# Who determines if a mathematical proof is valid? [closed]

I'm studying mathematics and as you all know the most important things in mathematics are proofs.

My question is, who determines if a proof that someone invents in mathematics is valid? Is there some mathematics professors who check all people's proofs in the world?

If I invented a new proof, where do I send it to? Can anyone invent their own mathematical proofs?

## closed as too broad by Qiaochu Yuan, kjetil b halvorsen, JonMark Perry, user91500, SchrodingersCatNov 18 '15 at 12:44

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• In general it is a social process. If a published result is deemed important then many people will read it and find bugs in the proof. Maybe. – copper.hat Nov 18 '15 at 7:41
• For a proof of a theorem to be validated, a searcher needs to communicate on his proof. He needs to explain it in some conferences and also to find a journal of mathematics to publish it, when he sends his proof to the journal a so-called "reviewer" will review his proof, if the reviewer decides that it is worth be published then it is published. Finally when "enough" mathematicians have seen the proof and nobody found a problem people consider the proof to be valid. – Clément Guérin Nov 18 '15 at 7:42
• Wow @ClémentGuérin thanks for explaining. My next question is are there examples of proofs who were accepted but then 100 or 200 years later were discovered to be invalid? – bodacydo Nov 18 '15 at 7:44
• @bodacydo, as far as I know the system is efficient, so there are no spectacular examples but for instance you have a French book called "Infirmation de l'hypothèse de Riemann" (rough translation : the Riemann hypothesis is false). The book exists (I had it in my hands when I was a student) and pretends to prove that Riemann hypothesis is false. The book is actually a proof (I don't say anything about the validity of the proof) with a lot of mathematics. The point is that the author did not follow the usual steps (publication in a journal rather than using an editor of "norrmal" books) – Clément Guérin Nov 18 '15 at 7:55
• Usually they're not totally invalid. One example is that Euclid thought he had pinned down all the axioms he needed for Euclidean geometry, but he accidentally used his intuition to derive some results, and so technically those proofs are wrong because they do not follow from the axioms that he specified. More than 2000 years later, this was pointed out by Pasch, and the extra axiom needed is called Pasch's axiom. Euclid also did not specify clearly axioms stating the invariance of certain quantities under Euclidean transformations, so by modern standards his proofs were not completely solid. – user21820 Nov 18 '15 at 7:59