Anonymous at Fri, 25 Oct 2024 08:41:12 UTC No. 16448624

Try Jane Street's monthly puzzle:
>https://www.janestreet.com/puzzles/current-puzzle/
You can walk into a $250k salary if you can come up with an elegant solution.

Anonymous at Fri, 25 Oct 2024 09:12:32 UTC No. 16448645

>>16448608
In mathematics, most of the problems the best and brightest are struggling to figure out involve the interactions between anabelian geometry and the general solutions to geometry obtained by manipulation of set-valued prestacks. So start reading up on prestacks, my guy.

Anonymous at Fri, 25 Oct 2024 09:24:43 UTC No. 16448655

>>16448608
Depends on you personally. I had an abstract algebra professor who said he sucked at analysis. I also had an analysis professor who said he sucked at abstract algebra. Both were very respected in their own fields.

Anonymous at Fri, 25 Oct 2024 09:27:09 UTC No. 16448657

>>16448608
Create some differential equations of your own and then try to solve them.

Anonymous at Fri, 25 Oct 2024 09:28:55 UTC No. 16448658

>>16448608
Calculus is hard

Anonymous at Fri, 25 Oct 2024 10:24:30 UTC No. 16448694

>>16448608
Navier-Stokes equations. The general forms are unsolvable but in certain scenarios it's quite useful.

Anonymous at Fri, 25 Oct 2024 10:26:32 UTC No. 16448698

>>16448694
Most non-linear diffeqs are unsolvable. Even something as simple as the three-body problem. The main issue with NS is existence and uniqueness of solutions and not finding the actual solutions. We have state-of-the-art numerical methods for the latter, but the former would guarantee that these methods won’t fail at some weird edge case.

Anonymous at Fri, 25 Oct 2024 11:04:18 UTC No. 16448728

>>16448698
Can't you just plot some non-solutions in the phase space and expand their neighbourhoods until you hit the contour of the solution surface(s)?

Anonymous at Fri, 25 Oct 2024 11:06:22 UTC No. 16448730

>>16448728
There is no guaranteed unique solution. That’s what the Millennium prize is for. Proving that there is. Your method is not guaranteed to work until there is proof of existence and uniqueness.

Anonymous at Fri, 25 Oct 2024 11:25:11 UTC No. 16448737

>>16448608
Topology in higher dimensions