Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
I have a MSc in mathematics so I am by no means an expert in mathematics proofs but I get the gist of it. To me a proof is literally a logical argument that you can follow to "believe" that a theorem is true. I do worry how many people actually understand or verify mathematics proofs. How many people have actually read and verified Perelman's or Wiles' proofs (I'm only singling them out because they're famous, not because they're particularly sketchy). We seem to think that once a proof is published in a reputable journal then it is definitely true, but really we should only think "a small number of qualified people have read it and think it is fine". The foundations actually seem a bit shakier to me than people seem to appreciate. Perhaps machine-verified proofs will be the answer one day.