I recently acquired a copy of the new volume 6 of Atiyah’s collected works, which contains things he wrote from the late eighties until very recently (the latest article is his joint paper with Graeme Segal on twisted K-theory). Unfortunately the price of this book is very high (about $200). I’ve bought cars for less than what I paid for the book.
Even more expensive is the full six-volume set, which Oxford intends to sell for $1000. Luckily I bought the previous 5 volumes quite a few years ago at a somewhat more modest price. Atiyah is one of my great heroes among mathematicians. He’s up there among the top very few in any reasonable list of the greatest mathematicians of the second half of the twentieth century, and the extent of his influence in bringing together mathematics and physics is hard to overestimate. Witten’s great work on topological quantum field theory was done very much because of impetus from Atiyah. One of the articles in the new volume is the write-up of Atiyah’s amazing talk at the Weyl Symposium in 1987, where he first suggested that there should be a four-dimensional QFT whose observables were Donaldson invariants and whose Hilbert space was Floer homology.
Atiyah is also known as Sir Michael. Before I heard about this I had always thought that the British system of honorary knighthoods was pretty silly, but the fact that they chose him gave me some respect for the whole system.
It’s a shame the books are so expensive, since they are wonderful documents that deserve wide distribution. Atiyah has not only discovered wonderful new mathematics, but he writes about it in an elegant, inspiring and lucid way. The books contain many expository pieces he has written over the course of his career, and these are pretty much all well worth reading. I regard a large part of my mathematical education as having come from spending a lot of time with these volumes over the years.
Thanks for pointing out the problem with the link, should be fixed now.
I don’t know if it’s just me, but the link on twisted K theory doesn’t work.
As for problem solvers? Um, Erdos is the only one that comes to mind for me at least.
Yes, they are expensive book,
but that are $200 when compared with the $1200 of
the Handbook of Molecular Physics and Quantum Chemistry by Whiley?
Noam Elkies (Harvard math) classified mathematicians in broadly two categories: “theory builders” and “problem solvers”. All three in the list are theory builders. Anyone know of major figures in the problem solver category (like Erdos)?
“About Beilinson and Drinfeld. They could learn a lot about exposition from Atiyah, Serre or even Grothendieck. Their writings make SGA look like a marvel of simple, lucid expository prose.”
Hahaha. Did you poke around their recent text? (Chiral Algebras, I believe)
But anyways, I agree; it isn’t pretty at all!
🙂
I didn’t include Weil in my list of greatest mathematicians of the second half of the twentieth century since much of his most important work was done in the 30s and 40s.
As for ranking Atiyah, Grothendieck and Serre; I guess I just don’t think their achievements are commensurable. All three have done amazing things, but of quite different kinds.
About Beilinson and Drinfeld. They could learn a lot about exposition from Atiyah, Serre or even Grothendieck. Their writings make SGA look like a marvel of simple, lucid expository prose.
Interesting thoughts. I guess it’s hard (or perhaps a bad question to pose in the first place) about who is the “better” mathematician. Hm. Personally I’d lean towards Weil, Grothendieck or Serre.
…
BUT since I’m at U of C, I have an obligatory vote for Beilinson and Drinfeld.
Didn’t Andrew Wiles (of the Fermat’s last theorem fame) also get a British knighthood a few years ago?
If I had to list the greatest mathematicians of the second half of the twentieth century, I’d choose Atiyah, Grothendieck and Serre. Grothendieck and Serre are much more algebraists than Atiyah, who is much more a geometer than an algebraist. The parts of mathematics that have interacted strongly with physics in recent years have been much more geometrical than algebraic. So of these three, because my main interests lie at the intersection of math and physics, Atiyah is the one whose work I have found most directly relevant.
Grothendieck is an amazing figure, and he had a revolutionary impact on mathematics during the fifties and sixties. Unfortunately for mathematics, he stopped doing research during the seventies. If he had remained active, it would have been very interesting to see his reaction to the new ideas coming into mathematics from physics during the late seventies and eighties.
And what are your thoughts on Grothendieck? Just curious. I’ve read of some of his work (Riemann Roch, etc), but I was curious of what you thought about it.
Best,
Anon
Peter said: “It’s a shame the books are so expensive, since they are wonderful documents that deserve wide distribution. Atiyah has not only discovered wonderful new mathematics, but he writes about it in an elegant, inspiring and lucid way. The books contain many expository pieces he has written over the course of his career, and these are pretty much all well worth reading. I regard a large part of my mathematical education as having come from spending a lot of time with these volumes over the years.”
Peter, books will get even more expensive in the next hundred years, since they are becoming antique and outdated. Try to buy a mechanical typewriter today and it will probably cost you more than an old car, if you could ever find one.
We are now in an age where information is more readily distributed and accessed through electronic means, it makes less and less sense to rely on dead trees that can decay and rot, as means of dissipating information. Both for the sake of environment protection, and for the sake of not letting book shelfs clog up the limited living space of your home, it is better to avoid buying books at all if you can.
I have accumulated books that fill cabinets lining up a whole 20 feet of wall at my home. Most of them contain outdated and useless information and I do not know what to do with them since I rarely have time to read any of them. I have stopped buying books where similar information is already accesible on the web.
As for the expensiveness of books. Part of it goes to the cost of killing trees and make paper and printing on them. A little part goes to the loyalty of the authors. And the biggest chunk goes to the greedy commercial publishers, especially publishers of scientific materials.
I think if it were not for publishers, today’s scientific information would have been much more readily available on electronic medias and for very low cost or even free. wouldn’t most paper authors agree that they would be happier if more people can access their work more easily? So publishers are really an obstacle to science developments.
Quantoken
I am glad Atiyah has chosen Edinburgh University, my old undergraduate stomping ground. (Higgs is there too). I don’t know where publishers get their prices for these kinds of books. There are many such books out there I would like but simply can’t afford. If they would put out good paperback versions at reasonable prices I am sure they would actually make more money and shift more copies. Students (and even some professors) don’t have that kind of money to spare. Incidently, Sir Roger Penrose has a knighthood too.