[electronvolt]

Proofs are actually incredibly hard to review. Problems will be found in what had been accepted to be a "good" proof years to decades later. There's a whole movement to move proofs over to something/anything more verifiable (e.g. representing all proofs in Coq--but even then you're relying on the Coq proof assistant to have zero bugs).

Furthermore, the standard for mathematical proof has also changed over time, most significantly in the early 20th century. This led to a number of existing results needing to be re-proved (or thrown out! Some were incorrect!).

Exactly what qualifies as a proof is a FASCINATING debate. Mathematics is created by consensus, just like all other knowledge.

[killjoywashere]

Proving a math problem is mentally challenging, but there are other interesting definitions of hard. In medicine, for instance. None of it requires particularly fancy logic. But can you cite any instances in math here you had to invest, say, $10-15M and collect data from every available human patient at multiple hospitals over 2-3 years in order to replicate?

[selestify]

What are some examples of proofs that were originally accepted and then later shown to be incorrect?

[dagw]

Here are a few of them:

https://mathoverflow.net/questions/35468/widely-accepted-mat...