3 ms·
That's literally what the slide says. Your guess is as good as mine, and my guess is that there's an extra word, "generate"
by bagels 3y ago
That's literally what the slide says. Your guess is as good as mine, and my guess is that there's an extra word, "generate"
- Animats 3y agoProbably. The talk covers many computer-assisted proofs where the big problem was a huge case analysis. The cases have to be generated and machine checked. The proof of the four-color theorem (1,482 cases) was the first major proof like that. It upset many mathematicians.
- senfiaj 3y agoWhy did it upset? Machines are just tools. Is using something beyond a pen and a paper considered a cheating. There are some problems where the easiest way is to just to use brute force. The God's number (the maximum moves to solve the Rubik's cube from any state) was calculated with brute force. If you can formally verify an algorithm I see no problem.
- nicf 3y agoI'm a mathematician, although I'm too young to have been around for this. I feel like I might be able to add a little cultural perspective, though. My impression is that most of the people who were "upset" didn't think that the result was false, or even that the work that went into the Four Color Theorem didn't constitute a proof. It's more that we mathematicians tend to like a proof more when it helps us understand why a fact is true rather than just that a fact is true. So an argument that ends with "and then we checked thousands of cases on a computer and it turned out they all worked" feels unsatisfying, since it feels like it doesn't fully explain what's going on.