Post #2125752

2026-05-02 15:23 UTC

The reason the Erdős problems are interesting is that he set them with the idea that solving them would require some new understanding, which was the real goal; if it happens that the problem can be solved “simply” by aggregating existing understanding (even in a very sophisticated and expensive way), it indicates only that the setting of the problem failed in its goal. You aren&#39;t going to use the solution to an Erdős problem to suddenly crack the problem of economical nuclear fusion or quantum error correction or some other thing of economic significance. It&#39;s a herald only.

Replies (2)

@jonmsterling@mathstodon.xyz 2026-05-02 15:27

In mathematics, the nature of the solution matters a lot. If you solve an open problem using only old techniques, people will take it as proof that the person who made the conjecture simply missed a trick, and you don't really get rewarded by the Mathematical community very much. If on the other hand, your solution to an open problem provides compelling evidence that the problem really couldn't have been solved without new ideas, and your solution contains those new ideas, then you are going to be rewarded with prestige, money, jobs, grants, etc. Mathematics has always been about the ideas. Even in problem-oriented areas, where seemingly weird / useless problems are strategically placed like mines as Idea Heralds.

Open ##2644271
@ofc1996@mathstodon.xyz 2026-05-02 15:36

@jonmsterling@mathstodon.xyz I don't think he did that, at least not conciously. He was writing a paper a week at some points in his career. I think an Erdos problem just meant "I couldn't immediately see how do this."

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