Wrong proofs of Riemann hypothesis

[Silviu]

Hello! I read some stuff about the Riemann hypothesis and the formulation seems pretty clear. I also read that many proof of it (well basically all of them) are wrong. I was just wondering in which way are they wrong? (I haven't find a page with the wrong proofs, together with explanations of why they are wrong) Some proofs are 2 pages long and I assume that people with good knowledge in the field attempted to prove it. So how can they be wrong, without being aware of it? Thank you!

 

[mfb]

Most people with good knowledge in the field don't think they have a proof. If someone claims "I have a proof", especially if it is just 2 pages long, you can bet that this person doesn't know much about mathematics.

Wrong proofs typically have one of those flaws, or a combination of them:
- The author doesn't even understand what the question is about and the whole "proof" is incoherent nonsense.
- The proof includes a step "A => B" where B does not follow from A. Sometimes A follows from B and the author doesn't understand the difference.
- The proof contains some generalization that is not valid, e. g. it is assumed that every integer satisfies some condition, but numbers divisible by 13 don't do that.
- Some stupid mistake. An addition mistake or similar.

There are many ways to wrongly claim A=>B, some more obvious, some much more subtle.

A good way to check proofs is often to test them where the result is known. As an example, you can find hundreds of simple (!) "proofs" of Fermat's last theorem. Half of them don't even put conditions on the exponent - if they would be valid, there would also be no a,b,c such that a+b=c or a²+b²=c². That is obviously wrong - you can tell the proof has to have a mistake without even looking at the individual steps.