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AI in mathematics is forcing big questions

spectrum.ieee.org

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Re: AI in mathematics is forcing big questions

#4

Post by gerdesj »

glouwbug wrote: post #3

Turns out you have to be Terence Tao to know when an LLM is right or wrong

"I imagine my work could be completed with AI assistance in a matter of days—maybe hours."

Would some one with tokens to burn mind checking that statement out and post back. Be sure to use long dashes too.

Re: AI in mathematics is forcing big questions

#5

Post by lubujackson »

The article poses if AI will be a tool, a collaborator or an oracle. Why not all 3?

If mathematics is human understanding of logical consequences, understanding is the priority. But if AI proves something we can't understand but can utilize, that is a different sort of useful.

We are getting awfully close to "the answer of the universe is 42" and having it not be a joke...

Re: AI in mathematics is forcing big questions

#7

Post by fn-mote »

lubujackson wrote: post #5

The article poses if AI will be a tool, a collaborator or an oracle. Why not all 3? If mathematics is human understanding of logical consequences, understanding is the priority. But if AI proves something we can't understand but can utilize, that is a different sort of useful. We are getting awfully close to "the answer of the universe is 42" and having it not be a joke...

I don’t know about “close”, but there are certainly results in math that are considered deep because they require the use of a “Hard Theorem” at some point. That kind of building on top of something Very Difficult is still possible without understanding the “Very Difficult” part. I’d say a lot of not-amazing math is built by believing the platform works but not being able to built it yourself.

I couldn’t build an internal combustion engine or even a plastic box, so maybe there’s nothing wrong with this approach.

Re: AI in mathematics is forcing big questions

#8

Post by paulpauper »

It's amazing how much attention this issue has gotten. What is lost in the hype is no AI can tell you if a proof is correct. An AI can produce a convincing looking proof, but it can have a subtle but critical error or make an assumption that is unfounded. Thus, it ultimately comes down to humans. A mathematician has to craft the prompt, and mathematician to interpret/check the results. Also, these programs are very expensive and propitiatory. They are not like the commercial AI that regular people use. It takes considerable prompting and trial an error to solve even Olympiad/Putnam problems, and tons of work by humans pouring over the results to see if it's correct. For every Erdos problem that captures the headlines, there are many where it failed or untold hours of prompting and token burn to get that result, and manhours verify it.

Re: AI in mathematics is forcing big questions

#10

Post by ares623 »

paulpauper wrote: post #8

It's amazing how much attention this issue has gotten. What is lost in the hype is no AI can tell you if a proof is correct. An AI can produce a convincing looking proof, but it can have a subtle but critical error or make an assumption that is unfounded. Thus, it ultimately comes down to humans. A mathematician has to craft the prompt, and mathematician to interpret/check the results. Also, these programs are very e…

But just imagine...

(edit: lol didn't realize the sibling comment below is essentially my comment)

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