Very interesting question. I thought a lot why some math facts seem boring to me while others are interesting, sometimes exciting.
I believe interesting math facts are interesting because they clash with intuition. Like you expect some freedom for a second prime factor to be anything it likes, but no, it has a very small median.
I misunderstood the claim at first, counted primes in reverse order and was really surprised by an idea that second largest prime factor is so small and started to think of Eratosthenes but continued to read. When I discovered my mistake and then it came to Eratosthenes it got almost obvious and not interesting really, I didn't even read it when it got techical. Though if not my disappointment I'd probably found it interesting, because while I believe I could find 37 as a median and prove it without any hints, I would need a nudge: I needed to be told that median of a second prime factor is a small number.
I believe that the practice of noticing these confusions and resolving it is a basis of a mathematician's mind. As a mathematician you need a highly tuned intuition that matches real theorems, because you start with intuition, formalize it as a theorem and then you look for a proof.
Intuition guesses theorems to prove or to look in literature. But if my intuition can be surprised by some fact it means it cannot guess it. And probably it cannot guess a lot of other related facts.
I believe interesting math facts are interesting because they clash with intuition. Like you expect some freedom for a second prime factor to be anything it likes, but no, it has a very small median.
I misunderstood the claim at first, counted primes in reverse order and was really surprised by an idea that second largest prime factor is so small and started to think of Eratosthenes but continued to read. When I discovered my mistake and then it came to Eratosthenes it got almost obvious and not interesting really, I didn't even read it when it got techical. Though if not my disappointment I'd probably found it interesting, because while I believe I could find 37 as a median and prove it without any hints, I would need a nudge: I needed to be told that median of a second prime factor is a small number.
I believe that the practice of noticing these confusions and resolving it is a basis of a mathematician's mind. As a mathematician you need a highly tuned intuition that matches real theorems, because you start with intuition, formalize it as a theorem and then you look for a proof.
Intuition guesses theorems to prove or to look in literature. But if my intuition can be surprised by some fact it means it cannot guess it. And probably it cannot guess a lot of other related facts.