Both the Kempe and Tait proofs were widely and warmly accepted for over a decade, before they were both discovered to be flawed. There was also a flaw in Principia Mathematica, which wasn't discovered for about 50 years. It makes one wonder what the intense value of formal rigor actually consists of. You can at least run computer programs against real problems, and flush out their more blatant bugs--proofs, once generated, seem to just sit around enjoying the veneration of formal mathematicians.
I don't recall that, but I'm quite sure it's true. I'm a bit surprised in that the 4-color theorem was a holy grail of sorts. This is always the problem with long and complicated proofs. Also, refereeing is a thankless job, so there's no incentive to be careful other than love of the profession.
Wiles' proof took years to check and they even found a hole (which was fixable, but nontrivial).
There was also a flaw in Principia Mathematica, which wasn't discovered for about 50 years.
You're talking about Newton's PM, right? (There are a few people who have published works with the same name.) That era was much less rich with professional mathematicians and the standards were not well-established. Gauss did yeoman's work in formalizing all of mathematics.
But you'd expect a flaw there. After all, PM was essentially a physics text. :)
It makes one wonder what the intense value of formal rigor actually consists of.
It's the best we have and a higher bar than any other field.
You can at least run computer programs against real problems,
True, but you cannot check an infinite number of cases, unless you have a really powerful computer. The really interesting problems are on absurdly large systems. One nice area is models of the Internet.