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Why does society have mathematicians right now? It's some mix of "the people find mathematics intellectually worthwhile" (public universities) and "we sometimes

Why does society have mathematicians right now? It's some mix of "the people find mathematics intellectually worthwhile" (public universities) and "we sometimes need to ask them to solve hard problems". If AI makes it less intellectually interesting, the first reason goes away. If engineers can just ask the AI to solve a hard problem instead of the mathematician, they don't need the mathematician as a middle man. So AI also breaks this reason. > I suspect most human effort will be spent inventing new ways to push the AI further. Assuming the AI can't just do that itself too.

yohannesk 4y ago
I am quite interested in this AI that can improve upon itself or come up with genuinely new and novel ideas. What are you referring to exactly? LLMs?
- thomasahle 4y ago
  I'm replying to a comment about a hypothetical AI that can do math better than the mathematicians.
wholinator2 4y ago
You know, this conversation had given me a short story idea. I wonder if anyone's written anything like this. Humanity produces an intelligent mathematical AI. It starts by solving already solved problems, then leaps to relatively simple unsolved problems, then leaps directly to solving any problem that can be defined to it, including problems that humanity has battled for centuries. It even will give fully consistent proofs and the small group of researchers we're following are astounded. The resident proof experts say that the proofs it's giving are strange and sometimes inelegant but always logically sound. They go about proving many different problems until eventually someone disagrees with the request, saying obviously this one isn't true, it's logically impossible, it won't be able to prove it. But then the machine does, and gives a perfectly valid and consistent proof that to the highest of humanities knowledge, appears correct. Then the mathematician requests it to prove the inverse to explore his fault logic, and again the ai spits out a fully consistent and valid proof, for the opposite condition. No one can find any fault in either proof. They go through asking it to prove all the opposite conditions as they had requested earlier and it always outputs intelligent and fully self consistent proofs. No one can find a flaw in anything it outputs, even when it outputs conflicting information. It's as if it's playing on some higher plane, able to just toy with the absolute maximum of human knowledge to make the results look like anything it wants. Our once thought rigorous foundation is easily thrown away by the machine. Everyone claps and looks scared. The end

yohannesk 4y ago

I am quite interested in this AI that can improve upon itself or come up with genuinely new and novel ideas. What are you referring to exactly? LLMs?

thomasahle 4y ago
I'm replying to a comment about a hypothetical AI that can do math better than the mathematicians.

wholinator2 4y ago

You know, this conversation had given me a short story idea. I wonder if anyone's written anything like this. Humanity produces an intelligent mathematical AI. It starts by solving already solved problems, then leaps to relatively simple unsolved problems, then leaps directly to solving any problem that can be defined to it, including problems that humanity has battled for centuries. It even will give fully consistent proofs and the small group of researchers we're following are astounded. The resident proof experts say that the proofs it's giving are strange and sometimes inelegant but always logically sound. They go about proving many different problems until eventually someone disagrees with the request, saying obviously this one isn't true, it's logically impossible, it won't be able to prove it. But then the machine does, and gives a perfectly valid and consistent proof that to the highest of humanities knowledge, appears correct. Then the mathematician requests it to prove the inverse to explore his fault logic, and again the ai spits out a fully consistent and valid proof, for the opposite condition. No one can find any fault in either proof. They go through asking it to prove all the opposite conditions as they had requested earlier and it always outputs intelligent and fully self consistent proofs. No one can find a flaw in anything it outputs, even when it outputs conflicting information. It's as if it's playing on some higher plane, able to just toy with the absolute maximum of human knowledge to make the results look like anything it wants. Our once thought rigorous foundation is easily thrown away by the machine. Everyone claps and looks scared. The end