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First, this: http://www.latimes.com/news/opinion/commentary/la-oe-wertheim16may16,0,252151.story The article seems to me to confuse some of the issues rather wilfully (no, an assertion of the statistical likelihood of a large number's prime-ness does not constitute proof that it is a prime. There are an infinite number of primes. If you permit any degree of uncertainty in your determination of whether a number is prime or not, you then will have to live with an infinite number of false positives. If they're sparse, and computationally very expensive to differentiate from real primes, then they might still be useful in cryptography. But usefulness to cryptographers is not the defining property of a prime number, and there is no scope for "definitional drift" in the matter). Some of the issues are real nonetheless. The question of whether proofs performed or assisted by computer are mathematically acceptable is interesting, because an answer in the negative would tend to rest on the assumption that conscious grasp of a proof by a human being is required for it to be valid. This is an odd metaphysical phantom, which yokes consciousness to truth and places anything that falls or strays outside of the immediate ambit of consciousness - writing, say - under suspicion. Who knows where a computer-generated proof has been? Better get it checked out by a meat-head, just to be sure... Mathematics qua "that thing that mathematicians do" is, I don't doubt, as "postmodern" and "socially constructed" as anyone who wished for that sort of thing might wish. But mathematics qua the object of mathematicians' enquiry I think is not. Committees may very well meet to confer on the validity of a candidate for proof of some conjecture, but the validity of the candidate does not in fact depend on their consensus. They might all agree that it's a very fine proof, only for a flaw in its reasoning to be discovered some months later. The flaw was always there, and will always have been there, and there is no way that anyone can make it go away just by changing their minds about it. Dominic