tea.mathoverflow.net - Discussion Feed (Question for mathematics researchers)

VP comments on "Question for mathematics researchers" (7476)

VP — Thu, 22 Jul 2010 00:33:50 -0700

A valid question along these lines would concern a list of references about motivations for doing mathematics. Come to think about it, such a question may have already been asked... Anyway, "Mathematics people" and its sequel are good older complements to current interviews in the Notices.

WillieWong comments on "Question for mathematics researchers" (7450)

WillieWong — Wed, 21 Jul 2010 10:56:14 -0700

Roy's mention of Terry's article reminded me that Alain Connes also wrote something on this subject. http://noncommutativegeometry.blogspot.com/2007/02/good-mathematics.html

As you can see, there are many different perspectives on this issue.

Roy Maclean comments on "Question for mathematics researchers" (7449)

Roy Maclean — Wed, 21 Jul 2010 10:33:30 -0700

Regarding goals of mathematics, there is Terry Tao's "What is good mathematics?" http://arxiv.org/abs/math/0702396

Pete L. Clark comments on "Question for mathematics researchers" (7446)

Pete L. Clark — Wed, 21 Jul 2010 09:30:50 -0700

@Robin: I appreciate your response. Please feel free to contact me personally if there is anything else to be said. Respectfully...Pete

Craig comments on "Question for mathematics researchers" (7445)

Craig — Wed, 21 Jul 2010 09:14:18 -0700

Robin,

Your comments came across to me and Pete as disparaging. Given that you said it was not your intention to be disparaging, I take back my accusation about cyber-bullying.

Robin Chapman comments on "Question for mathematics researchers" (7442)

Robin Chapman — Wed, 21 Jul 2010 08:29:25 -0700

To Pete,
It has not been my intention every to disparage any other
mathematician here, either professional or amateur.

That said, Mr Feinstein has just made an extraorinary accusation in
this forum. Mr Feinstein (who for some reason does not use his surname
in MO or meta.MO) has asked a so-called survey question about
the motivation of mathematicians. To me, asking about my motivation
is a personal, not a mathematical, question. When asked a personal
question I feel it entitled that I know something about the
enquirer and his/her motives, so that any information I may divulge
is properly used. I know nothing about Mr Feinstein save for his
contributions over the years to sci.math and the math.GM section
of the arXiv. Based on these sources I do not feel that Mr Feinstein
is someone to whom I wish to vouchsafe any personal information
whatsoever. Of course others may feel differently. In any case
viewers of meta.MO can now view a sample of Mr Feinstein's writings,
which may or may not influence them in dealing with him.

Craig comments on "Question for mathematics researchers" (7441)

Craig — Wed, 21 Jul 2010 08:22:43 -0700

Emerton,

Thank you, I'll check these out. As I said before, I also posted my question on sci.math here:
http://groups.google.com/group/sci.math/browse_thread/thread/52d2f705fb43a9c8?hl=en#

so if anyone has any other comments, since MO and meta-MO are not the right forums, you might as well comment there rather than here.

Emerton comments on "Question for mathematics researchers" (7439)

Emerton — Wed, 21 Jul 2010 08:02:30 -0700

Dear Craig,

Regarding your initial question, about mathematicians' motivation for doing mathematics: As you probably know, the Notices of the American Math Society are freely available on the AMS website, and frequently contain interviews with celebrated mathematicians (in particular with Abel Prize winners, if I am remembering correctly); it is also easy to find online interviews with various recent Fields Medal winners. If you read these interviews, you will get a sense of the motivations of these mathematicians, and I don't think that there is that much reason to believe that the motivations of less celebrated mathematicians are particular different. This seems like a more fruitful way to understand the motivations of professional mathematicians than attempting to survey MO users. (As others have already noted, conducting such surveys is not really appropriate for MO, which is suppose to be a place for questions of interest to research mathematicians, not questions about research mathematicians.)

Craig comments on "Question for mathematics researchers" (7436)

Craig — Wed, 21 Jul 2010 06:55:34 -0700

@Pete: Robin's posts are an example of this: http://en.wikipedia.org/wiki/Cyber-bullying. They have no place in a professional forum, as they harm your profession.

WillieWong comments on "Question for mathematics researchers" (7430)

WillieWong — Wed, 21 Jul 2010 03:19:05 -0700

@Harry: I thought that's where you came in... =)

Harry Gindi comments on "Question for mathematics researchers" (7429)

Harry Gindi — Wed, 21 Jul 2010 00:30:58 -0700

If you have managed -- against steep odds and heavy competition -- to make a permanent living doing mathematics, you might as well be a gracious winner.

Can't you guys just act like rappers and be anything but gracious winners? It's funnier to watch. ;)

Pete L. Clark comments on "Question for mathematics researchers" (7428)

Pete L. Clark — Wed, 21 Jul 2010 00:26:48 -0700

@Robin: From a professional mathematician to a more established professional mathematician: I don't think it's necessary to make disparaging comments to amateur mathematicians. I think everyone here knows that having a paper posted on the "General Mathematics" branch of the arxiv is a far cry from being published in a refereed journal. I'll bet even Craig Feinstein knows this in some sense, or at least that he has been told so several times before.

This is just my opinion, of course. Some would call my attitude patronizing. I think of it like this: if you have managed -- against steep odds and heavy competition -- to make a permanent living doing mathematics, you might as well be a gracious winner.

Harry Gindi comments on "Question for mathematics researchers" (7427)

Harry Gindi — Tue, 20 Jul 2010 23:59:27 -0700

@Robin: Is there any reason why all of your posts are in poem form?

;)

Robin Chapman comments on "Question for mathematics researchers" (7424)

Robin Chapman — Tue, 20 Jul 2010 23:34:37 -0700

I hadn't realised that papers deposited on arXiv
counted as "publications". I'll have to inform
my university's authorities about that.

Scott Morrison comments on "Question for mathematics researchers" (7414)

Scott Morrison — Tue, 20 Jul 2010 20:27:14 -0700

@Craig,

yes, you misunderstood my intent. I wanted to suggest that if you didn't understand why your question was closed, you should ask on meta, or argue there against the closure.

Craig comments on "Question for mathematics researchers" (7405)

Craig — Tue, 20 Jul 2010 18:25:50 -0700

Thank you Will, I received it. I remember reading another version of it on arxiv.org a few years ago. I also posted my question on sci.math here:
http://groups.google.com/group/sci.math/browse_thread/thread/52d2f705fb43a9c8?hl=en#

Will Jagy comments on "Question for mathematics researchers" (7402)

Will Jagy — Tue, 20 Jul 2010 17:23:51 -0700

Craig, I just emailed you an essay by Steven G. Krantz called "Through a Glass Darkly." It is also available at
http://arxiv.org/abs/0807.2656

Craig comments on "Question for mathematics researchers" (7396)

Craig — Tue, 20 Jul 2010 16:56:11 -0700

@Qiaochu

I guess I misunderstood Scott.

@Yemon

I'll try it on sci.math then. I would have asked it there originally, but it seemed to me that you get better and faster answers on MO.

Yemon Choi comments on "Question for mathematics researchers" (7392)

Yemon Choi — Tue, 20 Jul 2010 16:04:37 -0700

Roy: MMO is, as I understand it, primarily is for discussing the workings of MO, and not for providing a home for the kind of discussion thread which Craig seems to desire. See Qiaochu's comment above.

That said, I want to venture one "off-topic" remark: I don't think your list should be expanded - indeed, there are several items on it that in my view need serious clarification/development, possibly even excision. It seems like you want an anthropological study done by getting the subjects of the study to do the work for you.

Craig: I suggest that if you sincerely want an answer to your original question, you go and discuss it with some professional mathematicians over a beer, coffee or other social beverage, or chat with them on whichever electronic forum (e-pub?) people use for such things.

Qiaochu Yuan comments on "Question for mathematics researchers" (7391)

Qiaochu Yuan — Tue, 20 Jul 2010 16:04:10 -0700

Why can't I get a single answer to this question and why was this question closed on MO? I wonder.

Because MO is not the place to ask it.

When Scott suggested you go to meta, he meant to ask about whether the question was acceptable (which it isn't), not to ask the question itself.

Andy Putman comments on "Question for mathematics researchers" (7390)

Andy Putman — Tue, 20 Jul 2010 16:03:47 -0700

@Roy : I don't think that would be a good question for MO either. Again, it's far too broad and open-ended.

Some people here dislike "soft" questions. I personally don't have a problem with soft questions, but they have to be novel and specific. I can't really imagine the question you listed getting answers that are interesting enough to justify its existence.

Craig comments on "Question for mathematics researchers" (7389)

Craig — Tue, 20 Jul 2010 15:56:32 -0700

@Roy Maclean,

Thank you for your comments. I hope for more comments like this.

@Willie Wong,

I should have phrased it differently. I only intended to use your phrase "job/grant applications". I didn't mean to imply that this was your goal or motivation for researching mathematics.

WillieWong comments on "Question for mathematics researchers" (7387)

WillieWong — Tue, 20 Jul 2010 15:13:23 -0700

@Craig: I resent that characterization of what I wrote.

Roy Maclean comments on "Question for mathematics researchers" (7386)

Roy Maclean — Tue, 20 Jul 2010 15:07:48 -0700

What motivates anyone to do anything ? Some combination of getting paid/enjoying it/being forced to do it/I was better at this than anything else/addicted to it/curiosity/peacocking/patriotic duty/drifted into it/I was actually studying biology but was led into a mathematical question/was introduced to a problem years ago and now can't let it go until it is solved/goodness knows how many other possible reasons.

What are the goals of your research?

Perhaps a more focused question is: cw: Big-list: What are the general types of activities that constitute research mathematics: (these answers will probably apply to other sciences as well)

Some answers:

1) Solve a specific known problem. Solve lots of specific problems in a particular area of mathematics.

2) Create variations of known problems, and solve those instead because the original problem was too hard.

3) Generalize a theorem.

4) Strenghten a theorem for more specialized case.

5) Strenghten a theorem because the original theorem wasn't the sharpest possible statement.

6) Find counterexamples to some conjecture.

7) Use Computer algebra systems/numeric software to generate lots of examples to search for patterns to write theorems about.

8) Invariants: Search for things that stay the same when the situation as a whole is changed.

9) Survey. Read all papers on a particular subject and summarise them in a paper or book.

10) Read widely and then identify similarities between different things that point to a new common structure that hasn't hitherto been written about.

11) Try to chip away at some problem by narrowing the lower and upper bounds.

12) Gowers completing the square. If theorem A is modifed in different directions into theorems B and C, then what is the theorem D that is to B what C is to A, or that is to C what B is to A. If theorem A is modified in many directions then you have the opportunity of completing the lattice.

13) Just keep reading as many books/papers as you can and doing all the exercises in the books until a question occurs to you that your brain won't let you rest until you've solved it.

14) Write software for your area of mathematics that performs calculations/manipulations that were previously done by hand.

15) Study real world problems and mathematize them. At one time games weren't a theory. Information wasn't a theory.

16) Find new techniques/methods/ways of approaching something, and then try these techniques out on other problems.

I for one would be interested to see this list expanded and particularly any comments about "how likely to be productive" each type of activity is.

jbl comments on "Question for mathematics researchers" (7385)

jbl — Tue, 20 Jul 2010 14:49:10 -0700

+1 Mariano

Andy Putman comments on "Question for mathematics researchers" (7384)

Andy Putman — Tue, 20 Jul 2010 14:47:46 -0700

+1 Mariano

(there was originally a serious reply here, but Mariano posted a much better response while I was writing it)

Mariano comments on "Question for mathematics researchers" (7383)

Mariano — Tue, 20 Jul 2010 14:43:50 -0700

Yes.

Craig comments on "Question for mathematics researchers" (7382)

Craig — Tue, 20 Jul 2010 14:36:06 -0700

Qiaochu, I posted here because Scott Morrison recommended I do so. See http://mathoverflow.net/questions/32660/question-for-mathematics-researchers-closed

Why can't I get a single answer to this question and why was this question closed on MO? I wonder.

Is it because there are no goals or motivations for mathematics research other than get money from "job/grant applications", as Willie Wong said?

Qiaochu Yuan comments on "Question for mathematics researchers" (7380)

Qiaochu Yuan — Tue, 20 Jul 2010 14:25:43 -0700

This is not a question about MO, so it doesn't belong on meta. This question has already been closed twice on MO, so you already know it's not appropriate there either.

Andy Putman comments on "Question for mathematics researchers" (7379)

Andy Putman — Tue, 20 Jul 2010 14:12:09 -0700

@Craig : As Willie said, your question is wildly broad. I could give a snarky answer (eg my goal is to prove theorems, and I do it because it's fun), but for anything more than that I'd have to write a longish essay, and I certainly don't have the time to do that. I suspect that the same could be said for most people.

WillieWong comments on "Question for mathematics researchers" (7378)

WillieWong — Tue, 20 Jul 2010 14:06:05 -0700

@Steve: oh yes. I've discovered that just this past weekend. I'm actually pretty good at it thanks to my physical proximity to the other maths department at my current home institution (and the fact that I crash their seminar lunches for free pizza).

@Craig: I don't see how it relates to your original question either. But your non-answer to Robin Chapman's query certainly didn't help. The open-ended nature of your question is essentially asking us to reproduce our research statements that we write for job/grant applications.

VP comments on "Question for mathematics researchers" (7377)

VP — Tue, 20 Jul 2010 14:02:27 -0700

Thank you, Steve, I was just thinking the same thing. I've seen statements by some pretty famous people on blogs admitting to their arXiv vs snarXiv sins.

Craig comments on "Question for mathematics researchers" (7375)

Craig — Tue, 20 Jul 2010 13:52:13 -0700

Those are my publications on arxiv.org. I am proud of my publications. If you want to have fun with them, knock yourselves out, but I don't see how it relates to my original question.

Steve Huntsman comments on "Question for mathematics researchers" (7373)

Steve Huntsman — Tue, 20 Jul 2010 13:33:39 -0700

@Willie: http://snarxiv.org/vs-arxiv/

Andy Putman comments on "Question for mathematics researchers" (7370)

Andy Putman — Tue, 20 Jul 2010 13:27:46 -0700

@WillieWong : =)

I think of it as a secret guilty pleasure (like reading the Weekly World News). It would somehow be less fun if I didn't feel a little embarrassed by it...

WillieWong comments on "Question for mathematics researchers" (7368)

WillieWong — Tue, 20 Jul 2010 13:24:42 -0700

Unlike Andy, I am comfortable enough in my mathematician pedigree that I have the math.GM list sent to my real e-mail address. Though for comedy I find general physics and hep.th more reliable on a day-to-day basis.

Andy Putman comments on "Question for mathematics researchers" (7365)

Andy Putman — Tue, 20 Jul 2010 13:17:56 -0700

I have to admit that I have a fake email address to which I have the daily math.GM mailings sent. I even download some of the papers. There's (comedy) gold in them hills!

Scott Morrison comments on "Question for mathematics researchers" (7363)

Scott Morrison — Tue, 20 Jul 2010 13:15:59 -0700

hehe, I love math.GM :-) Publishing on the arxiv is a double-edged sword.

Craig comments on "Question for mathematics researchers" (7354)

Craig — Tue, 20 Jul 2010 12:40:48 -0700

Robin, do what you please.

Robin Chapman comments on "Question for mathematics researchers" (7338)

Robin Chapman — Tue, 20 Jul 2010 11:34:11 -0700

Well, I for one am not about to satisfy the curiosity of the author of
http://uk.arxiv.org/find/math/1/craig+alan+feinstein/0/1/0/all/3/0 .

Craig comments on "Question for mathematics researchers" (7337)

Craig — Tue, 20 Jul 2010 11:32:36 -0700

Craig wants to know because Craig is curious.

Robin Chapman comments on "Question for mathematics researchers" (7335)

Robin Chapman — Tue, 20 Jul 2010 11:22:26 -0700

Who wants to know, and why?

Craig comments on "Question for mathematics researchers" (7331)

Craig — Tue, 20 Jul 2010 10:54:43 -0700

My question is a survey question for professionals and amateurs who do research in mathematics: What motivates you to do mathematics research and what are the goals of your research?