The fact that he is sympathetic to radical (Communist) causes just reinforces that judgment. Groth is the Che Guevara of mathematics.173.61.94.34 (talk) 18:00, 9 January 2010 (UTC)Lestrade

## Long March

I am not going to restore the "misleading wikilink" that another editor removed, because I do not want to get into a pointless edit war, but I want to explain why it was not misleading and why removing it may not have been a good idea. As the entry itself points out, Grothendieck is a leftist, and he was certainly familiar with the Long March. His title La Longue Marche à travers la théorie de Galois is a clear allusion to that. The reason I added the link was to explain why I changed the previous (bad) translation "The Long Walk," and now that the link isn't there I suspect someone who doesn't understand the allusion will think "Why 'long march'? Marche can be translated 'walk' or 'journey' or 'path'" -- and the entry will be graced with another mistranslation. Languagehat (talk) 16:54, 18 August 2008 (UTC)

I completely agree that the allusion to the Long March is quite obviously intentional. However, when a book's title (or a part thereof) is wikilinked, I think readers have the right to expect the link to point to a page directly discussing the book or its content. I did think of adding a footnote such as "Name apparently an allusion to the Long March of Mao's Red Army in China", but without a suitable source for such statement I think it would have been soon removed as WP:OR. In any case, thanks for fixing the translation, it is now as it should be - most readers will likely be able to make the connection anyway. Stca74 (talk) 17:15, 18 August 2008 (UTC)
OK, that makes sense. Thanks for responding so quickly! Languagehat (talk) 18:48, 18 August 2008 (UTC)

## "Birth name" in the first two lines

It seems slightly comical to give great emphasis to Grothendieck's supposed birth name - or, rather, as the source puts it, the name under which he was initially recorded. This name - Alexander Raddatz - is little more than a legal accident: Grothendieck was born to Hanna Grothendieck while she was still legally married to a Mr. Raddatz. Very soon after his birth - here again I am following the source cited in the first two lines of this article - Mr. Raddatz took the question of Alexander G.'s paternity to court; Alexander Schapiro/Tanaroff acknowledged his paternity. Presumably Alexander G.'s automatically took his mother's name, though somebody with more legal expertise on matters of paternity in the Weimar republic could enlighten us. Feketekave (talk) 00:18, 29 December 2008 (UTC)

## Enough with the edit war

Okay, guys (User:Feketekave and unnamed IP), you can stop now. Please have your argument here about whether Grothendieck was French or German or both, not in the edit comments. Ryan Reich (talk) 16:02, 29 December 2008 (UTC)

I just read this. The unnamed IP has been shadowing my edits on several articles; he has also made provably false claims about my edits repeatedly. I was advised by an administrator to leave him a warning that he or she has not heeded (and may not have got, since his or her IP address keeps shifting; all we know from now is that it is a Deutsche Telekom user).

I have absolutely no interest in getting into an ethnic edit war; my point is precisely that a classification by descent is misleading and unnecessary, besides being vaguely Naziesque. One can give all the importance one wants to Grothendieck's background in Germany; to make him into a Volksdeutscher by descent is offensive. I do not see any tags classifying him by any other sort of descent, and neither do I mean to introduce any.Feketekave (talk) 04:36, 30 December 2008 (UTC)

We're not talking about somebody who's great Grandfather once was born in Germany, we're talking about a man, who was born in Berlin to a German mother and (by law) a German father. Is it "racialist nonsense" [5] to call him German? There are hundreds of categories "..of xy descent", are they all introduced by racialists? Or is it "Naziesque" to say someone who's born in Germany as a German citizen is a German? Strange View. I'll leave Feketekave alone but he should be more careful with accusing others of racialism and Naziviews. 84.139.214.7 (talk) 08:26, 30 December 2008 (UTC)

There is an obvious argument that G. is of German descent, since his mother was undeniably German, and of course he was born in Berlin. It is also claimed that he never had French citizenship, so is not French, though of course he lived and worked all his life in France so is a French mathematician at the least by acclamation. For these reasons, he is in Category:People from Berlin and Category:French mathematicians; it is both redundant and misleading to put him in an "intersection category" since although at first glance he belongs to both parts, he is also said to be stateless (he used to be in Category:Stateless persons, but I don't know what happened to it). A more specific category is more useful than a more general one, since it provides arguments for its own inclusion as well as making more helpful navigational distinctions.

I don't wish to make generalizations about the habits of Wikipedia users, but I think much more energy has gone into using this category as a proxy for personal (or possibly nationalist) opinions than is justified by the possibility of anyone ever finding this article in a category as general as "X people of Y descent". A lot of big categories must be pretty useless as navigational aids unless you actually know what you are looking for, which defeats the purpose; it is really not appropriate to use inclusion in a category to claim the subject for one or another purpose. In this case, much more is known about G. than simply that he is "French" and some anscestor was German, and so rather than put him in the simplistic classification, we have him in the nuanced ones, which should satisfy the IP editor unless the words themselves matter to him. And that is not right. Ryan Reich (talk) 14:31, 30 December 2008 (UTC)

AG could simply not have spent the last 90% of his life in France, being married to a French citizen, being a professor in French institutions (all of which, I remind you, are branches of the government thereby making each professor into a civil servant) without being a French citizen. This is an undeniable fact. There's no such thing as a "stateless" person. If AG weren't at least a French permanent resident, he could not have the life he's had. He moved to France when he was 10 years old. He is now 80. Grothendieck was born a man in Germany, he was born a mathematician in France. He published exclusively in French. —Preceding unsigned comment added by 84.72.92.4 (talk) 19:50, 14 April 2009 (UTC)

## Early career

"After the war, the young Grothendieck studied mathematics in France, initially at the University of Montpellier. He had decided to become a math teacher because he had been told that mathematical research had been completed early in the 20th century and there were no more open problems.[10] However, his talent was noticed, and he was encouraged to go to Paris in 1948."

I don't see where, in the article by Allyn Jackson or in the original text of Récoltes et Semailles, it says that he decided to become a math teacher. Certainly there is this quotation that Lebesgue had developed his theory of integration and thereby "completed" mathematical research, but I don't see anything about Grothendieck thus deciding to teach. Am I missing something obvious here? 99.231.110.182 (talk) 11:52, 20 August 2009 (UTC)

That is true, the cited sources do not support the claim. Neither do other sources I've seen. I have removed the corresponding text from the article. Stca74 (talk) 18:17, 20 December 2010 (UTC)

## Translation

The article mentions that there is a translation into English underway. I wanted to let a friend of mine read a portion of it, so I would not mind translating the part I need. Is there a website I can submit my translation? —Preceding unsigned comment added by --UVa IP address-- (talkcontribs) 00:32, 22 December 2009 (UTC)

## Subjective declaration

In the "Retirement into reclusion" section, the following statement is made: "It's worth noticing that the letter may be read as a piece of recursive humor…." This is a personal opinion, not an objective fact.Lestrade (talk) 21:54, 16 February 2010 (UTC)Lestrade

## Doctoral Students

Hi, the link to doctoral student Jean Giraud is wrong. It leads to the comic book writer, not the mathematician. I couldn't figure how to edit, because the little edit link on the right-top of the page didn't appear to me. Thanks. —Preceding unsigned comment added by 88.171.187.191 (talk) 03:34, 8 May 2011 (UTC)

## Statelessness

Curious that he is legally a stateless person. Though the infobox states this, no information on how this came to pass is in the article. I suggest this is included in the appropriate part of the biography. LukeSurl t c 21:23, 5 October 2011 (UTC)

He was long stateless due to his not having asked for French citizenship, to which he was presumably entitled (but didn't automatically possess, since he wasn't born in France). I have just come across a source that states that he did finally apply for (and, it is implied, of course got) French citizenship in 1971, once he became too old to be conscripted. See [[6]]: "... et ne demandera sa naturalisation qu’en 1971, une fois certain qu’on ne lui demandera plus de faire son service militaire.". The page should now be edited accordingly, though it would be best to get a source that explicitly says that he currently holds French citizenship. Feketekave (talk) 00:22, 9 February 2012 (UTC)

Done, in this edit.
The 1971 date looks wrong: his colleague Cartier gives "1980s", and in 1977 Grothedieck was put on trial as a foreigner (Cartier 2001), so presumably he wasn't a French citizen then. In any case his long-term statelessness is notable and sourced, so that is also included.
—Nils von Barth (nbarth) (talk) 14:39, 2 April 2014 (UTC)
It seems that the "foreigner" mentioned in (Cartier 2001) was not Grothendieck but a Japanese Buddhist monk who had been found in Grothendieck's house and had held an expired French residence permit, according to (Cartier 2009). --Stomatapoll (talk) 07:06, 21 November 2014 (UTC)

## Children of Grothendieck

Maybe it should be mentioned somewhere that Grothendieck had 3 children. Serge and Johanna and ??. It is written in the NOTICES OF THE AMS VOLUME 51, NUMBER 10... --helohe (talk) 23:57, 29 December 2011 (UTC)

Mireille Dufour with three children and Justine Skalba with one child have been mentioned. — Preceding unsigned comment added by Where456is456this345spam456from (talkcontribs) 11:06, 28 October 2014 (UTC)

## Jargon and sources - a need for in text clarification

Large swathes of this article make grand but esoteric claims without sources. The need for sourcing is straight forward, but the article can't be read by anyone without a degree in mathematics, unless constant use of links is used to discovery the meaning of terms not defined in the text. For example, I have a bachelor's degree in biology and took every course upto but not including linear algebra, but "Grothendieck's early mathematical work was in functional analysis." Is meaningless. This can easily be fixed by an expert adding brief explanations along the lines of: "Grothendieck's early mathematical work was in functional analysis, the study of how X affects Y in the context of Z". This allows the reader to read the article without having to follow four score links to understand it. μηδείς (talk) 19:20, 15 November 2014 (UTC)

BTW, I don't think we ever did answer your question here about what functional analysis really is, and the lead of the functional analysis article is not particularly helpful (your complaints about things being too technical really might have merit with respect to that article). I'm hardly an expert, but let me try anyway. An over-abbreviated but possibly helpful description is that functional analysis takes the point of view that mathematical functions themselves are points, in large (often infinite-dimensional) spaces of possible functions, and asks what the properties of those spaces are. But this description is too general to be able to say anything specific about what Grothendieck actually did in this subject. —David Eppstein (talk) 06:28, 17 November 2014 (UTC)
I think the effort to draw attention to the technical parts of the article is a bit misguided. There is no way at all to describe Grothendieck's works in an encyclopedia article to someone without some knowledge of mathematics. We can explain some of these things, but I think you will find that it's "turtles all the way down". Functional analysis, for example, is probably his easiest contribution for someone without much knowledge of mathematics to understand. Functional analysis is the study of continuous linear operators on infinite-dimensional topological vector spaces. Grothendieck's chief contribution concerned the different topologies on locally convex spaces, and in particular identifying the "completion" of a locally convex space. This is analogous to the "completion" that we teach to first year undergraduates: the completion is the set of equivalence classes of Cauchy sequences in a metric space, except in a locally convex space one does not have a metric. Sławomir Biały (talk) 20:41, 15 November 2014 (UTC)
You lost me at operators. I don't think in your example you are defining functional analysis in terms of more basic concepts, but are describing it in even more esoteric terms. As a biologist speaking to a layman, I would define pleiotropy as the fact that one gene can affect seemingly unrelated traits; for example, the fact that a gene that produces blue eyes in dogs also causes their deafness. This is much better than saying pleitropy is an emergent epistatic phenomenon in which regulatory genes cause the partial or complete penetrance of non-wild type traits during an organism's ontogeny.
It really should be possible to say something like functional analysis deals with how simple mathematical manipulations affect theoretical spaces with infinite dimensions, assuming that's anywhere close to correct--you should get the idea. The article should be written for an audience that has had basic exposure to calculus. It can be done, one doesn't just intuit abstract concepts. It's not turtles all the way down. They are always learned from more simple concepts that one has learned earlier, otherwise one wouldn't learn counting, addition, subtraction, multiplication, division, fractions, powers, algebra and geometry, trigonometry, derivative, integrals and series and in that order. Otherwise one could just start with linear algebra if the conceptual hierarchy were arbitrary. We need brief asides that give the educated reader at least the gist of what is being discussed. μηδείς (talk) 21:54, 15 November 2014 (UTC)
To put things into that sort of context, trying to explain the mathematical works of Grothendieck to a layman would be like a biologist trying to explain what pleitropy is to someone who has never encountered any biological entity before (much less knowing what a "gene" is), and who only speaks a dead language. It can certainly be done. A few books and maybe a couple of years of study and one should have enough background to grasp the basic concepts involved (think "you lost me at operators"). But it is ridiculous to suggest that an encyclopedia article (a biographical one at that) would be the appropriate venue for such an expansive treatment of mathematics. Sławomir Biały (talk) 22:17, 15 November 2014 (UTC)
I suspect that's an exaggeration, and we do expect readers here to speak English, and we aim at educated laymen as the audience, not mummies. You have pointedly not said that these terms could not be explained briefly and less abstractly for readers with some exposure to Calc and Trig. There's no burden on you yourself to address this problem, but it remains a problem for the article. See MOS:JARGON and Wikipedia:Make technical articles understandable. — Preceding unsigned comment added by Medeis (talkcontribs)
From Wikipedia:Make technical articles understandable: "Every reasonable attempt should be made to ensure that material is presented in the most widely understandable manner possible." I agree with this. Yet most of the works of Grothendieck, their significance, etc., are not going to be understood by an educated layperson. Period. That is an unreasonable standard. Your confident assertion that it is not, against the assessment of someone who has studied at least some small part of the works of Grothendieck, is rather baffling. Sławomir Biały (talk) 22:42, 15 November 2014 (UTC)

Medeis. The part of the article that you see as jargon soup is the two-levels dumbed-down simplified explanation of Grothendieck's work, which to understand properly requires years of graduate study. It has at least been simplified to a level where someone with an advanced mathematics education should be able recognize the topics and follow the links for more information. To simplify it further we would have to say "he did advanced mathematics" and leave it at that. Maybe you want simple:Alexander Grothendieck. —David Eppstein (talk) 02:41, 16 November 2014 (UTC)

Practically the entire article is jargon. Things like the Riemann-Roch theorem should be described (assuming my understanding is correct) as something along the lines of "which allows complex topologies to be dealt with algebraically" Any science major will understand such a description. Please pay attention to MOS:JARGON:
Avoid excessive wikilinking (linking within Wikipedia) as a substitute for parenthetic explanations... When the notions named by jargon are too complex to concisely explain in a few parenthetical words, write one level down.
Removing tags without resolving the underlying issue will not get the article posted, and will result in a report for edit warring. μηδείς (talk) 04:10, 16 November 2014 (UTC)
As you cited, write one level down, not ten levels down. The guideline clearly states don't oversimplify. I have removed the tag because there is consensus here and you ask us to violate this guideline, which isn't going to happen. Cenarium (talk) 04:27, 16 November 2014 (UTC)
Are you telling me a grad student would not understand this material? That hed have to be a post^9-grad student to understand this material? How did this article get written? You can read all the opposes and supports on the Wikipedia:In the news/Candidates page, they all are predicated on clean-up. and edit warring with me is not going to get you anywhere. μηδείς (talk) 04:36, 16 November 2014 (UTC)
A grad student not afraid of abstraction would broadly understand the meaning, even with only a passing understanding of some of the terms. The ten levels down was rhetorical, the point is that if this gets further simplified, it will only be meaningless generalities, or worse, misleading. As for other comments at ITN/C, they are mentioning issues with references, not jargon. Cenarium (talk) 04:51, 16 November 2014 (UTC)
Μηδείς, I think this page is already in agreement with MOS:JARGON -- this is a very 'dumbed-down' overview of Grothendieck's work, and this biography is not the place for an introduction to those subjects. I would like to see more discussion of the applications of his work to other fields, though, especially as this might be the only thing which would be explicable to the educated layman (except in extreme overview like "he worked in ring theory and topology" [but even that is misleading at best]). CRGreathouse (t | c) 05:52, 16 November 2014 (UTC)

Medeis writes at ITN discussion: "At this point you are just outright lying, no one has said anything about making the article 'accessible to someone with zero mathematical knowledge', I have mentioned a familiarity with calculus on the article's talk page..." I think this points to Medeis's primary misapprehension, that some familiarity with calculus is somehow going to be helpful here (he even mentions trigonometry and linear algebra). No, the mathematics involved is incredibly advanced. It is often not even encountered in graduate school. Even most mathematicians with PhDs lack the required background knowledge (myself included for many of his contributions). Some individuals have built their careers, even won Fields medals, by just understanding a small part of Grothendieck's work. Mentioning calculus as though it were a prerequisite is, to make a biological analogy, like someone saying "I saw a bird once. So please explain the biochemistry of bird behavior." When I point out that the person would need to know some biology, he says "But you're lying. I just told you that I saw a bird once." He then goes on in that same discussion to call mathematics contributors "incompetent". Well, yes, insofar as we are not able to convey advanced mathematics in a few pithy phrases, we are incompetent. Sławomir Biały (talk) 14:53, 16 November 2014 (UTC)

I think μηδείς's points are quite good. This is not an article about mathematics, it's an article about a mathematician; extreme simplifications of his mathematics are compeltely appropriate here. μηδείς even offered a concrete example: "[Riemann-Roch] allows complex topologies to be dealt with algebraically," and I this sort of comment would indeed make the sentence much more understandable to a layperson. Unfortunately so far none of the (other) mathematicians here seem to have engaged with this particular suggestion. To take another example: the sentence "Grothendieck's emphasis on the role of universal properties brought category theory into the mainstream as an organizing principle" is not very helpful to anyone who doesn't know what it means for there to be an "organizing principle" of mathematics; I think it would be very reasonable to expand this comment out somewhat to say something about what sorts of objects to treat as fundamental when doing mathematics (or whatever; I have thought about this for all of 30 seconds), and to assess the actual significance for practicing mathematicians of this viewpoint (which, at least in some fields, seems to be substantial). Obviously not every single sentence requires this sort of addition, but sprinkling in a few of them among the fields of jargon would greatly improve the article. --JBL (talk) 23:33, 18 November 2014 (UTC)

I made a stab at adding a bit of clarification and explanation of some of the concepts mentioned in the Influence section. We'll see what others think. --Mark viking (talk) 02:19, 19 November 2014 (UTC)
Thank you, I think this was a really big improvement. --JBL (talk) 19:43, 19 November 2014 (UTC)

I have had my edits reverted, and was referred here. Procedurally that is OK; but the revert was not so good, in the sense that I removed material that was in fact meaningless. The expository problem with Grothendieck is major (even for mathematicians talking to other mathematicians). Nothing can be done about it if some abstraction is not permitted. "Organizing principle" should be OK. It is abstract, but it is perfectly correct as a description of what is going on. This is an occasion for paraphrase using "in other words". More colloquially, one would say that Grothendieck's "big picture" was on a broader canvas than others had used.

The GRR theorem does not relate "topological properties of complex algebraic curves to their algebraic structure". That is quite wrong, and should not have been put back into the article. What Riemann and Roch did related to curves, which were complex. What Hirzebruch did related to complex varieties of higher dimension. What Grothendieck did related to mappings from one variety to another, over any field, not just the complex numbers. So the old version is factually simply incorrect.

There is actually a structural problem. The "Influence" section is placed where a more introductory exposition might be, in an "inverted pyramid" conception. Logically, how can one talk about the influence of Theorem A and its content at the same time? In Grothendieck's case the style of proof may be as influential as the content, also.

I suggest the "influence" section be moved down. I have just checked that "influence of Grothendieck" has a decent number of hits in Google Books; so the whole thing can be reconstructed with citations of what people in the field say the influence has been, which is how it should be. That is a way to deal with one of the problems. The expository problem as such should be recognised, but it is a different issue.

By the way, the "use of links is used to discover the meaning of terms not defined in the text" is certainly inevitable. Charles Matthews (talk) 06:24, 25 November 2014 (UTC)

Hi User:Charles Matthews, thanks for coming here to discuss. I agree that the exposition problem with Grothendieck is difficult. I do not have the expertise to discuss the particular details of the text in question, but I think in the second case (the GRR theorem) we just have a case of sloppy phrasing, not mathematical incorrectness: the phrase you removed was meant to describe RR, not Grothendieck's extension of it. I don't have any disagreement with the restructuring. --JBL (talk) 23:57, 2 December 2014 (UTC)

## Structure before wording

I've moved the "Influence" down, divided it up, and add some fresh references. The old structure of trying to have it as both an exposition, and an account of Grothendieck's influence, clearly wasn't working. The lead section can have some broad-brush comments: that is what it is there for, after all. The choice of language really has to be postponed until the structure has been improved. Charles Matthews (talk) 13:47, 26 November 2014 (UTC)

## Potential source for readable description of his mathematical work

See http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html for an obituary by David Mumford and John Tate that was intended to be published in Nature as an introduction to Grothendieck's work that could be readable to a non-specialist but educated audience. Unfortunately it was not published because the editors were afraid of even that much math appearing in their journal, but I think we can still use it as a source under the established expert clause of WP:SPS. —David Eppstein (talk) 18:30, 16 December 2014 (UTC)

That's a very nice obituary. I agree that this could be used under the expert clause. Tate and Mumford were invited by Nature editors to write the obit, so the two are clearly considered experts on Grothendieck's work (as if there would be any dispute). Concepts like 'function space', 'rings of polynomials', and 'finite fields' are way beyond the experience of most scientists and even most physicists I know; it's unfortunate that Nature panders to the lowest common denominator of mathematical knowledge. --Mark viking (talk) 19:54, 16 December 2014 (UTC)