Math field for a literal genius?

I don't get why you equate hard to intuit with worthwhile?

what are your goals?

>>8467155
Algebraic topology is a prerequisite for most research, but it isn't a research field.
It's like saying that you're researching trigonometry.

>>8467157
Not hard to intuit, hard to understand. There are honestly difficult subjects. If I'm going to continue doing math, at least I want to do something smug and to be looked with awe by other mathematicians.

>>8467164
Yeah I get that, but that's my limited experience.

>>8467171
>limited experience
What's your current mathematical background?

>>8467175
I finished my AP Calculus with great grades.

>>8467175
I did not graduate in may but everything at undergrad level with few selected topics at grad level. Measure theory, set theory, logic, real and complex analysis, topology, etc... you name it. I have a solid background except for algebra (except for Lie algebras).

>>8467188
>may
Math.

>hardest
number theory

number theorists have spent hundreds of years trying to understand zeta functions and it's the only field to have more than one millennium prize problem. similarly of hilbert's 23 problems, 2 of the 3 that are still unsolved are in number theory.

>>8467155
Number theory.

>>8467188
>Measure theory, set theory, logic, real and complex analysis, topology
None of those are graduate courses, but you're set up very well for stochastic analysis, which fortunately for you has a very active research field.
Speaking of which, my university has someone who obtained a fields medal in stochastic pdes:
https://en.wikipedia.org/wiki/Martin_Hairer

>>8467196
>>8467201
Lang mentions something about the Szpiro conjecture in Undergrad. Algebra. Truly fascinating that the conjectures are easily understood, yet they are crazy difficult to prove.

>>8467217
>Szpiro conjecture
extremely unlikely anyone in undergraduate algebra knows enough about elliptic curves to fully understand the statement of the conjecture, but i guess you could give the equivalence with the abc conjecture which is much easier to understand

File: szpiro.png (24KB, 655x134px) Image search: [Google]

24KB, 655x134px

>>8467221
Lang - Undergraduate Algebra.
Paragraph IV-10. The abc Conjecture.

>>8467264
just looked it up in the book and what he calls the 'generalized Szpiro' conjecture is just the 'commonly accepted' Szpiro conjecture stated for one single elliptic curve instead of all elliptic curves

it's nice that he brings it up in connection to abc but it really doesn't tell you what's supposed to actually be happening in the world of elliptic curves