The joys of parenthood. The excitement of new love. The tragedy of aging. The rise and fall of a great family. Jealousy, vengeance, embarrassment, righteousness, venality. You obviously couldn’t create an all encompassing map of the terrain, but human art has a lot of recurring themes that are clearly “worth exploring” because they’ve consistently been explored in the past. I think the same kind of repetition probably also exists to some degree in other areas of human endeavor. An artificial intelligence could probably suss out a lot of those themes and produce valuable (if not maximally valuable) work without being a mind reader.
I was refering to going beyond and deciding what to explore. There are infinite paths in mathematics and a lot of ways you can describe and denote a particular theory. And the choice of notation and exposition is an art in some way.
You could probably say that "no, but this is done by minimizing memory usage in human brains so that its understandable by humans, maximizing compressability of previous ideas, and a link with some utility in the real world, etc"
But that just one example of loss function. There are many possible ones.
Do i think that there is a universal loss function that captures it all? Probably yes, in the limit, on the infinite energy regime. Are we in that case in practice? Probably not.
I tend to think that AI will fully replace us the same moment we are able to master prime factorization with our time and energy constraints.
Like we can even know what the future of math is this early
It’s not like you can just declare that up front, it’s something that happens naturally when people spend time using the tools
Of course, general improvements may be sufficient to continue to drive math improvements even without specific attention - we’ll see.
Could also be that some things are not possible in some ways. I wonder if there is some general theory on "shortcuts".
https://en.wikipedia.org/wiki/Computational_chemistry
https://en.wikipedia.org/wiki/Computational_biology
https://en.wikipedia.org/wiki/Computational_materials_scienc...
These fields are all going through a tremendous acceleration right now.
For useful materials science the numbers are still large but far lower than the numbers involved in 'a glass of water'.
And why would IPO remove incentive that's present pre-IPO? Somehow math progress will influence price at IPO but won't influence stock price post-IPO? Or will they just stop caring about stock price once they are public. None of these options makes any sense.
That's the playbook, right - keep interest/investment flowing until you can figure out the actual commercial value/model. Until then, do whatever you need to keep the hype as high as possible and maximise your runway.
The alternative is sitting around and doing nothing and waiting for this God-like AI to come into existence, but you'd look pretty silly if you threw away years of your life only for that not to actually happen.