Absolutely. But you must admit, not everyone (human) is capable of reaching the level of the mathematical community. Even if they really wanted to. AI, as it learns, achieves such heights much faster and more efficiently than most people. For example, in mathematics, it already surpasses you and me 
That’s perhaps the attitude Tim was addressing - that a faster steam engine can do anything.
By steam engine, alas, we have to mean a human who, unfortunately, can’t get any faster, because he is limited by his biological nature.
Hopefully we aren’t so stupid to think we don’t need educational institutions.
I would say on the contrary: to use AI as a tool, one has to have good understanding, good education, about the issue you are working on with the help of AI. If you don’t have that underlying understanding, you are yourself as clueless as the LLM’s themselves and can easily create just nonsense, that only seems to be intelligent.
And anyway, I wouldn’t panic about mathematics or panic about AI in general. We are just living through a hype connected to a tech-bubble (just as the internet or railroads were earlier “bubbles”) and will see the actual reality in a few decades from know. And it won’t be so revolutionary as people are hyping it to be now. I’m not worried about mathematicians being replaced by AI at all.
Hmm…
Not so sure.
Yes, you and I know that, but there are those others, who haven’t heard of the Dunning-Kruger effect, and don’t know that they have no idea…
Just like all those folk in the typing pool whom we once thought would be replaced…
A Washington Post article on the topic (Gift Link).
In early August, top mathematicians gathered at the offices of ChatGPT maker OpenAI in San Francisco for a summit on an existential question: What will be left for human math experts to do if artificial intelligence soon leaves them all behind?
“I think there’s a chance that we end up in a world where there’s no high-quality mathematics research, and human expertise in mathematics is totally lost,” said Daniel Litt, a professor at the University of Toronto. He gave a talk at the event titled “The End of Mathematics.”
It does sound daunting for mathematicians.
In the area of Creative Arts - I’ve watched a bunch of the flood of ‘historical reconstruction’ vidoes on YouTube - things like Life in Ancient Rome, The History of London, Establishment of New York. The better of them are completly indistinguishable from footage made with actual actors and props (although there are always giveaways, like the humans tend to be far better looking than regular people.) But it’s moving towards the point where you will be able to turn out a feature-length film with no actual cast and crew.
This seems similar to the time when electronic calculators were invented. How horrendous.
So back to the thesis of this thread, and the nature of proof. A theorem is not proved when it is calculated, but when it is accepted by the community. But AI cannot replace the community. Hence there is a place for mathematicians still.
There are fates worse than death.
You mean if a community rejects a correct proof then the proof and the theorem it proves are wrong and false, respectively?
No.
A theorem that is unproven is not thereby false. Perhaps proof, not truth, is communal.
Interesting remark.
So a proof is correct/incorrect because a community says so. Wouldn’t that mean that a correct proof of the Pythagorean theorem would be incorrect if a community says it is incorrect?
The suggestion is, a proof is successful iff it convinces the community. Correct/incorrect is ambiguous - do you mean that it is convincing, or that it is valid?
We again have the difference between a description, in which the words are changed to fit what is the case, and an evaluation, in which what is the case is changed to fit the words. Accepting an argument as valid is forming an attitude towards the argument.
Now to the question of the nature of validity…
For what you say to work the community has to be logically strong.
Mathematicians tend to be.
In the math community an unproven theorem is called a conjecture. If a counterexample surfaces the conjecture usually fades or is altered to accommodate the example.
I suspect AI may reach the point of verifying even complicated proofs. Even if a proof is not forthcoming, a conjecture may suggest an interesting avenue of exploration. The Riemann Hypothesis is an example. Results have been “proven” in the sense that they assume the Hypothesis is true.
What is it to verify a proof? I tis to adopt a particular attitude towards the proof. it might be worth examining what this implies, given that AIs are subject to confabulation.
If I can jump in here, I’d say of course. From my POV, only a tacit mathematical platonism tends to obscure this.
A proof is a role that many role-equivalent empirical “documents” play.
Of course I’d suggest that we read “truth” as just as communal. Again a tacit god’s-pov mathematical platonism obscures this.
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Would you agree that a weakly logical mathematical community can decide on the correctness of a proof?
I’ve no idea what that asks. I’m just pointing to the distinction between a theorem being true, and it’s being proven. The former is a property of the theorem, the latter, an attitude adopted by a community. The relevance is that if an AI proffers a claimed proof, under what circumstances do we accept it? That it is on offer is not sufficient.
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You provide a description of reality. It is an accurate description. 