If the aim of mathematics is to promote greater human understanding, then surely elevating everyone’s grasp and appreciation of math is of greater import than chasing another theorem feather for our hats - especially if AI can automate the plucking.
You could give me the most well crafted, comprehensive document ever and I would still misread bits of it, or miss some crucial bit of information that contextualises the rest or whatever.
With LLMs I can ask endless dumb questions in a way that just would not be practical otherwise. The quality of the responses doesn't even have to be particularly good for it to be extremely useful - it's basically a turbo charged rubber duck for learning new concepts.
More like The Young Lady's Illustrated Primer [0] than our current chatbot paradigm.
I expect there are 48956789560984 startups trying for this now, though, so... soon?
I'm experimenting with this at https://miletus.app
I'm also curious about training models with that singular goal. If anyone is exploring similar ideas, I'd love to chat.
It seems to me that it would be cool if that could be solved automatically for any learning goal/target
It's def not as robust as Math Academy's graph yet, they spent years hand-building and testing it on real students. But I bet a few more iterations of frontier models get there, especially once there's learner data to correct it.
I can't imagine anyone but someone extremely gifted at first parse understanding learning mathematics from wikipedia. No effort is made to make it understandable for the average reader.
Is this the aim of mathematics?
There's no such consensus. Read Hardy's "A Mathematician's Apology" to get a better understanding.
Here's a quote which gives some idea of where Hardy was coming from: "I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world."
Hardy valued math for its beauty, elegance, and permanence, and he's far from the only mathematician who would push back on the idea that mathematics should be "useful to humanity", except perhaps in the sense that art is useful to humanity.
Ironically of course the answer is yes.
It's also very risky to frame it that way, because that immediately leads to the idea that mathematical endeavors should be judged and funded according to their expected utility. That's product development, not research.
Think of it like this: when your extremely efficient 2-3 SD brain that could pattern match more aggressively than mere mortals seems to be losing ground to aggressively scalable stochastic parrots that can pattern match faster than you, you replace your contempt for teaching and pedagogy with sudden epiphany and awakening that nurturing curious Math lovers and developing the human spirit is what it's all about. It's a good gambit.
> are you projecting some past trauma
That you seem to have difficulty parsing the comment you're replying to, to the point of assuming it's about an individual rather than the community, is in itself a diagnosis that may benefit from professional help. The amateurish psychoanalysis hobby can probably wait while you get that sorted out.
Possibly you're just a jerk? That would explain why you're insulting both Terry Tao and me.
I'm willing to let you find comfort in your attempt to prove a negative. There's safety in numbers, as it were.