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Comment by t6jvcereio | Hacker News Reader

The Riemann hypothesis is that the zeta function has all its (nontrivial) zeros with real part 1/2. To disprove this you need only to present a single zero with real part != 1/2. So what's that number you found then? No need to write a paper, just show me the number.

I'm not even going to bother opening the link.

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This result is almost certainly bullshit, but there is nothing wrong in principle with a non constructive proof.

Sometimes it is much easier to prove a counterexample exists than to demonstrate that a specific number is a counterexample.

Here's the canonical example of this:

We want to show that there exists irrational numbers a, b s.t. a^b is rational (with b != 0).

If sqrt(2) ^ sqrt(2) is rational then we are done. Otherwise, (sqrt(2) ^ sqrt(2)) ^ sqrt(2) = 2 so that is a counterexample.

In this case, it is possible to prove that sqrt(2) ^ sqrt(2) is irrational, but this requires much more work.

Suppose sqrt(2)=a/b, a reduced rational. Then 2b*b=a*a, so a is even. But the right side has two a's therefore two 2's, so b is even. Contradiction!

You proved sqrt(2) is irrational not sqrt(2)^sqrt(2)

d'oh!

Hmm, while it is in all likelihood not true it doesn't look like your average crackpot and it doesn't look like the proof was posted in bad faith.

Whether you want to put a lot of effort into it is your call but it's still interesting to see what kind of approach they chose.

True, this paper really doesn't look like that of an average crackpot. However, it would be truly astonishing if the RH were to be solved in only 4 pages by some unknown author.

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