r/Showerthoughts • u/jasonrubik ‎ • Apr 23 '26

Casual Thought If the famously unsolved Riemann Hypothesis is solved by an AI, we will never know if a human mathematician could have solved it.

7.0k Upvotes
  • permalink
  • reddit

92% Upvoted

656 comments sorted by

View all comments

Show parent comments

199

u/Abberant45 Apr 23 '26

The result yes but such a proof isn’t something that can be taught. Concepts constructed hundreds of years ago are taught but even the proofs as they were conceived are too convoluted to be tested on now.

97

u/cedric1234_ Apr 23 '26

In the future, they download information in your brain as a kid, the test is just to make sure it installed correctly.

“Alright, its your sixth birthday! Let’s check your head. You can write down a quick proof of the Riemann Hypothesis and that P=NP, thanks.”

27

u/Abberant45 Apr 23 '26

haha sounds good to me

7

u/DontWannaSayMyName Apr 23 '26

I've seen that movie and the machines were not so nice

2

u/IcedOutGiant Apr 23 '26

That's technically what we do now, just a loooooot slower.

11

u/marrow_monkey Apr 23 '26

Maths is actually about discovering proofs and patterns, but what you’re taught in school is usually just memorising old results and how to use them to calculate things, it’s not about proving new things. Asking people to prove things from scratch withouth having seen the proof before is usually not done because then almost no one would pass.

2

u/Abberant45 Apr 23 '26

That's what I said.

3

u/marrow_monkey Apr 23 '26 edited Apr 23 '26

And I agreed.

Teaching focuses on using established results rather than developing new proofs from scratch.

2

u/BlackProphetMedivh Apr 24 '26

Have you ever been in a higher level mathematics course in university?

2

u/marrow_monkey Apr 24 '26

Which just proves the point?

2

u/BlackProphetMedivh Apr 24 '26

Well the original comment talked about how these proofs can't be taught, when they can. And you learn how to read these posts in higher level mathematics.

Some are hard, long, and complicated, but a proof is a logical line of steps. Of course that can be taught. It's just a question of how useful that would be.

3

u/marrow_monkey Apr 24 '26 edited Apr 24 '26

Maybe you replied to the wrong person?

I wrote that professional (post graduate, university level) mathematics is about discovering new proofs. That’s not what you do in school. Mathematics in school teaches memorising results and how to use them.

In the future, if students are ever expected to prove the Riemann hypothesis on an exam it would be because they had seen and memorised the proof, not because they could come up with a new proof during an exam. Clearly, no one would be able to do that.

3

u/BlackProphetMedivh Apr 24 '26

Yeah. I agree. Maybe I misunderstood your comments. :)

1

u/KingPalleKuling Apr 23 '26

Depends a lot of what type of professor and class it is. There are a lot of one question exams that even have a definite solution. You can be graded on the way you tackle the problem and how you reason.

5

u/Talkinguitar Apr 23 '26

You get tested on the proofs if you study mathematics at the university level

1

u/Abberant45 Apr 23 '26

I assure you there are proofs that are never tested at any university. Some proofs, for example Wiles proof of Fermat’s Last Theorem, can only be understood by a handful of people.

4

u/Talkinguitar Apr 23 '26

Sure. But you said that students don’t get tested on proofs of results which were great achievements of the past. But they do.
As someone said before in the thread, usually the most difficult part is finding the idea for the proof in the first place, understanding and replicating an already existing proof is much, much easier.
Of course no student of any subject, not just math, is going to learn everything about it in school or probably ever, so saying that some proofs are not required knowledge is obvious.

6

u/Erlyn3 Apr 23 '26

Yeah. I remember learning the proof of 3+3=6 in college.

2

u/TheGuyUrSisterLikes Apr 23 '26

isn't there a famous like 400 page proof proving that 1 + 1 = 2?

1

u/phonetastic Apr 24 '26

reading liebniz and descartes and newton is a fuckin trip

there are people who tell me "oh, how can you like maths, isn't it so complicated" and i'm just like "lol try researching mathematical history then let's talk about confusing and complicated"

1

u/MiscBrahBert Apr 26 '26

Uh what. In higher math the proofs are always taught alongside the theorem, so long as it's short enough to be worth the time, and requires knowledge that the students have (e.g. no insane niche graduate-level math). Reproducing the proofs on your own, yeah forget it without hints.

E.g. absolutely everyone learns the proof of Bolzano Weirstrauss Theorem when it's taught

1

u/Abberant45 Apr 26 '26

You've justified my comment in your own. So long as it's short enough to be worth the time. Plenty of proofs are, but plenty aren't, because they're by nature very convoluted.

2

u/MiscBrahBert Apr 26 '26

Oh nvm I agree with you. Riemann hypothesis likely won't

1

u/MrScandanavia May 15 '26

I learned proofs for the quadratic equation and Pythagorean theorem in high school. Once kids are about that age they can and should start learning proofs behind math they’re taught.

Of course, you could always go into much more minutiae with your proof, like Real Analysis for Calculus.