What's the hottest topic on Mathematics this days, friends?

>>8240261

Proving integration by parts.

It truly is amazing to think that after centuries of blind acceptance, no one has yet found a completely rigorous proof of this simple (conjectured) identity.

>>8240263
gtfo

P = NP

>>8240261
Triple integrals.

>>8240261

The Poincare conjecture.

>>8240268
>t. undergrad

>>8240261
Creating numbers large enough to describe how massive your mother is.

machine learning

>>8240261
HoTT, that shit literally prints grant money.

abc conjecture
riemann hype

>all these shitposts

i'm not entirely sure, but i'd be willing to bet algebraic geometry is what all the cool kids are doing

>>8240261
Harnack inequalities...

get it? Because they model heat-like PDEs?

that prime numbers thing

File: 1387738259495.png (504KB, 610x720px)

504KB, 610x720px

>>8240261
Any announcement from this guy? Did he really solve ABC conjecture?

>>8241043
You mean the Riemann hypothesis or the Zhang-Proof-Thing, which says that there are infinitely many primes that are at max 70000000 apart?

>>8241130
its much lower than 7000000

>>8240261
Stochastic calculus.

File: 1455482022681.gif (4MB, 280x175px)

4MB, 280x175px

>>8241172
sauce?

>>8241342
polymath 8a and 8b

>>8241342
What the fuck is going on here??!?!?!?!?!

>>8240276
Already proven by Grigory Perelman.

>>8241510
no he proved Barnett's Identity

>>8241369
owels

>>8240263
d/dx ( f(x) g(x) ) = f'(x) g(x) + f(x) g'(x) |Integrate both sides
f(x) g(x) = Integrate[f'(x) g(x), x] + Integrate[f(x) g'(x), x]
<=>
Integrate[f(x) g'(x), x] = f(x) g(x) - Integrate[f'(x) g(x), x]

P = NP

Proving this will forever change the future.

>>8241724
I expect P != NP

>>8241724
I expect P = NP but with some catches that make it harder to utilise

>>8241179

This!!!

>>8240784
The best environment for doing derived algebraic geometry is in (∞,1)-categories and -topoi, so really homotopy theory is a great language for doing algebraic geometry. This brings us to motivic geometry and all that jazz. So, one could say in that vein that homotopy theory, algebraic geometry, spectra, Eckmann-Hilton related stuff, and QFT are all at the forefront of algebraic geometry. These are also very active fields!

>>8241128
There was recently a major conference dedicated to digging into it, and things are looking really good. Another conference is coming this winter to further the whole thing, and we should have a verdict within the next year, if not sooner.

>>8241724

Why is it not written as [math]\mathrm{P} \subsetneq \mathrm{NP}\,?[/math] This whole equal sign thing is what confuses the normies and cranks im pretty sure

>>8242283
>a major conference

name of conference please

>things are looking really good

give me the crude, bullet point version of why

>within the next year, if not sooner

where does that time frame come from? why not two years or three years?

>>8242406
The basic question is whether or not the two sets are precisely equal.

>>8241128
Take your pedophile cartoons back to >>>/a/.

>>8241724
Is there a quality video explaining this problem? Thanks.

>>8243406
Here.

https://www.maths.nottingham.ac.uk/personal/ibf/files/kyoto.iut.html

>>8243658
youtu.be/YX40hbAHx3s

>>8243687
Is it of good quality? I'm a computer engineer who needs to send it to a mathematician friend of mine.

>>8243690
It's a great video. It's not a technical video, but it talks about the relevant topics well and in depth.

>>8243690
What's your problem with wikipedia?

>>8243677
Oh, and, I estimated under a year because a MathOverflow post regarding this conference ended up informing me that some of the major obstacles in the proof being true (including some vital inequality) ended up being certainly true, and there was a lot of optimism going on between all of this algebraic geometry experts.

>>8241128
>>8242283
>>8243406
>>8243677
>>8243705

http://www.nature.com/news/monumental-proof-to-torment-mathematicians-for-years-to-come-1.20342

Still, Kedlaya says that the more he delves into the proof, the longer he thinks it will take to reach a consensus on whether it is correct. He used to think that the issue would be resolved perhaps by 2017. “Now I'm thinking at least three years from now.”

>>8243817
I see, thank you!