121–130 of 144 posts
Earlier quoted context omitted.
Generating new conjectures is easy. It's generating novel conjectures that's hard.
On the other hand, quantity has a quality all its own. Conjectures that survive the gauntlet of immediate proof/disproof could also be interesting.
When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…
I don't mean to be dismissive, are these just old puzzles with no practical use whatsoever?
even the ZMachine it's an astounding example of running virtual machines on 8 bit machines 20 years earlier than Java.
When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…
My perception is different. I start from the axiom that AI is a massive compressed corpus of knowledge. That it can find solutions suggests to me that the solutions were already known, but simply lacked publicity. This is less about discovery and more about pattern-matching.
So it's just a matter of combinatorics.
Earlier quoted context omitted.
I get the impression that the value of unproven conjectures is more in the new math and techniques that may be discovered - by humans - trying to prove/disprove them, rather than much utility in any eventual result. Take something like Fermat's last theorem - I'd be curious to hear of any use of the result itself, but there was a massive amount of new mathematics generated by those working on it, whether ultimately s…
It just occurred to me that this "it's not the destination, it's the journey", what you learn and contribute by trying to solve a problem, may point to what I'm guessing is an unpopular conclusion... It may actually be a negative, rather than a positive, for AI to have solved these problems. If humans had continued to work on these problems, then its quite possible they may have invented new math along the way and be…
Or another angle. Given that, from my amateur understanding, a lot of these problems are proof by counter-example, could you not argue that at least AI eliminates low hanging fruit and more important problems can gain focus.
Of course, I could equally argue that the low hanging fruit is needed to train up mathematicians.
So yeah, in the end, I don't know. But am pretty certain that AI is not going to be limited by these sort of proofs for much longer.
The mathematics are above my intellectual capacities, but I still find the man and his lifestyle fascinating. Though I admit his heart attack probably wasn't a coincidence, sadly. I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS. I often see comment…
Look at all of the crazy stuff made by unemployed trans people/autists over the past decade, disproportionately from countries with strong welfare states.
something i've just realized : today long-standing maths problems are falling. It's great intellectually but won't probably have an immediate impact on our lives. Now, what will happen once long-standing physics ( and chemistry and biology) problems will start to fall and at the same rate ? Then we're going to enter a totally different world.
But yeah, most problems in physics, chemistry or biology require labs on top of actual hard thinking. You need to be able to design experiments in a certain way. Once you have the funding, the right tools, the right people to use those tools, then you can use LLMs to increase the speed of the calculations and so on.
There have been other discoveries though by deepmind: https://deepmind.google/blog/millions-of-new-materials-disco...
When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…
Theoretical science isn't about usefulness per se, but knowledge and understanding for its own sake, so a better way to say this is to point out that you only benefit in such cases if you understand things yourself. If understanding is the goal - which it is in the case of true theory - then the only way to attain that goal is to actually attain understanding. What good is it if an LLM produces a valid proof, but no one grasps it? This isn't like digging a ditch where it doesn't matter who does it or how he does it as long as you have a ditch. Here, the ditch is knowledge, as it were.
When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”. Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound? How can we possibly make use of these breakthroughs if we don’t understand them? How coul…
What are the odds that this random FOSS project has solved the problem of building software and nobody noticed. Close to 0. Don't confuse accidental complexity for transcendental depth.