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C'mon AI companies, pivot to lawyers or doctors already. Trying to convince us that mathematics and software engineering are "solved" is getting very tiring. The pushback would probably be too much for the soon-to-be IPO-ed companies.
Does it matter? It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers. The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.
You’re prescribing elegance to a stochastic generator trained on the wealth of humanity, including 4chan. Let’s set our expectations a bit.
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It’s possible, but there’s a difference between vastness and difficulty. Humans can’t compete with AIs on vastness of material they are familiar with, or the depth of effort they are willing and able to throw at a problem. But scale isn’t the only aspect of difficult scientific endeavours. There’s also theory. And advancements sometimes come through hard graft of knotting together many things. And sometimes they come…
I don't think that's true. Human intelligence is limited, and our brains are inefficient machines. The tools we built to replace muscles have mostly obsoleted raw strength for tasks like excavating earth. There's no reason to think we can't do the same for brains. And then we'll never need to think for a living again. Some people may want to do it as a commercially insignificant hobby, of course, the way people lift…
For this to actually work in a way that benefits our species, humans will need to become something else/next through their interaction with the technology.
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I don't think that's true. Human intelligence is limited, and our brains are inefficient machines. The tools we built to replace muscles have mostly obsoleted raw strength for tasks like excavating earth. There's no reason to think we can't do the same for brains. And then we'll never need to think for a living again. Some people may want to do it as a commercially insignificant hobby, of course, the way people lift…
A good mother doesn't raise children to be dependent upon her for all their needs. For this to actually work in a way that benefits our species, humans will need to become something else/next through their interaction with the technology.
Anyways, sipping wine on the beach and doing puzzles when I feel like sounds nice.
It's also "out-brute forcing them." It just never gets tired. If a mathematician picks a research direction and spends a whole week on it and it doesn't pan out, they will likely be annoyed, need a break for a while, etc. This thing just does not ever get tired or discouraged or care; it's just onto the next thing until something ends up working.
https://en.wikipedia.org/wiki/J._Robert_Oppenheimer#:~:text=...
Does it matter? It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers. The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.
I think perfect rationality doesn't exist, because it is rational to reject something that you don't understand. So rationality of a given physical system will always be bounded.
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The key here is that it’s depending on the human inability to connect the sum of relevant knowledge, but said knowledge comes from humans. Theres going to be this field day of low-hanging fruit that ML can round up, but after that I suspect it will be in fits and starts as a “connection maker” rather than some proof producer.
It's not only going to be "connection maker". If and when robotics advance to a point where the LLMs are embodied, they can run experiments in the physical world and find new knowledge.
Does it matter? It's going to produce proofs far more intricate than humans can understand, outdoing humans and opening new frontiers. The age of humans comprehending things is coming to an end: our brains just won't have the capacity to make meaningful contributions to science, math, or technology.
We don’t trillions of dollars in LLM investment to build things mathematicians don’t understand. We already have plenty of those, even from ancient times. As to your second point, Terry Tao already has an answer [1]: the proof isn’t the contribution, shared understanding is. This issue was already raised back when the four-colour theorem was proved. Machine proving and machine proof checking are useful tools but they…
Why is it so hard to imagine we can build tools to think thoughts we can't comprehend?
If there's commercial value, I think it's inevitable. We don't fund mathematicians because it's cute when they understand a problem, but because their work tends to have applications with commercial value. The value can be captured without understanding the details.