tea.mathoverflow.net - Discussion Feed (Bourbaki thread)

quid comments on "Bourbaki thread" (20906)

quid — Wed, 19 Dec 2012 06:46:43 -0800

...since almost 24 hours.

geraldedgar comments on "Bourbaki thread" (20905)

geraldedgar — Wed, 19 Dec 2012 06:25:49 -0800

This question now has 4 reopen votes ...

quid comments on "Bourbaki thread" (20904)

quid — Wed, 19 Dec 2012 05:58:55 -0800

By contrast I am virtually certain one has one vote to close and one vote to reopen.

Emil J comments on "Bourbaki thread" (20903)

Emil J — Wed, 19 Dec 2012 05:19:41 -0800

@bsteinberg: If I am not mistaken, you cannot vote twice to open/close the same question, even if its status has changed meanwhile.

bsteinberg comments on "Bourbaki thread" (20897)

bsteinberg — Tue, 18 Dec 2012 12:32:56 -0800

Ok, I apologize. I thought it still had votes to delete. With only 8K I cannot see votes to delete. I will vote to close if it becomes active again.

Bill Johnson comments on "Bourbaki thread" (20895)

Bill Johnson — Tue, 18 Dec 2012 11:19:49 -0800

@bsteinberg: There were no delete votes when you voted to reopen this bad question--François removed then, as he explained early in this thread. The only thing your vote to reopen accomplished is to increase the probability that the question will again junk up the first page.

bsteinberg comments on "Bourbaki thread" (20894)

bsteinberg — Tue, 18 Dec 2012 11:10:54 -0800

I voted to reopen because my understanding is that open questions cannot be deleted. I believe that deletion should be reserved for HW/spammy types of questions. This question is a bad question, although the re-edit by andres is better. But it isn't exactly HW and Spam and it does have answers with positive votes, so I don't believe it belongs in the deletion category just to avoid having it reopened or appear on the active page as Scott and Francois indicate above.

quid comments on "Bourbaki thread" (20893)

quid — Tue, 18 Dec 2012 10:23:01 -0800

I just deleted my (old!) comment

This question has two votes to delete. Not sure it is is a good idea to delete it. Perhaps, before a final vote is cast a meta could be created.

as it possibly contributed to this, while being (in view of the content of meta directly linked below it, obviously) obsolete.

Ryan Budney comments on "Bourbaki thread" (20892)

Ryan Budney — Tue, 18 Dec 2012 10:08:54 -0800

bsteinberg: You are not asked to make a binary choice between re-opening and deleting. The default (and what appears to be largely consensus in this thread) is to keep it as-is, which is simply closed.

Todd Trimble comments on "Bourbaki thread" (20891)

Todd Trimble — Tue, 18 Dec 2012 09:54:19 -0800

@bsteinberg: if you think it's a bad question, then why do you think it should be reopened? The number of upvotes seems like a very weak reason -- people can upvote for all kinds of reasons, many of them not good.

bsteinberg comments on "Bourbaki thread" (20890)

bsteinberg — Tue, 18 Dec 2012 08:03:22 -0800

Although I do not like the question, a question with an upvoted answer with 11 votes probably should not be deleted so I have voted to reopen.

jonbannon comments on "Bourbaki thread" (20889)

jonbannon — Tue, 18 Dec 2012 06:14:48 -0800

BTW: I've proposed a site for hosting philosophy of math questions, for those who may be interested: http://area51.stackexchange.com/proposals/48664/philosophy-of-mathematics

I'm not sure if this is interesting or not, but there it is.

Bill Johnson comments on "Bourbaki thread" (20880)

Bill Johnson — Mon, 17 Dec 2012 17:49:21 -0800

@François: I considered the question as being very worthy of deletion, but ordinarily would not vote to delete because of the upvoted answers. However, the threat of this off topic question again appearing on the first page and pushing reasonable questions down forced my fingers to hit the delete button.

JDH comments on "Bourbaki thread" (20878)

JDH — Mon, 17 Dec 2012 13:54:37 -0800

Oh yes, that is what I would call structuralism. This seems to be very different from the theory-building use of the term in the original question, which was also a theme of the Gowers article.

jonbannon comments on "Bourbaki thread" (20877)

jonbannon — Mon, 17 Dec 2012 12:41:31 -0800

@JDH: You're welcome. I found out about all of this by googling after your comment. I appreciated the comment. In fact, I included the link to the article in the Notices because of the sentence: "Very roughly, Structuralism is the claim that mathematics is concerned, not with particular mathematical objects, but only with general patterns and structures. Particular objects are defined by their positions within such structures- i.e. in relation to other elements of the structures- but they have no identity conditions outside those structures." The article goes on do mention category theory as a natural place to develop structuralism. This doesn't sound to me very different than what you said above. Is it?

JDH comments on "Bourbaki thread" (20876)

JDH — Mon, 17 Dec 2012 12:29:18 -0800

Just for the record, I wanted to say that I find high-level high-quality questions in the philosophy of mathematics to be on-topic for MO, and I would encourage you to post them on MO. Such questions are interesting and admit of knowledgeable answers that treat the topic with the same care and technical precision that our other mathematical questions and answers here do. In particular, I dispute the claim sometimes heard here that questions in the philosophy of mathematics are necessarily discursive and unsuitable for this site. I am disheartened when questions in the philosophy of mathematics that seem perfectly fine to me are closed, sometimes even with dismissive comments. Meanwhile, we have numerous experts in the philosophy of mathematics here, who are both interested in and able to answer such questions. Furthermore, I believe that the kind of questions I have in mind are enjoyed by a large segment of the MO community, even those who haven't particularly studied the philosophy of mathematics, and so I find that they really add value to MO.

But about "structuralism", and thanks Jon for bringing it up again. In the philosophy of mathematics this term is usually used to describe a position in mathematical ontology, by which one holds that what exists in mathematics is not mathematical objects, but rather mathematical structure, relations between objects. (e.g. see Daniel Isaacson's paper "The Reality of Mathematics..." for a great account of it). This is the view that it doesn't matter what the real numbers are really made out of, as objects, as long as they form altogether a complete ordered field, which is the structure that characterizes them. This philosophy of structuralism, of course, runs through the heart of category theory, and some use it to criticise set theory, although this is misguided in my view, since of course set theorists don't care what their sets are made out of either, as long as the set-membership relation has its characteristic properties, which is the relevant structure for set-theorists. In this sense, the philosophy of structuralism is pervasive in contemporary mathematics. Meanwhile, in the question and in the links you provide, it seems that the term structuralism is used differently, not as a matter of mathematical ontology, but rather simply as a mathematical methodology or attitude, a predisposition towards building theories rather than solving problems. But I'd like to learn more about the distinction, which is what I had meant in my comment.

Angelo comments on "Bourbaki thread" (20875)

Angelo — Mon, 17 Dec 2012 12:17:48 -0800

I would love to see more questions on the philosophy of mathematics, in particular the philosophy of mathematical practice. If they are well-formulated and thought-out, they are certainly a lot more interesting than the soft questions of the type "Paper with a title with a very large number of vowels" (ok, I am exaggerating, but not much).

jonbannon comments on "Bourbaki thread" (20873)

jonbannon — Mon, 17 Dec 2012 11:05:55 -0800

@Andres: I'll let it lie at Math.SE and see if there are any good answers there, and if not will then revive it here. I also linked to the wrong one of gowers's articles. I meant to link to his "does mathematics need a philosophy?" paper...https://www.dpmms.cam.ac.uk/~wtg10/philosophy.html

I don't want to post this until the Bourbaki thing is gone. There should only be so many softballs floating around the front page.

Andres Caicedo comments on "Bourbaki thread" (20868)

Andres Caicedo — Mon, 17 Dec 2012 10:01:04 -0800

Hi Jon. This looks interesting, and I expect it may have more informed answers here than at math.se.

jonbannon comments on "Bourbaki thread" (20867)

jonbannon — Mon, 17 Dec 2012 09:44:29 -0800

Thanks for the edit, Andres. I posted (and then quickly removed) the question below in order to find a home for math philosophy questions that may be of interest to mathematicians (mainly JDH's curiosity about `structuralism' which I encountered in the linked article). I've removed the post and sent it over to math.se, so as not to keep the Bourbaki free-for-all alive:

Certain philosophers of mathematics are interested in aspects of [the philosophy of mathematical practice.][1] Mathematicians, perhaps, would be interested in [philosophy that may affect their day to day work][2].

JDH's curiosity about structuralism on a recent Bourbaki thread makes me wonder:

>**Question:** Is there an appropriate "stack exchange" for questions on the philosophy of mathematical practice?

I think questions about the philosophy of mathematics are inappropriate for MO in general, but may be interesting for mathematicians if handled elsewhere. Unfortunately, philosophy.stackexchange doesn't seem very helpful for the type of question I'm thinking of. I'm also not interested in a site that is dominated by questions targeting old foundational issues more than contemporary practice. I imagine, also, that many naive questions would populate such a forum and so am not necessarily suggesting that one would be a good idea.

[1]: http://www.ams.org/notices/201203/rtx120300424p.pdf
[2]: https://www.dpmms.cam.ac.uk/~wtg10/2cultures.pdf

If anyone wants this to live, they can re-post it or modify it.

Andres Caicedo comments on "Bourbaki thread" (20866)

Andres Caicedo — Mon, 17 Dec 2012 08:59:33 -0800

Edited, following Gil's suggestions.

gilkalai comments on "Bourbaki thread" (20864)

gilkalai — Mon, 17 Dec 2012 05:20:19 -0800

As the new version is really bad, the old version is unsatisfactory as well, below is how I would edit it while still trying to be loyal to the OP's intentions. As I said, this is not meant as an endorsement for reopening the question.

Does Bourbaki's (and Grothendieck's) approach to mathematics survive today?

I am curious if the `Bourbaki's approach' to mathematics is still a viable point of view in modern mathematics, despite the fact that Bourbaki is vilified by many.

Even more specifically, does anyone actively approach mathematics from the more "yielding" point of view famously practiced by Grothendieck? Which, or what type of, research areas are welcoming to (or practicing) Grothendieck's approach to mathematics?

Motivation:

To me, there is a deep question regarding motivation of mathematicians over time which is addressed by this viewpoint. An emphasis on resolving hard technical problems is quite depressing, generally, whereas the idea of finding a general framework which presents a natural and explanatory solution through the development of a vast theory seems very motivating. In such a view, the open problem only serves to motivate a better development of the general theory surrounding the core difficulty, bringing into focus a clearer picture of the essential issue at hand.

It seems to me that carefully developing a general (sometimes axiomatic) theory is analogous to performing scientific experiment. One is not looking to be clever, but instead is filling in data which may, when examined later, reveal clear and natural answers to mathematical questions. Obviously such an approach can be exhausting, in that one must spend much more time to fill in an entire picture than to, at some point, jump to a resolution of a particular question. On the other hand, It may be possible to persevere longer at such a task, as one is not so sensitive to one's loss of quickness or cleverness and can simply engage the task at hand.

Is this viewpoint valid?

Ryan Budney comments on "Bourbaki thread" (20851)

Ryan Budney — Sun, 16 Dec 2012 15:29:21 -0800

I agree with the general sentiment in Todd's reading of the question, and that the question should stay closed.

Todd Trimble comments on "Bourbaki thread" (20850)

Todd Trimble — Sun, 16 Dec 2012 14:44:14 -0800

I agree with you, Gil, about the quality of the question, and I think your recommendation (7) is the critical one. But the recent edit at least has the virtue of making it clearer to me that the poster is someone young (in mathematics). It looks as though s/he has gotten an idea from Grothendieck that there are the 'clever' types like Serre who crack the nut by aiming the chisel judiciously and striking hard, and then there are other 'yielding' types (like Grothendieck) who let the nut soften in liquid for a long time, etc. -- a 'yin' approach, as it were. And the main question is which communities support the latter style. There are some seemingly confused ideas about structuralism and axiomatization thrown into the mix.

If that reading is correct, I can see why the underlying idea might be seductive. Unfortunately, this question (if I've understood it correctly) is almost certainly not right for MO (and unfortunately for JDH, I doubt the OP really wants to talk about structuralism in any sense of the word).

gilkalai comments on "Bourbaki thread" (20849)

gilkalai — Sun, 16 Dec 2012 13:08:55 -0800

Yes, it is getting even worse. I agree that the question should be left closed, but I feel tempted to edit it *not* as an endorsement for reopening but to delete the repeated really-bad parts. Maybe the OP can do it
himself: Here are my suggestions:

1) Delete any mention of quackery (irrelevant)

2) Delete any mention of "needing to publish" (irrelevant)

3) Don't repeat the same idea/question twice or more

4) The question should not include comments that you have on the discussion. If you want to comment, then comment elsewhere. (Here, for example.)

5) Delete or reduce drastically references to "cleverness."

6) I propose not to form the question as trying to understand what the "mathematical community" thinks, simply ask the question.

7) Make an effort to think clearly what is it that you are trying to ask. It does take some cleverness to develop a useful and fruitful theory a la Grothendick and it even takes some cleverness to ask a useful and fruitful MO question.

quid comments on "Bourbaki thread" (20848)

quid — Sun, 16 Dec 2012 12:37:09 -0800

The question just got significantly edited. For the record, I also consider the edited version as unsuitable, and feel even more convinced that it was right to close the original.

Todd Trimble comments on "Bourbaki thread" (20847)

Todd Trimble — Sat, 15 Dec 2012 19:58:32 -0800

Discussion of "mathematical structuralism" or "categorical structuralism" certainly could (and to some extent already does) take place on MO; see writings by Awodey and McLarty for what these terms might signify.

I did however feel that mention of Bourbaki wasn't pertinent to the question, which I took to be whether doing mathematics in the manner of a Grothendieck was still 'viable' (whatever that means exactly). I would feel that way all the more if "Bourbakian structuralism" were brought up.

Scott Morrison comments on "Bourbaki thread" (20846)

Scott Morrison — Sat, 15 Dec 2012 19:49:37 -0800

I agree with François that voting to delete because of votes to reopen seems like inappropriate use of one's power to delete.

Harry Gindi comments on "Bourbaki thread" (20845)

Harry Gindi — Sat, 15 Dec 2012 18:29:03 -0800

Words like "structuralism" have no place on mathoverflow. This term means something very different (and very stupid) in philosophy.

Todd Trimble comments on "Bourbaki thread" (20844)

Todd Trimble — Sat, 15 Dec 2012 16:44:57 -0800

I opined that even were the question to be improved (e.g., by removing the bit about 'quackery') it might still be too discussion-y to be a good MO question. This is despite the fact that I find the topic very interesting. (By the bye, part of me wonders at the accuracy of the image of Grothendieck as someone who likes to work with axiomatics; as I said in another comment there, the feeling I get is that choosing one's axioms is something that a "Grothendieck-type" might put off for a very long time indeed, until the time, or 'nut', was fully ripe.)

François G. Dorais comments on "Bourbaki thread" (20843)

François G. Dorais — Sat, 15 Dec 2012 15:18:45 -0800

I cleared all the votes to reopen and delete and then I unlocked. I hope that we can all work within the usual system norms after a fresh start.

François G. Dorais comments on "Bourbaki thread" (20842)

François G. Dorais — Sat, 15 Dec 2012 14:10:35 -0800

Felipe and Bill, that's an abuse of the system, please quit doing that. Either let close/reopen battles happen or, if there is really good cause not to reopen, flag for moderator attention and ask us to lock the question closed.

Bill Johnson comments on "Bourbaki thread" (20841)

Bill Johnson — Sat, 15 Dec 2012 12:53:02 -0800

I voted to delete because of the votes to reopen.

François G. Dorais comments on "Bourbaki thread" (20840)

François G. Dorais — Sat, 15 Dec 2012 12:00:54 -0800

Locked it. Open vs delete wars are not the right way to deal with this. This is the second one in a week!

I'll unlock after I see that this is going somewhere productive.

voloch comments on "Bourbaki thread" (20838)

voloch — Sat, 15 Dec 2012 11:39:37 -0800

This is similar to another recent case. I do not think the thread should be deleted, as long as it stays closed. If there is a chance that it's going to be reopened, I'd rather have it deleted.

Angelo comments on "Bourbaki thread" (20836)

Angelo — Sat, 15 Dec 2012 11:27:18 -0800

I voted to close, and still think it deserves to stay closed; nothing borderline about it, in my opinion. However, deletion seems a bit extreme.

Ryan Budney comments on "Bourbaki thread" (20835)

Ryan Budney — Sat, 15 Dec 2012 11:18:30 -0800

This "is structuralism quackery" thread has three votes to re-open and two votes to delete.

http://mathoverflow.net/questions/116201/does-bourbakis-and-grothendiecks-approach-to-mathematics-survive-today-clos

I don't think it deserves to be re-opened. I'm not so sure if it should be deleted. But this could be a borderline case people want to discuss.