Hacker News Reader

Comment by brotchie | Hacker News Reader

The impact on the psyche on some Mathematicians of this AI progress must be pretty brutal. To me, it breaks the mystique of Mathematics a lot.

You still need a lot of skill to digest and understand the proofs, but "this is the worse it will ever be." I'd imagine part of the motivation of a large set of mathematicians is to be the "first" or to crack the nut that others couldn't. If Mathematics becomes working with an AI to get a Lean certificate, and then essentially reverse engineering that into something digestible, then it's fundamentally a different pursuit.

Software Engineering feels a little less impacted? Though if you identify with loving coding, then perhaps similarly? I've always liked the outcome of what writing code can do, and enjoyed the craft hand coding for the past ~30 years. But I haven't once ever missed writing code by hand since Opus 4.6, I couldn't go back.

View on HN

My motivation to do mathematics is some combination of wanting to understand the system of mathematics deeply and enjoying the craft and puzzle of working on research problems. If I never had to publish again and the computer was 1000x better than me, so that I can live on my 20k a year UBI, then I’m fine with that. The anxiety is that this isn’t realistic at all so I’ll likely have to spend my life doing something different than pondering math now.

Software Engineering feels a little less impacted?

I don't think so - software engineering has already been completely up-ended; we are showing mathematicians what is next for them.

Sure though wrt your point about mystique there is a difference in psychological importance and cultural meaning - maths at the highest level is far more intellectually challenging and even "glamorous" and represents one of the peaks of human achievement. Ironically though if we allow the invention of AI belongs to our (software engineering) field, this is the first time we've matched those peaks.

I agree with you on not missing manual coding, which in some way surprises me - but it's been a long time since I had the passion of my youth for it.

I am a mathematician and I never believed in this kind of mystique (maybe in other, more resilient mystiques).

I have always expected machines will be able to do math. Since late 2018, I expected them to be able to do math long before physical stuff (basically Moravec paradox).

it does not in any way break the mystique of mathematics for me, though that mystique continues to attach to proofs that are in some way beautiful or elegant, whether produced by humans or machines.

as for software engineering, I've definitely used claude to help with both complex problems that I could have worked through myself but with greater expenditure of time and effort, and with problems that I would not have been able to do without spending a lot of time learning my way around a whole new domain, but in both cases what I am most keenly aware of is that I am benefitting from some human (or many humans) having solved this problem before.

I am ABD in mathematics. That was a long time ago. I taught math for many years at a community college. My amateurish but knowledgeable perspective is that these developments shatter the mystique for me.

What AI is showing is that mathematics is mostly just pattern searching and AI can do this far better, faster, and with a much wider base than humans can. When I was working on my thesis problem I realized that I worked much less than my fellow students. I was an average student in my program but even for the best students they had to spend a lot of time thinking about stuff. They put in a lot of effort.

Is the difference between me and Tao mostly effort and that he has a much better memory of mathematical facts than me?

This is only the "problem solving" side of mathematics. Completely missing the theory builders who have completely reshaped the world of mathematics (and far beyond). AI is a long way from matching original thinkers of the calibre of Euclid, Al-Khwarizmi, Newton, Leibniz, Euler, Galois, Riemann, Cantor, Hilbert, and Grothendieck. Or Turing, Gödel and Von Neumann?

According to Tao and Gowers there are AI results that did proofs in clever ways. That’s one way new theories come about.

I lean more towards the "proofs from the book" mindset - if there's a really beautiful proof of some theorem out there I would be happy to see it no matter whether it was discovered by a human or a computer, and conversely if a computer has churned through a search space and generated a clunky proof in 100000 lines of lean code that just means that people trying to find a nice proof can do so with the assurance that the theorem is true. note that mathematicians didn't give up on trying to find a better proof of the four colour theorem once a clunky computer assisted proof showed the theorem was true.

The question is, will universities continue to fund graduate programs to the extent they currently do so that people can find elegant proofs of AI derived theorems? I’m skeptical. A lot of good mathematicians tried to prove or disprove the Jacobian Conjecture and AI did easily. The value added by human mathematicians seems to be low return on the investment.

that is a genuine concern, yeah :( but at least for me it's unrelated to the mystique of mathematics itself.

Reply on news.ycombinator.com