The point is human understanding. If the LLMs understand, but the humans don’t, where does that leave humanity? Building things we don’t understand is a sure path to facing consequences we can’t predict.
Your comment also conveniently ignores the plagiarism aspect of it all. Who is coping here?
We've developed plenty of things that "work" and we don't understand exactly how or why they work, nor do we fully understand the potential for short term or long term consequences. For example: pharmaceuticals.
Any serious mathematician would read the LLM output and rework their understanding.
I read a bourgain paper a week in grad school and they're probably worse than an LLM generated paper. I still had to recreate the tricks in my own language.
As far as I can tell the plagiarism accusations are also coping to the fact that the new models are super human at slam dunking research projects.
Do we think that OpenAI is going to try and slam dunk more projects in the future at 15 million a pop? No lol
>Building things we don’t understand is a sure path to facing consequences we can’t predict.
We don't understand all of physics yet we were able to do plenty. Even before Newtonian physics we were still able to build things that last. The idea that humans have to understand everything and abstracting things will lead to ruin is not supported.
Part of math is building abstractions so that you can be able to use other people's work without fully understanding it. No one person has a full understanding of mathematics.
What benefit is there if the machine has unlocked understanding but no human has? What incentives are there for humans to learn and gain such understanding from machines?
Is "loving math for maths sake" just about knowing the answers? I think one can love math for exactly the process and understanding that a several-thousand-line uncommented Lean proof denies. If a deity rearranged the stars to spell out "The Riemann hypothesis is false" for a night, would that be intellectually sufficient?
the way LLMs write math is not beautiful. it is exactly analogous to the software that LLMs develop is not beautiful. it may achieve impressive end products, but if you like understanding the methods/architecture, looking under the hood is often a field of horrors.
The usual incentives in academia: publishing papers. Consider the difference between publishing a paper that introduces a novel method to do X, versus publishing a paper that merely interprets Claude’s method to do X. The latter might not even be publishable.
Not quite, all the proofs or disproofs so far AFAIK were using existing methods that humans developed and were already using to attack the problems, but AI is just more thorough. What AI can't do currently is develop new mathematical methods to attack problems that can't be solved with existing methods and AFAIK there is no known path to get current gen AI to do so.
You can steal lemmas, rough proof directions, conceptual ideas etc without stealing the full proof.
Any of that done unattributed is plagiarism.
Either OpenAI is incompetent or evil if they can't publicly prove the allegations wrong. Or even at least state categorically they didn't train on their conversations (even without proof).
Please don't sneer on HN. The guidelines make it clear we're trying for something better here. https://news.ycombinator.com/newsguidelines.html
Apologies. Noted
Many thanks!
The point is human understanding. If the LLMs understand, but the humans don’t, where does that leave humanity? Building things we don’t understand is a sure path to facing consequences we can’t predict.
Your comment also conveniently ignores the plagiarism aspect of it all. Who is coping here?
We've developed plenty of things that "work" and we don't understand exactly how or why they work, nor do we fully understand the potential for short term or long term consequences. For example: pharmaceuticals.
Any serious mathematician would read the LLM output and rework their understanding.
I read a bourgain paper a week in grad school and they're probably worse than an LLM generated paper. I still had to recreate the tricks in my own language.
As far as I can tell the plagiarism accusations are also coping to the fact that the new models are super human at slam dunking research projects.
Do we think that OpenAI is going to try and slam dunk more projects in the future at 15 million a pop? No lol
For your sake, based on your comments throughout this post, I hope you didn't pay for any stage of your education.
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There are many points.
>Building things we don’t understand is a sure path to facing consequences we can’t predict.
We don't understand all of physics yet we were able to do plenty. Even before Newtonian physics we were still able to build things that last. The idea that humans have to understand everything and abstracting things will lead to ruin is not supported.
Part of math is building abstractions so that you can be able to use other people's work without fully understanding it. No one person has a full understanding of mathematics.
What benefit is there if the machine has unlocked understanding but no human has? What incentives are there for humans to learn and gain such understanding from machines?
Because it's beautiful. Because you love math for maths sake and not some weird egotistical game
Is "loving math for maths sake" just about knowing the answers? I think one can love math for exactly the process and understanding that a several-thousand-line uncommented Lean proof denies. If a deity rearranged the stars to spell out "The Riemann hypothesis is false" for a night, would that be intellectually sufficient?
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the way LLMs write math is not beautiful. it is exactly analogous to the software that LLMs develop is not beautiful. it may achieve impressive end products, but if you like understanding the methods/architecture, looking under the hood is often a field of horrors.
You feel lean4 proof, that you 99.999% chance not understand is beautiful?
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The same incentive there always was: Because you wanna know. What incentive were you thinking of?
The usual incentives in academia: publishing papers. Consider the difference between publishing a paper that introduces a novel method to do X, versus publishing a paper that merely interprets Claude’s method to do X. The latter might not even be publishable.
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Not quite, all the proofs or disproofs so far AFAIK were using existing methods that humans developed and were already using to attack the problems, but AI is just more thorough. What AI can't do currently is develop new mathematical methods to attack problems that can't be solved with existing methods and AFAIK there is no known path to get current gen AI to do so.
That's fair and I agree. But stockfish can play successful middle games and there's no reason that AI cannot create research programs
The biggest cope is buying OpenAI's "We can't prove we didn't plagiarize"
Apparently, we have AGI that can solve Millennium Prize problems but can't trace simple data flows lol.
How is it plagiarism if no one else had the full proof idea first?
You can steal lemmas, rough proof directions, conceptual ideas etc without stealing the full proof.
Any of that done unattributed is plagiarism.
Either OpenAI is incompetent or evil if they can't publicly prove the allegations wrong. Or even at least state categorically they didn't train on their conversations (even without proof).