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Topic Title: Bourbaki and Finance
Created On Mon Oct 20, 03 10:15 PM

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LongTheta
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Posts: 1506
Joined: Aug 2003

Thu Oct 23, 03 03:08 AM

Mathematics is a science. Great mathematics is an art. I couldn't careless whether EGA is useful for anything. Not more than I would care whether Vermeer's paintings are useful for anything. But they open windows of perception.

I don't want a better TV screen or a fancier car or any of this nonsense (though I perfectly appreciate the attraction, and I have no problem whatsoever with anyone who wants them), but I really, really want to know why the topological string vertex on Calabi-Yau manifolds has anything at all to do with the asymptotics of plane partitions.

You have to learn just a little bit about what Grothendieck did (and I'm not the right person to explain it) to appreciate how powerful and deep the human mind can be. You will never get the idea unless you try your hand at algebraic geometry (in his case).

It's like, you'll never appreciate Olympic level gymnastics unless you try the simplest exercise.

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Time is on my side.

Edited: Thu Oct 23, 03 at 03:10 AM by LongTheta

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pobazee
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Posts: 246
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Thu Oct 23, 03 12:55 PM

I read some of the Bourbaki work, and I?m still been influenced by their work as evident by the appeal to Strasbrough School of Probability in mathematical finance literature. It is obviously the case that Harrison, Kreps, and Pliska read C. Dellacherie and P.A Meyer?s Probability and Potential vol. 1 and 11 and J. Jacod's "Calcul Stochastique et Problemes de Martingales" in putting together their path-breaking work in continuous-time finance. If you read Harrision?s classic lecture note on stochastic calculus that feed the intellectual curiosity of D. Duffie and C. F. Huang you would no doubt detect some of P.A. Meyer wonderment. One can ascribe the success of Stanford finance program to their early embrace of the approach of Strasbrough School of Probability to stochastic calculus, as opposed to MIT program that went the route of H. P. Mckean and N. Wiener, which shaped the approach of P. Samuelson and his student ? Robert Merton.

Obviously, one would have to also mention the work of K. Ito, H. Kunita, S. Wantanabe, J. L. Doob, etc. not necessarily in connection with Bourbaki legacy in finance rather in providing some of the essential tools for mathematical finance.

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"The Bourbaki were Puritans, and Puritans are strongly opposed to pictorial representations of truths of their faith."
--- Pierre Cartier, June 18, 1997

Edited: Thu Oct 23, 03 at 01:22 PM by pobazee

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elan
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Posts: 348
Joined: Apr 2003

Thu Oct 23, 03 02:12 PM

Quote
Originally posted by: LongTheta

I have a hard time debating someone who thinks that N is a "very smart man". I am out of here, dude.

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For whosoever hath, to him shall be given

Posts: 1887
Joined: Sep 2002

Thu Oct 23, 03 03:09 PM

Quote
It's like, you'll never appreciate Olympic level gymnastics unless you try the simplest exercise

If: you've tried to prove something remotely related to the Riemann hypothesis, and there's this guy Deligne out there at the margin, offering up a tool which has been proven to contribute something to One Of The Great Mathematical Problems, and you wanted to understand qualitatively why it works, beyond the essential intuition, then: the attitude behind SGA, which is basically derived from Bourbaki, is a big fucking roadblock. The kind of thing for which that the French have become quite well known.

So, while I understand that they have something of value to me, I don't really have much in the way of appreciation for what they are offering up. It's a form of bad sportsmanship.

A community doesn't exist without leadership. In research, this leadership is provided through the referee system. The 'linear approach' of Bourbaki directly works against the referee system. The general trend in mathematical research has been an overall loss of focus on the problems already identified to be of interest. Sounds a little like Hilbert, I guess - I don't know when that went out of style.

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Fools!
I'm Nonius!!!!

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ScottCaveny
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Posts: 340
Joined: Oct 2003

Thu Oct 23, 03 04:20 PM

Edited: Tue Dec 23, 03 at 05:27 AM by ScottCaveny

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LongTheta
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Posts: 1506
Joined: Aug 2003

Fri Oct 24, 03 03:02 AM

Quote
Originally posted by: elan
Quote
Originally posted by: LongTheta

I have a hard time debating someone who thinks that N is a "very smart man". I am out of here, dude.

I have a hard time debating someone who can't tell the difference between "smart" and "on the right track".

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Time is on my side.

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LongTheta
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Posts: 1506
Joined: Aug 2003

Fri Oct 24, 03 03:26 AM

I found Cartier's short biography very perceptive and moving. He didn't mention the fact that when he (and another well known French mathematician whose name escapes me) went to the South of France to present Grothendieck with the two volumes dedicated to his 60th birthday, he opened the door, saw them, and slammed it shut in their faces. (Account told to me by a French algebraic geometer who should know).

Two comments:

1. Cartier says he doesn't know G's father's first name. It's Alexander. Young Grothendieck was named after his father.

2. C says that G's memoires remain unpublished. Actually, Recoltes et Semailles has been translated into Japanese and published in Japan. The main reason why it remains unpublished in the West is that G names names and has lots to say about those he despises, many of them are still around and very active.

PS I've read bits and pieces of Recoltes et Semailles and it's not pretty reading.

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Time is on my side.

Posts: 2816
Joined: May 2003

Fri Oct 24, 03 03:27 AM

I have a hard time debating someone who can't tell the difference between "smart" and "on the right track".

I'd say that's a fair assessment. Along the way I also bumped into some interesting things related to the Riemann hypothesis and roots of the Zeta function,
1/2 +bI, and why this means there is no Dehn twist.

Edited: Fri Oct 24, 03 at 03:31 AM by N

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LongTheta
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Posts: 1506
Joined: Aug 2003

Fri Oct 24, 03 03:37 AM

Quote
Originally posted by: N
I have a hard time debating someone who can't tell the difference between "smart" and "on the right track".

I'd say that's a fair assessment. Along the way I also bumped into some interesting things related to the Riemann hypothesis and roots of the Zeta function, 1/2 +bI, and why this means there is no Dehn twist.

Excellent

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Time is on my side.

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LongTheta
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Posts: 1506
Joined: Aug 2003

Fri Oct 24, 03 06:36 AM

Okay, I've just read Arnold's article on Bourbaki (I've actually read it a couple of years ago, but forgot all about it). It's a very strong attack on Bourbaki. I understand what he's saying, and I now remember how for a long time I've always thought that science, as presented by Bourbaki, is a dead body.

But I also think that Arnold is wrong in saying that the Bourbaki men ganged together because they were weak mathematicians. I think another reason why people get together is that they like each other's company. These people really needed each other's company if only for the intellectual simulation that it provided. Read again Borel description of the meetings, the shouting, the arguments, and finally "l'esprit a souffle" (Wonderful

) They needed that. I can fully understand it. I wish I had the same.

I think there is more than one way to view Bourbaki. On the one hand, I greatly admire (at least some of) these men (I will never know even a small fraction of the mathematics that Dieudonne knew). On the other hand, their books may be suitable only for someone who already knows the subject, or at least guided by someone who knows it.

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Time is on my side.

Edited: Fri Oct 24, 03 at 12:53 PM by LongTheta

Posts: 1887
Joined: Sep 2002

Fri Oct 24, 03 02:21 PM

can't read .ps at the office, not installed correctly

I agree, to say that they were weak mathematicians is bull... actually A. Borel always scared me, his writing is incredibly demanding and I think his contributions are somewhat deeper than Weil's.

1/2 + b.i... dehn twist... something smells like Alain Connes... um, no thanks (and definitely no cigar)

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Fools!
I'm Nonius!!!!

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AVt
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Posts: 828
Joined: Dec 2001

Fri Oct 24, 03 03:41 PM

kr, find Arnold's view attached as pdf.

More or less i understand your feeling, but i do not see 'bad sportsmanship'.
Let me guess you wanted to look from analytic number theory to arithmetic
geometry? You would need a very good teacher/school, since the language is
rather complex (even if you ignore proofs).

ScottCaveny, for me the paper is not typical Bourbaki. One need not see it
as research report for travelling grands from Australia to Paris, but as far
as i get it Feynman path integrals are not properly settled in Math and see
it towards that (being happy taht i need not understand it, hehe).

(Arnold)OnTeachingMath.zip (22 KB)

Posts: 1887
Joined: Sep 2002

Fri Oct 24, 03 10:52 PM

thanks Axel...

This covers the issues more broadly and carefully than I did. In particular, to me,

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wonderful connection between things which seem completely different

is the 'real' essence of mathematics. This applied to alg arith geom as well, but in that direction I think that there hasn't been enough 'counting of soldiers'. The result is a poverty of education, exactly as described. Arnol'd didn't say it, but one infers from what he wrote that good teaching - in book form or in lectures - strives to make the teacher irrelevant, just as the concepts have an independent existence outside of the axioms. The bad sportsmanship occurs when the teacher wants to remain in front of the chalkboard all the time, having rigged the game in such a way that it is impossible to play without him.

These days, we even have Harris's Alg Geom, which really helps one build facility in a way that Hartshorne or Mumford cannot...

I had never seen I.M. Gelfand's comment on math vs. biology before... back when my office was a floor below his, I had heard that this whole business of mathematical finance had amused him at first, but he didn't completely dismiss it and started to ask more and more questions.

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Fools!
I'm Nonius!!!!

Posts: 2816
Joined: May 2003

Fri Oct 24, 03 11:29 PM

1/2 + b.i... dehn twist... something smells like Alain Connes... um, no thanks (and definitely no cigar)

It does smell like Connes doesn't it.

Edited: Sat Oct 25, 03 at 12:11 AM by N

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LongTheta
Senior Member

Posts: 1506
Joined: Aug 2003

Sat Oct 25, 03 07:43 AM

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These days, we even have Harris's Alg Geom, which really helps one build facility in a way that Hartshorne or Mumford cannot...

What do you mean by "these days"? Griffiths and Harris must be about 30 years old. Or do you find Harris' more recent books more readable? (Incidentally, both Hartshorne and Mumford were students of Grothendieck's, or at least had extensive contacts with him. I think it was Mumford who introduced G's Schemes in the US, or so I was told).

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Time is on my side.

Posts: 1887
Joined: Sep 2002

Sun Oct 26, 03 07:06 PM

yep, that's what I mean... Griffiths/Harris is too long and too comprehensive

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Fools!
I'm Nonius!!!!

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elan
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Posts: 348
Joined: Apr 2003

Sun Oct 26, 03 07:37 PM

Quote
Originally posted by: kr
Griffiths/Harris is too long and too comprehensive

I actually like Griffiths & Harris a lot. Very down to earth math, lots of good calculations, I've used it quite a bit.

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For whosoever hath, to him shall be given

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LongTheta
Senior Member

Posts: 1506
Joined: Aug 2003

Sun Oct 26, 03 11:51 PM

Quote
Originally posted by: elan
Quote
Originally posted by: kr
Griffiths/Harris is too long and too comprehensive

I actually like Griffiths & Harris a lot. Very down to earth math, lots of good calculations, I've used it quite a bit.

Were the proofs proofs?

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Time is on my side.