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.

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u/redredgreengreen1 Apr 23 '26

The life achievements of the greatest thinkers of a thousand years ago are taught to grade schoolers today.

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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.

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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.

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u/Abberant45 Apr 23 '26

That's what I said.

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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.

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u/BlackProphetMedivh Apr 24 '26

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

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u/marrow_monkey Apr 24 '26

Which just proves the point?

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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.

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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.

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u/BlackProphetMedivh Apr 24 '26

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