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It's weird, though, the idea that mathematics should have an awareness month. Try going a month (not to mention 11) *without* it figuring into your everyday life.

Also, gleuschk, the fact that mathematics is one of the rare and precious fields that are left to people who actually know what they're doing is a*good* thing!

posted by mattpfeff at 10:55 AM on April 29, 2002

Also, gleuschk, the fact that mathematics is one of the rare and precious fields that are left to people who actually know what they're doing is a

posted by mattpfeff at 10:55 AM on April 29, 2002

Mattpfeff, you'd be surprised (actually, probably not, but bear with the rhetoric) how many people are willing to tell me to my face that they hate mathematics. Whether they use any or not (I personally haven't balanced my checkbook in nearly a year), they'll insist that it doesn't have the slightest impact on their lives.

My understanding of Math Awareness Month is that it's more about the*mathematicians* than the mathematics. Many people don't even know that there are people in the world who refer to themselves as mathematicians (my dad still doesn't believe it). Next time you're at a cocktail party, try this: ask everyone to name a famous mathematician (they'll either say Newton or Einstein, both iffy but acceptable). Then ask them to name a famous *living* mathematician (if they've really been paying attention, they'll fumble to come up with Andrew Wiles' name). If anyone's still listening, ask for a famous female mathematician. Don't even try to combine living and female - nobody knows what would happen.

*mathematics is one of the rare and precious fields that are left to people who actually know what they're doing is a good thing!*

Sadly, not so much - more and more we have to wonder if we're unwittingly doing evil in the name of good (this is one reason I've chosen the least applied of all fields of mathematics). You've heard of Poor Pure Percy P? Or poor GH Hardy, who was so proud of the purity of mathematics, and became famous for the Hardy-Weinberg law on the propagation of genetic traits (thank Logos he didn't live to see his beloved Fourier series used to build a fighter jet).

posted by gleuschk at 12:57 PM on April 29, 2002

My understanding of Math Awareness Month is that it's more about the

Sadly, not so much - more and more we have to wonder if we're unwittingly doing evil in the name of good (this is one reason I've chosen the least applied of all fields of mathematics). You've heard of Poor Pure Percy P? Or poor GH Hardy, who was so proud of the purity of mathematics, and became famous for the Hardy-Weinberg law on the propagation of genetic traits (thank Logos he didn't live to see his beloved Fourier series used to build a fighter jet).

posted by gleuschk at 12:57 PM on April 29, 2002

By the way, this year's Math Awareness Month focused on Math and the Genome; you can see previous themes here.

posted by gleuschk at 1:41 PM on April 29, 2002

posted by gleuschk at 1:41 PM on April 29, 2002

This makes sense, of course; and I agree is quite deserving. It's scary what people naively say about mathematics; it is so fundamentally inextricable from everything we do.

(I do know GH Hardy, of course, but more for his A Mathematician's Apology (a remarkably powerful book, indeed) than for his research, of which I only know a little.)

(Also, I'm ashamed to confess I can't think of many female mathematicians myself. Noether, and my aunt. Hmph. I know I'm forgetting some names. ... )

posted by mattpfeff at 2:17 PM on April 29, 2002

More than you thought there was to know about women in science, particularly math. See esp. a big list at Agnes Scott of women mathematicians. Two who spring to mind are Hypatia and Grace Chisholm Young (my advisor's wife's grandmother, so weirdly my relation).

posted by gleuschk at 3:27 PM on April 29, 2002

posted by gleuschk at 3:27 PM on April 29, 2002

I could name lots of mathematicians, but only a few females. I came up with Emmy Noether too, Sonia Kovalevskaya, Sophie Piccard, and stretching it, Hypatia, ~Dido~, and Florence Nightingale (no, really). After that, er.... And you're right, few living ones beyond Wiles. Is Saunders MacLane alive? Is Gregory Chaitin a mathematician? It's interesting, because the history of mathematics is always taught as a kind of parade of heroic personalities, and modern mathematics seems kind of de-personalized (to an outsider).

posted by rodii at 4:26 PM on April 29, 2002

posted by rodii at 4:26 PM on April 29, 2002

Many of today's greatest mathematicians are, more properly, mathematical physicists. I, for one, nominate Witten as the greatest living mathematician. He won the Fields medal but his work is best known now within the domain of string theory.

There's also Grothendieck who went into seclusion after producing some of the deepest and most diverse work this century. He is mathematics answer to JD Salinger.

Finally, talking about math personalities, what about Erdos??

posted by vacapinta at 5:08 PM on April 29, 2002

Is that true, or are the true "greatest mathematicians," as determined from the point of view of, say, mathematicians of the year 2102, just little known outside their local communities? Are we being distracted by fame? This is not a knock on Witten--there's no contradiction between fame and greatness (cf. Feynman). But if "the greatest mathematician alive" only published in mathematics journals, would we know her?

I wonder who was deemed the "greatest mathematician" in 1902? Hilbert? Poincare? Dedekind? Cantor (surely not)? Would we agree with that judgment today?

posted by rodii at 5:41 PM on April 29, 2002

I had no idea Florence Nightingale had anything to do with math. Huh.

Anyway, sure, Mac Lane is alive (emeritus from Chicago, but still very active in math education). He comes to AMS meetings and is always easily identified: the old coot wearing three different plaids. And yeah, I'd say Chaitin is a mathematician (his bibliography lists something called Conversations with a Mathematician!).

I suppose that `many' of today's greatest mathematicians are in mathematical physics, but (1) I think that's mostly just because m.p. is sexy and that's where the grant money is, and (b) it's certainly not 'most'. Google says the nominees for greatest living mathematician are Grothendieck (who's not just in seclusion, but completely nuts - he insists that Satan is changing the speed of light to upset him), I. Gelfand, Einstein (ineligible), Gauss (ditto), Grothendieck again, Coxeter, and some guy named Joe. I think that's about right.

One way to settle on the greatest living mathematician would be to look and see who's talking at the International Congress of Mathematicians this fall in Beijing. That's certainly an honor (and I think it's indisputable that Hilbert was the g.l.m in 1902, when he gave the ICM talk with the 23 problems). The list is here - I only know about 4 names on it: Chang, Kac, Mumford, and Taylor. I don't really think any of them is anything close to the g.l.m., though Mumford's pretty close (having rebuilt algebraic geometry from the ground up with/against Grothendieck and now having moved on to applied math.).

posted by gleuschk at 7:24 PM on April 29, 2002

Anyway, sure, Mac Lane is alive (emeritus from Chicago, but still very active in math education). He comes to AMS meetings and is always easily identified: the old coot wearing three different plaids. And yeah, I'd say Chaitin is a mathematician (his bibliography lists something called Conversations with a Mathematician!).

I suppose that `many' of today's greatest mathematicians are in mathematical physics, but (1) I think that's mostly just because m.p. is sexy and that's where the grant money is, and (b) it's certainly not 'most'. Google says the nominees for greatest living mathematician are Grothendieck (who's not just in seclusion, but completely nuts - he insists that Satan is changing the speed of light to upset him), I. Gelfand, Einstein (ineligible), Gauss (ditto), Grothendieck again, Coxeter, and some guy named Joe. I think that's about right.

One way to settle on the greatest living mathematician would be to look and see who's talking at the International Congress of Mathematicians this fall in Beijing. That's certainly an honor (and I think it's indisputable that Hilbert was the g.l.m in 1902, when he gave the ICM talk with the 23 problems). The list is here - I only know about 4 names on it: Chang, Kac, Mumford, and Taylor. I don't really think any of them is anything close to the g.l.m., though Mumford's pretty close (having rebuilt algebraic geometry from the ground up with/against Grothendieck and now having moved on to applied math.).

posted by gleuschk at 7:24 PM on April 29, 2002

Ack! The Hoffman book is really a terrible reference for Erdos, not to mention that Hoffman didn't have the rights to publish the photos he used in the book and really upset Erdos' friends by doing so. (My aunt's brother-in-law is a Hungarian mathematician, who, consequently, knew him fairly well and published a few papers with him (of course).)

posted by mattpfeff at 8:15 PM on April 29, 2002

Graham, that google list is hilarious--thanks.

Would it be fair to say that Hilbert's stock has fallen since Godel's proof?

Florence Nightingale actually appears twice in the history of mathematics.

posted by rodii at 8:41 PM on April 29, 2002

Would it be fair to say that Hilbert's stock has fallen since Godel's proof?

Florence Nightingale actually appears twice in the history of mathematics.

posted by rodii at 8:41 PM on April 29, 2002

I actually (almost alone among math people I know) enjoyed Hoffman's book on Erdos (I don't know how to do the umlaut-thingy). I look at it the same way as A Beautiful Mind, the movie: a good story, just ignore the fact that it allegedly has something to do with a real person.

Rodii, no, I wouldn't say so. Godel's theorems don't really signify all that much to working mathematicians (that I know of). They're fascinating and sobering and all, and he was clearly a genius, but (esp. in algebra, esp. in commutative algebra) Hilbert is all.

posted by gleuschk at 9:24 PM on April 29, 2002

Rodii, no, I wouldn't say so. Godel's theorems don't really signify all that much to working mathematicians (that I know of). They're fascinating and sobering and all, and he was clearly a genius, but (esp. in algebra, esp. in commutative algebra) Hilbert is all.

posted by gleuschk at 9:24 PM on April 29, 2002

I was under the impression that Hilbert's formalist program was more or less wrecked by Godel, though I know his more specific achievements stand. And I guess it's the mathematics that wins the mathematicians over, not the metamathematics, eh? It's another of those distorting effects that outsiders get. I know in my field, non-linguistics people are always saying Chomsky this and Chomsky that, but it's so much more complicated on the ground.

posted by rodii at 9:40 PM on April 29, 2002

posted by rodii at 9:40 PM on April 29, 2002

Also, not the philosophy. That is, philosophers made a huge dealie out of Hilbert's program and Goedel's wreckage thereof, and they have also always had much more interest in logic (even of higher orders) than proper mathematicians do.

And big philosophical conundrums seem to have a way of eeking their way into the public consciousness, albeit in far less rigorous forms.

posted by mattpfeff at 9:54 PM on April 29, 2002

mattpfeff: Haven't read any of the Erdos books. Simply trying to counter rodii's claim that mathematics no longer had personalities. (So, your aunt's B.i.l. has an Erdos number of One.)

I'll also agree that arguing about the g.l.m. is a semantic black hole.

When i first read this FPP, I actually thought it was going to be about Hilbert's 23 problems, how they inspired math in the 20th century and why we dont have something equivalent today.

posted by vacapinta at 11:03 PM on April 29, 2002

I'll also agree that arguing about the g.l.m. is a semantic black hole.

When i first read this FPP, I actually thought it was going to be about Hilbert's 23 problems, how they inspired math in the 20th century and why we dont have something equivalent today.

posted by vacapinta at 11:03 PM on April 29, 2002

That's a great idea for a post, vacapinta. If you don't want to do it, let me know - I'll jump on it.

posted by gleuschk at 6:02 AM on April 30, 2002

posted by gleuschk at 6:02 AM on April 30, 2002

...and the best part is that we do have something analogous today: the Clay Millennium problems.

posted by gleuschk at 6:59 AM on April 30, 2002

posted by gleuschk at 6:59 AM on April 30, 2002

A recently-published, interesting-looking book I saw today: Benjamin Yardell's The Honors Class: Hilbert's Problems and Their Solvers. It describes the 23 problems (a chapter for each, grouped into rough subject areas) and how they were eventually solved. Supposedly for lay people (we'll see).

Isn't the reason for Erdos's fame (in the lay world), though, the fact that he had such an extremely weird personal life, rather than the mathematics? Compare him with, say, Gauss or Euler, whose fame is mainly from their mathematics, not their personal quirkiness (not that Euler, at least, didn't have an interesting life story). There are definitely some mathematicians, though, whose lives almost overshadow their math (Galois, Ramanujan).

(I wonder how much of my sense of the history of math was formed by Eric Temple Bell, who was one of the great mathematical popularizers?)

posted by rodii at 4:18 PM on April 30, 2002

Isn't the reason for Erdos's fame (in the lay world), though, the fact that he had such an extremely weird personal life, rather than the mathematics? Compare him with, say, Gauss or Euler, whose fame is mainly from their mathematics, not their personal quirkiness (not that Euler, at least, didn't have an interesting life story). There are definitely some mathematicians, though, whose lives almost overshadow their math (Galois, Ramanujan).

(I wonder how much of my sense of the history of math was formed by Eric Temple Bell, who was one of the great mathematical popularizers?)

posted by rodii at 4:18 PM on April 30, 2002

I'd guess it's a mix of both. Certainly the Hoffman book was popular, and in no small part because of the weird persona ascribed to Erdos (which I haven't actually asked my relations about). Erdos was also a remarkable mathematician, though -- and while his personal history may have been easier for the public to find fascination with, it was probably the mathematics that made him worthy of the attention in the first place. ...

(Probably I'm only expressing a semantic disagreement with you (rodii), if anything, but there it is.)

posted by mattpfeff at 5:27 PM on April 30, 2002

I'm a relatively math-literate layperson, and I couldn't tell you one thing about Erdos's work--not even about the areas he tended to work in. I just have this vague notion that he kind of did everything, as it swam into his ken during conversations. But I know about his views on "epsilons" and stuff. That's what I mean.

posted by rodii at 5:39 PM on April 30, 2002

posted by rodii at 5:39 PM on April 30, 2002

It's all yours, gleuschk.

(i didnt know that Cohen, disciple of Godel, solver of Hilbert problem, is still alive. Dont know what he's up to, though)

posted by vacapinta at 10:07 PM on April 30, 2002

(i didnt know that Cohen, disciple of Godel, solver of Hilbert problem, is still alive. Dont know what he's up to, though)

posted by vacapinta at 10:07 PM on April 30, 2002

Paul Cohen, winner of Fields medal and National Medal of Science, member of the National Academy of Science, is very much alive and still teaching at Stanford.

Rodii, keep an eye out for Paul Roberts, solver of the 14th problem (he gave a counterexample to a statement about invariant theory) and hell of a nice guy. Drink you under the table, too.

ET Bell was indeed a great expositor of mathematics and mathematicians. Unfortunately, many of his best stories seem to have been made up. He also wrote science fiction (under a pseudonym) and apparently couldn't ever let a dull story go unlivened. (He's also an ancestor of mine, and one of my favorites.)

Erdos mostly did combinatorics, graph theory, and number theory. Nobody has ever seen a mathematician like him before or since. He used to get 6-8 people in a hotel room, station them around it, and go from one to another solving problems with them. By the time they figured out what he meant and where it was leading, he'd be back around the room to blow their minds again. It was like those massively multi-player chess games. Stunning.

posted by gleuschk at 8:27 AM on May 1, 2002

Rodii, keep an eye out for Paul Roberts, solver of the 14th problem (he gave a counterexample to a statement about invariant theory) and hell of a nice guy. Drink you under the table, too.

ET Bell was indeed a great expositor of mathematics and mathematicians. Unfortunately, many of his best stories seem to have been made up. He also wrote science fiction (under a pseudonym) and apparently couldn't ever let a dull story go unlivened. (He's also an ancestor of mine, and one of my favorites.)

Erdos mostly did combinatorics, graph theory, and number theory. Nobody has ever seen a mathematician like him before or since. He used to get 6-8 people in a hotel room, station them around it, and go from one to another solving problems with them. By the time they figured out what he meant and where it was leading, he'd be back around the room to blow their minds again. It was like those massively multi-player chess games. Stunning.

posted by gleuschk at 8:27 AM on May 1, 2002

Jumping in: Rod, I'd guess that one of the reasons that people like mathematicians who lived interesting lives (including Galois, although I'd say Galois is a vastly more important mathematician than the Ramanujan, who had a brilliant intuition but wasn't doing anything particularly groundshaking) is that people don't understand the concepts being discussed. If you don't understand *why* Galois theory is something interesting or why it shocked people that not all extensions of the integers were unique factorization domains (and why should you if you're not a mathematician?), you won't care about the mathematics. Chaos theory and fractals produce neat graphics, are just ontologically interesting, and can be explained in a reasonable way that non-math-oriented people can follow in about two pages. So can the four-color map theorem (although it lacks ontological interest), GĂ¶del's incompleteness theorem (although the explanations you get at that length are usually pretty bad)and the P = NP question. But I don't think even a really talented science writer could do the same with Hilbert space or the Eilenberg-Steenrod axioms or some of the crazy moon talk that Graham puts forth.

Most scientifically literate people know about pi, so Ramanujan's work is more immediately accessible; further, Ramanujan lived an interesting life and had a popular biography written about him. Most scientifically literate people don't know anything about combinatorial topology*, so if you were to see a biography of James Waddell Alexander, I can guarantee you that it would make some Martin Gardner-style stabs at explaining the math but spend most of the time talking about Alexander's life and politics.

* This is not a sin.

posted by snarkout at 8:50 AM on May 1, 2002

Most scientifically literate people know about pi, so Ramanujan's work is more immediately accessible; further, Ramanujan lived an interesting life and had a popular biography written about him. Most scientifically literate people don't know anything about combinatorial topology*, so if you were to see a biography of James Waddell Alexander, I can guarantee you that it would make some Martin Gardner-style stabs at explaining the math but spend most of the time talking about Alexander's life and politics.

* This is not a sin.

posted by snarkout at 8:50 AM on May 1, 2002

Footnote: Rudy Rucker has had at Hilbert space again and again. It seems to be one of his primary founts of inspiration.

posted by rodii at 9:14 AM on May 1, 2002

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posted by gleuschk at 6:26 AM on April 29, 2002