> In either case I believe people who can put AI to the most value are the mathematicians themselves
The net output of math will increase, and mathematicians have more work now to unravel all this, and make it useful. AI plays the role of a monkey in the infinite monkey theorem [1]. We now need an LLM corollary - Something like: A finite number of LLM agents will almost surely find all theorems given an infinite token budget.
"Given infinite thinking time a finite number of humans will solve all theorems"
I also love the angle that this was not intelligence just brute force. As if the mathematicians didn't reeaaally want to solve this they were just too lazy to give it a good try.
What does AI have to actually do before you realize these things are actually smart?
Machines have a much higher capacity for work than human beings. Saying that these proofs did not require equivelant intelligence, but benefitted from sheer volume, does not strike me as unreasonable.
It feels goalpost-movey to downplay exploring a large search space efficiently in regards to "intelligence". If we dug into a human genius's brain and found it was somehow trying out a million ways to solve a a problem at once, no one would seriously suggest the person isn't actually intelligent.
And our brains must something like that at some physical level. You can't have a "turtles all the way down" of reasoning - the building blocks must be simpler. It must reduce to something like pathfinding and brute force at some point, weighted by factors in the system and maybe some randomness.
We have a romantic view of intelligence, perhaps stemming from intuition within the context of scientific discovery. Given enough intelligence, and enough context, a brilliant person can have a stroke of inspiration that allows them to make a major leap (a-la General Relativity or Fermats last theorem). We haven't seen THAT same capacity from a machine, but we see the more ordinary, unsexy grinding type of progress that represents 99.9% of scientific reality.
Is there truly anything new under the sun? Hasn't all of existence alway been here? All math, all physics? We could have merely discovered it. Intuition might be nothing more than combinations of what already exists rather than some sort of divine insight that unlocks previously unknowable mysteries.
Agreed. I don't believe intuition and creativity would be more than pattern recognition, remixing ideas, and trial and error combined with a kind of "genetic algorithm" approach if you deconstructed them into what the brain is actually doing.
I would find it very interesting to train a model on information only available prior to the discovery of e.g. relativity or calculus and see if it can invent it. My intuition is that modern frontiers absolutely could. Not to take away from their brilliance, but Newton and Einstein were brilliant people who also happened to be in the perfect place at the perfect time - there's not so much "low hanging (i.e. approachable by one brilliant individual) but immensely valuable fruit" anymore.
bwfan123 · · focus · HN ↗
The net output of math will increase, and mathematicians have more work now to unravel all this, and make it useful. AI plays the role of a monkey in the infinite monkey theorem [1]. We now need an LLM corollary - Something like: A finite number of LLM agents will almost surely find all theorems given an infinite token budget.
[1] <a href="https://en.wikipedia.org/wiki/Infinite_monkey_theorem" rel="nofollow">https://en.wikipedia.org/wiki/Infinite_monkey_theorem
johnsmith1840 · · focus · HN ↗
"Given infinite thinking time a finite number of humans will solve all theorems"
I also love the angle that this was not intelligence just brute force. As if the mathematicians didn't reeaaally want to solve this they were just too lazy to give it a good try.
What does AI have to actually do before you realize these things are actually smart?
alansaber · · focus · HN ↗
jimmaswell · · focus · HN ↗
And our brains must something like that at some physical level. You can't have a "turtles all the way down" of reasoning - the building blocks must be simpler. It must reduce to something like pathfinding and brute force at some point, weighted by factors in the system and maybe some randomness.
alansaber · · focus · HN ↗
williamcotton · · focus · HN ↗
jimmaswell · · focus · HN ↗
jimmaswell · · focus · HN ↗