Theoretical knickers are presently in a twist about the threat of AI rendering theorists obsolete (or such is the impression I’ve gleaned from article headlines). But, while only vaguely interested in AI, I suspect it’s only really good at extending extant ideas. Does it get curious on occasion, even playful, and try out ideas well outside its database, the information in which is likely established by people without the playful gene.
For example, many many moons ago my interest in number theory led me to wonder what the graph of the natural log of the least common multiple of the integers from 1 to n would look like. I am not a number theorist; this was just inspired playfulness. And this is what I found:
ln(lcm{1,…,n}) ❤️ n-1
This is more than just a good, or best fit; it is Nature’s intended fit. The ❤️ connotes “Nature’s intended fit”. (I will go to my grave believing this.) I used this to derive an astoundingly good formula for the number of primes from 1 to n (I believe Riemann got the same result in a more rigorous way; my write up on this is on researchgate).
So anyway, yeah, can an AI be inspirationally playful? I think of AIs like graduate students, who attach themselves to some eminence grise. This exalted being has a vested interest in seeing to it that their charge stays in a lane that will enhance their … ok, so, in general inspirational playfulness will be met with censure.
My work applying the division algebras (C, H, O) to elementary particle physics arose from pure inspirational playfulness (and obsession; can an AI obsess?). Let’s assume that work is fundamentally correct. I don’t see an AI taking an initiative to try something new like this.
So, anyway …