I got into an interesting historical discussion with someone on main a few days ago. People think that Cauchy came up with epsilonics, but he really didn't. It was Bolzano and Weierstrass. There's apparently some erroneous math history publications.
It was coincidental, it was meant to be positive at first, but then I had to treat the other case and it became negative (proving the Raabe-Duhamel rule)
I have actually never found any history of math publication that didn't have a bunch of errors (except for ones about math in antiquity, a lot of those are pretty good)
@SteamyRoot My dad (who's a physicist) always makes fun of Villani cause he found a solution to the Landau equation that lasts $10^{-13}$ seconds or something, and is therefore completely useless
Not quite, I still have 3 exams for polytechnique this week (yup, on weekends), next week is ENS, and the week after that is Centrale (which I will probably not go to cause I'm sick and tired of it)
And a very subtle error in a not-so-good paper that Robert Bryant pointed out to me after the paper had been published. (Counterexample to my claim somewhere in E. Cartan, indeed.)
These were just speculations, but since I won't have much time to make a decision once I know the results (actually, coming to think of it I have to make a decision before the results are published), I'd prefer to take it now
well, Eric, you'll have to deal with something comparable when it comes to grad school admissions. Sometimes you have to stall and hope for a later decision on one you really want ...
I just put a comment, @Alessandro. I believe that right-continuity means that the map $\Bbb R_\ell\to\Bbb R$ is continuous. Then it follows from normality of $\Bbb R_\ell$.
@PVAL-inactive The thing I understand from Lurie is that we have triangulated categories which allows us to do geometry in a very abstract sense and what Lurie is doing is that he is providing a better frame work to doing geometry with $A_{\infty}$ categories which has better axioms than triangulated categories.
That all sounds a bit like "we have abstracts things which allows us to do geometry abstractly, and we have further abstractions which is better than the abstractions already present"
Symplectic manifolds come equipped with A_\infty categories pretty directly, but people then pass to the triangulated world when they do all the annoying algebra.
@BalarkaSen So there is this triangulated category which you could do homotopy theory then there is two ways to do geometry with this either you could do Balmer spectrum. Which is if you have tensor triangulated category you could build a topology out of the tensor product or a second way is to take the derived category of coherent sheaves
I've seen and I think understood proves that various sets of Lagrangians form an Aoo category, but then people somehow yoga things into triangulated categories and do all sorts of magic.
@Ted I think it's a rather remarkable fact for a given symplectic manifold to admit a closed exact Lagrangian at all, so in that sense the cotangent bundle is rather special.
But there is the European (particularly French) convention that $]a,b[$ is how you write open intervals. I sort of like that, to distinguish from ordered pair.
I think the point is more, you choose it over other books on complex analysis not because it's better at complex in particular, but because it's good at technique
Once or twice I have heard the term thrown around of a corresponding integral equation. Therefore, I ask if the following conjectures are true.
For all differential equations $D$ there exists an integral equation $I$, such that $Sol(D) \cap Sol(I) = Sol(D)$.
Note that $Sol(x)$ is the functi...
Once or twice I have heard the term thrown around of a corresponding integral equation. Therefore, I ask if the following conjectures are true.
For all differential equations $D$ there exists an integral equation $I$, such that $Sol(D) \cap Sol(I) = Sol(D)$.
Note that $Sol(x)$ is the functi...
