theHigherGeometerApr 8

Hilbert, by Constance Reid.

A great book, showing David Hilbert's passage from a bold young and ambitious mathematician to an old man surrounded by the ruin of the mathematics department in Göttingen in the 1930s. This helped me place a lot of names of contemporaries, and I can appreciate Minkowski's truncated career much better, I had no idea how big a deal he was in this whole circle, nor that he died early. The author treats the mathematics very well even though she's not trained in it, and from a modern standpoint it helps me connects back from post-1930s work to the previous generation's revolutionary developments.

Electronic version: https://doi.org/10.1007/978-1-4612-0739-9

#Read2026

Show threadJohn Carlos BaezApr 8

@highergeometer - I may have read this once; I should read it again!

Minkowski was more than Einstein's teacher - the guy who realized time is imaginary - but I don't know his whole institutional role.

Show threadTony Vladusich

@johncarlosbaez @highergeometer

I’ve been reading Gravitation by MTW. They seemed very unimpressed with Minkowski’s ict formulation. They even devote a small section to its “banishment”. 🤣

Apr 8 at 5:39amWeb
Show threadDavid QuinteroApr 8
@TonyVladusich @johncarlosbaez @highergeometer yet using time as imaginary was a key ingredient for the no boundaries proposal by Hawking and Hartle about the origin of the universe. You know, ideas obey Nietzsche's eternal return.
Show threadtheHigherGeometerApr 8

@davidsuculum I think it's ok as a technical crutch, but actually doing the Wick rotation using imaginary time is nontrivial. Witness @peterwoit slow burn trying to come to grips with how this is supposed to work on a serious level of modern math physics, even without fancy proposals for universe origins.

@TonyVladusich @johncarlosbaez

Show threadJohn Carlos BaezApr 8

@highergeometer - Woit is trying to come to grips with how the Osterwalder-Schrader theorem doesn't cover spinor fields.

@davidsuculum @peterwoit @TonyVladusich

Show threadJohn Carlos BaezApr 8

@TonyVladusich - in MInkowski spacetime the use of imaginary time is fundamental to a lot of work on quantum field theory - by which I mean not just writing the metric using 𝑖𝑐𝑡 as Minkowski did, but treating Minkowski spacetime and Euclidean spacetime as two different 'slices' of a 4-dimensional COMPLEX spacetime, allowing the use of complex analysis. I'm talking about things like the Osterwalder-Schrader theorem:

https://ncatlab.org/nlab/show/Osterwalder-Schrader+theorem

But in general relativity, where we have no favored coordinates, this is much more problematic, ... though Hawking made extensive use of it, using the relation between imaginary time and inverse temperature.

@highergeometer @davidsuculum