The Dark Night of Mathematics

> Progress is made by these people [...] Not by the industry.

Eh, debatable? Maybe a bit of both? Industry certainly brings research-level stuff to the masses. And has a way to winnow what's ultimately useful from the vast amounts of research that amounts to "huh, that's weird". And in turn that vast amount of stuff serves as the starting point, and round and round it goes. Research without industry would be pointless (from the masses perspective). And industry without research would be clueless or stagnant or outright dangerous.

Industry can also bring vast amounts of money into research. Just look at the field of Machine Learning.

> AI is stealing all the fun parts.

No one is stopping you from doing what you enjoy.

But lets get real here: no one asked for programming to be the way it is. It just too hard, too menial, too esoteric, too particular and too anal for 99% of the population. That's great if you're one of the 'wizards' and can charge huge amounts of money to make software that isn't exactly wizardry and more like just regular stuff people need for their lives and businesses. The quality and nature of software mostly reflects the mentality of those who wrote it, instead of those who use it. Multi-million dollar software projects continue to fail decades after the Mythical Man Month was written.

If programming as we know it disappears, few will mourn its loss, having suffered its consequences. Most people, including most programmers will just move onto the next great thing, whatever that is, and be empowered by it.

Meanwhile, welcome to what technology has been doing to everyone else for the last 100+ years.

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.

How much of the identity of a mathematician is tied up in being the first to discovery? How much of it is the contest between smart people producing excitement? Maybe someone could chime in on this.

For a mortal like myself, I've never discovered any new mathematics. All I can do is appreciate what I'm taught. But I can still appreciate it. I still watch videos of people solving high school/uni level questions. Why can't you appreciate this new counterexample, just because someone used an LLM to find it?

It's also worth looking at other times technology has changed our world. We invented various engines, so there's not a whole lot of economic value left in being a big strong guy anymore, but plenty of people still exercise because keeping in shape makes them happy.

> AI isn't a tame long term transition - in scale it is bigger than any transition since the first individual cells

You might need to put the phone / keyboard down, take a day off...