I will always find these type of explorations fascinating. Number theory is so mysterious. I liked these two sentences from the article:
> “Mathematics is not just about proving theorems — it’s about a way to interact with reality, maybe.”
This one I like it because in the current trend of trying to achieve theorem proving in AI only looking at formal systems, people rarely mention this.
And this one:
> Just what will emerge from those explorations is hard to foretell. “That’s the problem with originality,” Granville said. But “he’s definitely got something pretty cool.”
When has that been a "problem" with originality? Hahah but I understand what he means.
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.
youoy ·8 hours ago
> “Mathematics is not just about proving theorems — it’s about a way to interact with reality, maybe.”
This one I like it because in the current trend of trying to achieve theorem proving in AI only looking at formal systems, people rarely mention this.
And this one:
> Just what will emerge from those explorations is hard to foretell. “That’s the problem with originality,” Granville said. But “he’s definitely got something pretty cool.”
When has that been a "problem" with originality? Hahah but I understand what he means.
nomilk ·7 hours ago
> 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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paulpauper ·7 hours ago
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