[zmgsabst]

Computers allow us to scale what we analyze in math — and that’s a good thing.

Nobody examines structure of group diagrams because drawing interesting ones by hand is borderline impossible, but takes just a few minutes on a computer. However, they’re a natural way to arrive at algebraic/geometric equivalence. (And indeed, the first time I had an intuition for it.)

To me, you sound like someone lamenting swimming is meaningless because we invented boats.

[vouaobrasil]

Again, like so many, you are taking computer use in math as an indivisible whole. I never said that computers were NOT useful. Only that the use of creative AIs in math are counterproductive in the long run, hence implying a point of diminishing returns that we push towards (due to the peverse incentives of academia).

There is also a fundamental difference between swimming and math. There is no prisoner's dilemma situation when it comes to swimming: with swimming, people CHOOSE to swim because they like it. But due to different incentives, people will CHOOSE to use AI only because others use it and it will become the only path eventually.

In other words, swimming is still possible even though boats exist. People going into mathematics will not have the possibility of being of any use without AI, because the prisoner's dilemma (arms race) will ensure that math is no longer about anyone caring about math without AI.

[zmgsabst]

You ignored the thrust of my argument:

You’re lamenting that inventing boats has destroyed the beauty of swimming.

- - - Edit - - -

Responding to your expanded argument:

You could never swim to a new continent, which boats enabled. This is the same — people can choose to keep doing the same limited math themselves, in a slower way, but will never reach the places people can aided by tools. That’s simply how the world is. But we shouldn’t restrict the distance people can travel to adhere to the aesthetics of swimming.

You’re arguing precisely that: we must limit our intellectual journey because you don’t approve of the aesthetics of the tool to travel further.

[vouaobrasil]

I specifically gave a reason why boats and swimming is an entirely different situation. Due to different incentives, AI can take away opportunities for people to learn math the old fashioned way, but boats did not do that to swimming precisely because the incentives for swimming (moving without a boat) are different. But I added that in an edit before I saw your comment.

[zmgsabst]

Those reasons exist for learning math: mental fitness, personal enjoyment, sport, etc.

But you’ve subtly changed your argument: before you were arguing that the beauty was in creating mathematics, not merely learning already written mathematics.

My exact point is that learning surmathematics (math taken further by AI) is it’s own interesting pursuit — and appeals to my sense of aesthetics and adventure more than piddling around merely to say it was all done by human hands.

I’m not following where you believe the swimming and boat analogy breaks down: there’s still the same personal reasons to learn and do mathematics one might swim; but learning surmathematics is an adventure to a whole new land.

- - - Edit - - -

Responding to sibling comment as well:

> I am arguing that we should limit our intellectual journey, to preserve the humanistic aspects of the journey. That is exactly my position.

That’s exactly what I compared to swimming rather than boats — because you won’t reach the same places and it’s done for aesthetic reasons.

Some people (eg, myself) want the surmathematics adventure.

[vouaobrasil]

> That’s exactly what I compared to swimming rather than boats — because you won’t reach the same places and it’s done for aesthetic reasons.

For some reason, and I can't explain it, but I do believe that people still value personal physical achievements even when machines can do it better, but the same is not true of mental achievements. I take it as an axiom.

> Some people (eg, myself) want the surmathematics adventure.

That is where we fundamnetally differ, again axiomatically. I think it's offensive. But even if you do like it, that will eventually lead to the path where AI is just doing mathematics so well that no one will have much of a chance to understand what it is doing at all. And that ultimate conclusion, or even a probably chance of it, is enough reason to scrap the whole thing.

[vouaobrasil]

Yes, I am arguing that we should limit our intellectual journey, to preserve the humanistic aspects of the journey. That is exactly my position.