John: Sorry, I’m slipping into blogger jargon, which is like pirate speak but without the romance of the sea. Galois has it right. An open thread is a post where commenters can talk about whatever they want.

Galois: The book “Handbook of analysis and its foundations” by Eric Schechter is a general purpose reference for real analysis, but it’s particularly good for the set-theoretic underpinnings of each result.

What is a twistor, and why should I care? I tried to read “Introduction to Twistor Theory” by Huggett and Tod but it definitely seems like it’s written more for physicists than mathematicians.

Where can I find a good text about the applications of Lie groups to physics? When I asked on my own blog, a physicist regular suggested Lie Groups for the Pedestrian, but that text explains Lie theory to physicists, whereas I’m interested in seeing an explanation of physics written for the mathematician.

It’s odd, Alon, but all math/physics books I can recall fall into two types. Either they’re aimed at physicists or they’re aimed at mathematicians and immediately move away from actual physics into unrealistic models.

So here’s what I’d suggest, tailored to the applications in gauge theory: read “Gauge Fields, Knots, and Gravity” first. Then some more technical books to pick up the theory of fiber bundles (with an emphasis on connections in principal fiber bundles). Then go to a real physics book on gauge field theory (not one that purports to teach the math to physicists) and try to see the fiber bundles hiding behind the physicists’ prose.

I really don’t know of a book that would cover, say, the standard model aimed at a mathematician.

I remember Sattinger and Weaver, Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics, being a good book on that subject (but it’s been a long time since I looked at it).

Every time I look someone up in it and go back a few generations I always hit a really famous mathematicians (or physicists) like Gauss, Klein and Boltzmann. It doesn’t matter what area they work in, it always seems to go back to the same people.

Am I right to conclude that all doctoral supervisors from ~120 years ago were famous?

sigfpe: No, it’s just that the minor figures didn’t have many advisees of their own, and their lines have died out.

There’s a similar effect in actual genealogies. Almost everyone of Irish descent can trace ancestry to Niall of the Nine Hostages. Most people of German descent goes back to Charlemagne. And other than a few trace examples everyone of east Asian descent can go back to Genghis Khan.

Meaning what?

yes!

Does anyone know a good book about axiomatic math, i.e. ZF vs. ZFC vs. ZF + Lebesgue measurability? Perhaps something as much a history as a textbook?

I think he means just leaving a thread as a forum where I can post questions like above…

John: Sorry, I’m slipping into blogger jargon, which is like pirate speak but without the romance of the sea. Galois has it right. An open thread is a post where commenters can talk about whatever they want.

Galois: The book “Handbook of analysis and its foundations” by Eric Schechter is a general purpose reference for real analysis, but it’s particularly good for the set-theoretic underpinnings of each result.

Okay. Having my own blog, I don’t have any vast urge to talk about whatever I want on yours. But, it might be a nice thing for you to try.

What is a twistor, and why should I care? I tried to read “Introduction to Twistor Theory” by Huggett and Tod but it definitely seems like it’s written more for physicists than mathematicians.

Where can I find a good text about the applications of Lie groups to physics? When I asked on my own blog, a physicist regular suggested Lie Groups for the Pedestrian, but that text explains Lie theory to physicists, whereas I’m interested in seeing an explanation of physics written for the mathematician.

It’s odd, Alon, but all math/physics books I can recall fall into two types. Either they’re aimed at physicists or they’re aimed at mathematicians and immediately move away from actual physics into unrealistic models.

So here’s what I’d suggest, tailored to the applications in gauge theory: read “Gauge Fields, Knots, and Gravity” first. Then some more technical books to pick up the theory of fiber bundles (with an emphasis on connections in principal fiber bundles).

Thengo to a real physics book on gauge field theory (not one that purports to teach the math to physicists) and try to see the fiber bundles hiding behind the physicists’ prose.I really don’t know of a book that would cover, say, the standard model aimed at a mathematician.

I remember Sattinger and Weaver,

Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics, being a good book on that subject (but it’s been a long time since I looked at it).The complement of an open thread is a closed thread. It is possible for a thread to be neither open nor closed, e.g., the half-closed thread (0,1].

You know the mathematics genealogy project: http://genealogy.math.ndsu.nodak.edu/

Every time I look someone up in it and go back a few generations I always hit a really famous mathematicians (or physicists) like Gauss, Klein and Boltzmann. It doesn’t matter what area they work in, it always seems to go back to the same people.

Am I right to conclude that all doctoral supervisors from ~120 years ago were famous?

sigfpe: No, it’s just that the minor figures didn’t have many advisees of their own, and their lines have died out.

There’s a similar effect in actual genealogies. Almost everyone of Irish descent can trace ancestry to Niall of the Nine Hostages. Most people of German descent goes back to Charlemagne. And other than a few trace examples everyone of east Asian descent can go back to Genghis Khan.