/sci/ - Science & Math

>>11407982
>Jacobi died in 1851
>AMS founded in 1888

>>11330975
Given [math]f[/math] AC in [math]x[/math] and [math]L^1[/math] in t, and [math]\alpha[/math] Lipschitz in [math]x[/math] and BV in [math]t[/math], the Riemann-Stieltjes integral [math]F: x\mapsto \int_E d\alpha_x(t) f(x,t)[/math] is differentiable in the weak sense on a Borel set [math]E\subset\mathbb{R}[/math]. This suffices to prove your statement.

>>11107831
>spectral measure
>not some dollarstore EMF sensor

>>11071867
Spectral sequences that don't collapse at degree 2.

>>9062945
> now I want to see whats going on there...
Even just talking to a CS student is a pain in the ass lol.
>the lack of rigor is a problem in my opinion
Well sure, but you have to know that much of the "handwaving" had been rigorously formalized over the past several decades. Things like second quantization, Wick rotation, Wilson loops, chiral Ward identities, functional determinants, gauge fixing/ghosts, even theory of renormalization groupoids etc. all have adequately sound mathematical grounding. Once you've understood them it'd be hard to call all of physics "handwavy".
>a) increases the chance of errors
This I don't agree with. Physics is all about estimating real world phenomena and not about mathematical precision. If making phenomenological heuristics leads to the right description then that can't be considered an "error". Besides, following every single minute mathematical detail isn't guaranteed to lead us to the right physical picture, or even anywhere at all. Indeed (so far) constructive QFT can only define free boson/fermion fields, geometric quantization can only recreate WKB approximations in QM and a rigorous treatment of many-body phenomena can only deal with delta-function interactions.
>b) makes papers a lot harder to read
Depends on what kind of papers I guess. As I said, breakthroughs in physics aren't made with theorems and proofs so you can't expect every single author to cater to what you're used to. There are physics texts (e.g. Lehmann, Bertlmann) that follow the theorem/proposition [math]\rightarrow[/math] proof structure though, which I believe would give mathematicians the physical intuitions needed to read physics papers.
However what I've noticed is that there are more physicists that are willing to deal with this language barrier than mathematicians (this is anecdotal of course). You can't expect us to do all the work in bridging this gap.