alt Hacker News> the process is the result.
For who though?
Is it important that each person understand it on their own?
Why does it impact me if another human understands something or not?
It impacts me right now because that human can use that knowledge to explain things to me or to build new things using that knowledge.
But if an AI can explain and build better, then what good does it do having the other human know the thing?
Understanding might have intrinsic value to me, but intrinsic value to me doesn't pay the bills.
What am I missing here? I kinda expected better from Terrance given such an audacious title.
Replies
Expertise changes perception, not just knowledge.
I have dyscalculia so the math world is dead to me, I can't even add 2 numbers together in my head, but I've read here on HN many times over the years people describe some version of new maths frameworks tangibly changing how they view the world. For me, I went to film school - I have a natural ability to think in movies and pictures, memory is very visual for me, before film school I had a good sense of shape, colour, light. After film school and to this day some 20 plus years later, I mostly look at the world starting with the shadows. Russian speakers, whose language has separate basic words for light blue and dark blue, are slightly faster at telling those shades apart. Speakers of languages that use compass directions instead of "left/right" appear to develop a strong, constant sense of orientation.
These things can only happen through the process, so for who? For people who want to live richer lives, want to think differently, and for you, to be around people who have such.
> For who though?
For math, the value of proving a theorem is often not proving the theorem (which most people already believe correctly to be true or false), but the path taken there, the new math invented, and how it can be applied to other problems. The end result is therefore almost inconsequential in moving math forwards.
> For who though?
For the collective (humanity, mathematical/scientific community etc). Math is not done in isolation, and if somebody does so then feedback to the community does not work as well.
Mathematics, and basic science to a degree, face the issue that they create their own problems and paths through this kind of tranformation, where external feedback is secondary. It is not as if "I want to build an app/car/robot, I let AI do it". It is as if you decide to let AI decide what to build for you and how to build it, and you do nothing at all. Instead, the pursuit of understanding is the goal itself, and through the course of humanity we have learnt that this understanding can also be useful, but this is not necessarily guiding how this understanding is gained.
Most of the contexts people here have in mind are when problems are well and externally defined. Cure a disease, optimise an engine, make an app that does X, etc. This is not exactly the case in theoretical math and never was really.