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If you believe in "The Book", it follows that someday mathematicians someday will stop proving the prime number theorem, and the fact that people keep proving it indicates that the Book proof hasn't been found yet. I don't believe in The Book myself, I think which of multiple proofs is most elegant is largely subjective. But I'm not really a mathematician, just a guy who is interested in math.

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Yeah, it's debatable.

Should every proof in the book be based on simple theorems or it's ok to have a "best proof" on advanced proofs.

(That is, assuming that the book is built on the current understanding of mathematics and not some other very different set of axioms)

But I'm afraid if I start talking about it too much we'll end in a confusion of Russel's paradox analogues trying to prove there are infinite possible books for the infinite possible sets of axioms describing math.

what is "The Book"

It’s in the first sentence of the linked article.

“The Book” is the hypothetical collection of “best” proofs for each theorem. “God’s favorite proofs” if you will.

The mathematician Paul Erdős often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. He once said "You don't have to believe in God, but you should believe in The Book."

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