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

(www.quantamagazine.org)
97 points isaacfrond | 1 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. throw_pm23 ◴[15 Oct 24 18:03 UTC] No.41851247[source]▶
With primes I think a general question is to what extent they are "random". Clearly, they are defined by a fixed rule, so they are not actually random, but they have a certain density, statistics, etc. So we can try to narrow down in what sense they are like random numbers and in what sense not. Do they produce a similar "clustering" or (lack thereof) as if we would generate random numbers according to some density, etc. I see the twin primes question fitting in such a theme. Happy to learn if a number theorist has more insight.