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

(www.quantamagazine.org)
97 points isaacfrond | 2 comments | 15 Oct 24 13:10 UTC | HN request time: 0s | 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. madars ◴[15 Oct 24 17:07 UTC] No.41850663[source]▶
It's not arbitrary at all! We know that primes themselves get rarer and rarer (density of primes < N is ~1/log(N)), so it is natural to ask whether the gaps between them must also necessarily increase and, in general, how are they spaced.
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2. l33t7332273 ◴[15 Oct 24 18:27 UTC] No.41851566[source]▶
We know the primes are rich in arithmetic progressions (and in fact, any set with positive “upper density” in the primes is also rich in arithmetic progressions).

So we do know that there are 100,000,000,000! primes that are equidistant from one another, which is neat.