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Big advance on simple-sounding math problem was a century in the making

(www.quantamagazine.org)
129 points isaacfrond | 1 comments | 15 Oct 24 13:10 UTC | HN request time: 0.209s | source
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nomilk ◴[15 Oct 24 16:30 UTC] No.41850289[source]▶
How do mathematicians come to focus on seemingly arbitrary quesrions:

> another asks whether there are infinitely many pairs of primes that differ by only 2, such as 11 and 13

Is it that many questions were successfully dis/proved and so were left with some that seem arbitrary? Or is there something special about the particular questions mathematicians focus on that a layperson has no hope of appreciating?

My best guess is questions like the one above may not have any immediate utility, but could at any time (for hundreds of years) become vital to solving some important problem that generates huge value through its applications.

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1. bena ◴[16 Oct 24 13:29 UTC] No.41858843[source]▶
That is a large part of it. Maybe that solving this problem leads us to the answer to other problems.

If you could prove the twin prime conjecture, that means you have figured out something about prime numbers. If you found a pattern or formula for figuring out the distances between twin primes, that means you're able to identify certain primes.

And maybe that formula becomes the basis for a formula for the distance between primes in general. And once you have that formula, you have a simple way to test for primes.

And I'm not saying that is happening or will happen or is even possible, but that would be a reason to study proofs of the twin prime conjecture.