Math is having its DevOps moment. And yet, people who really understand networks are beyond valuable.

It’s ok to mourn the loss of a frontier and also support the thing driving that loss. The way it looks, the generation of mathematical results will become less and less of a human endeavor. There’s a way that’s sad even if on the whole it is a huge leap for society. This was a great article, and I applaud the author for acknowledging this head on.

Same as programming, I feel like the underlying tension is between math lovers who want new math to be done vs those who want to be the ones to DO the new math.

Both groups love math, but the later group is in a real bind because they have confounded their career with their hobbies/passions.

Counterpoint: Benoit Mandelbrot isn't notable for ever proving anything, but highly regarded for having put in years playing around with computers while asking interesting questions about what happens if you abuse the rendering parameters. Same thing with Mitch Feigenbaum uncovering a new constant by drilling down into very simple equations.

The joy and pride of lifting heavy chunks of mathematical infrastructure into place are being made redundant by industrial machinery that any amateur can rent or build for themselves. But it seems to me there's plenty of room to discover new mathematical vistas. The future of mathematical discovery is not cracking hard open problems that everyone in the math community agrees would be an impressive lift, but by bigging into things that nobody else thinks are interesting or important.

Suppose any theorem you set out to prove had already been proved in 100 wonderful ways

No matter how brilliant you are, no matter what intellectual heights you scale, you'll never be Pythagoras or Euclid or any of many famous mathematicians whose insights purchased immortality. Why even live?

To be frank, I occasionally feel this way because I am still absolutely knocked out by very simple things like plane geometry, powers, irrational numbers, exponentiation and logarithms etc. I smile and nod politely about reports of contemporary breakthroughs linking this obscure subfields with another - partly because I haven't put in the years of study to know a great deal about advanced and frontier topics, partly because I'm not smart enough to fully appreciate them, but mostly because they're often about the surprising obverse of some feature in a corner of a utility corridor in the dusty cellar of an annex in the grounds of the Grand Mathematical Temple. Nobody will be able to experience lighting a candle and illuminating the great structures of the main hall for the first time, just like no chemist can ever hope to wake up in the morning and discover a new element and most physicists have abandoned the idea that they will ever be able to do more than tinker around the periphery of the discipline in the hope of extending the precision of measurements by another decimal place.

But the amazement and perplexity about the unreasonable coherence of mathematics (and its equally unreasonable effectiveness in the natural sciences) are what make the field compelling in the first place. The capacity for curiosity and obsession are what yield big discoveries, more so fascination with extending a well-defined knowledge boundary out a little farther. Put another way, pointing out the existence of a problem can be more significant than solving it.

They are concerned mathematicians are obsolete and seem to be unaware that super intelligence means humans are obsolete.

You need to be thinking about an entirely different form of life for all of humanity, happening in the very near future. Focusing on one specific field that may be earlier in the obsolescence chain is a distraction.

Merit based society based on intelligence or work of nearly any kind is about to cease existence.

For some reason it feels to me that this should make mathematicians feels better. :)

A raw and powerful piece, thanks for sharing.

For years I've wanted to get back into self-studying mathematics, not to make serious contributions but just to appreciate its beauty; but the recent observation that I'll never be able to answer a pure mathematics question that a clanker could not has been off-putting, to say the least.

Unsaid here is that the companies involved have stolen so much (both literally in their plagiarism, and in their breaking of people's spirit), and given back so little. You still need to pay them cold, hard cash for them to help you prove theorems, and meanwhile, mathematicians working at these companies have themselves done little to contextualize and interpret results. That insight has mostly come from outsiders.

> The creation (or even the pursuit) of novel mathematics is one way that humans have historically accessed the ineffable and encountered the divine and mystical.

Would a mathematician please unpack this for me? A theorem is the opposite of ineffable. A conjecture may be ineffable but its pursuit reifies it. I am missing something.

Seems like maybe now we have sufficient tools to actually get on top of string theory. And ultimately it is all about coming up with explanations and formulas and tools that people can use in facing real challenges.

OP seems to need to touch some grass, spend time with friends and family, sit by the lake etc. Some sentences in there are quite disturbed.

Regarding math, the new tools are humanity's achievements, they weren't handed down to us from the sky. These tools are spiritual achievements. Just as much as calculators and computers in general. Just as much as the invention of writing and notation. You could also mourn the days when we'd calculate on our fingers only and would orally memorize certain calculation heuristics of geometry handed down the generations.

Regarding jobs, people aren't being paid for having a good time or for having fun and spiritual feelings. When you get paid, someone gives you money. The person or institution giving you the money has to have a reason for doing this. It is very basic logic, but academics don't seem to get this. If your work is pleasing for someone on an artistic or spiritual level, you can find a rich patron, the same way learned scholars did back in the day.

It's not any different from cashiers who get replaced by self-checkout or bank tellers by ATMs. You're not special. It's a job.

And I say this as someone who really appreciates the feeling of gaining insight when cracking a math puzzle or grokking how the definitions fit together and why something is the way it is, why a theorem works, I like mathematical elegance etc. But I don't think that is diminished in the least by being able to consult a smart AI about it.

Pretty sure software developers already had that moment with coding agents. They can't really admit it like this, as it affects their employability now.