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Comment by iLoveOncall | Hacker News Reader

> To give a sense of the scale of this claim: If correct, Zhang's work is the most significant progress towards the Generalized Riemann Hypothesis in a century.

Thanks, that totally failed to give any sense of scale.

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It's the moral equivalent of making major headway against P!=NP; or, proving that there are no global hidden variables in QM; or, that there's a clear path ("just engineering") to room-temperature semiconductors.

>room-temperature semiconductors

I suppose superconductors. Semiconductors are well in the room temperature regions :)

the path is just really, really clear

I can't decide if this is my favorite autocorrect, or least favorite. I'll let it stand — mostly because it's too late to edit!

I feel like saying this is similar to making progress on P!=NP is not accurate (extreme disclaimer: I have no formal math training). My understanding of P!=NP is that an answer to that has strong implications for the nature of the concept of determinism _of reality_, let alone most cryptography and lots of other stuff too. From my quick scan of the GRH wikipedia article, it doesn't appear that the GRH has the same widespread almost philosophical implications as P!=NP.

I think P != NP is extremely interesting, but I wouldn't say it has strong implications for the nature of the concept of determinism or reality. I think that the idea of a Turing machine / the notion of computability has deep philosophical implications, but even that I wouldn't say has implications for "the nature of reality."

If you think that prime numbers are interesting, then I can tell you that GRH is the single most central conjecture in the study of prime numbers. Personally, I think prime numbers are some of the most fundamental and intrinsically interesting objects in pure math, but of course, this is subjective!

>has deep philosophical implications, but even that I wouldn't say has implications for "the nature of reality."

what would be an example of "deep philosophical" implication that has no bearing on the "nature of reality"

>Moreover, I think this result would not only be a more significant advance than Zhang's previous breakthrough, but also constitute a larger leap for number theory than Wiles' 1994 proof of Fermat's Last Theorem (which was, in my opinion, the greatest single achievement by an individual mathematician in the 20th century).

Was the rest of the context not more enlightening?

E.g. Would constitute a larger leap than proving Fermat's Last theorem which was "the greatest single achievement by an individual mathematician in the 20th century"

After a glimpse to the Generalized Riemann Hypothesis wiki page, I'm afraid there's no football stadium or olympic pool for us.

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