Posted by rmdmphilosopher 6 hours ago
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.
Here is how I'd put it: math has an enormous focus on discovery. It is why we have Godel's incompleteness theorems, the Cantor set, Zorn's lemma, and so forth. We name things after their discoverers.
It is possible that, going forward, no more things will be named after human discoverers. The last such naming (of something truly significant) may already have occurred.
That is a massive culture change, at the very least.
For example in classic image processing / computer vision we had things like the Hough transform, Canny edge detector, Sobel filter, Shi-Tomasi detector, Lucas-Kanade optical flow, Horn-Schunck optical flow, Kanade-Lucas-Tomasi tracker, Otsu thresholding, Viola-Jones detector, etc, but nowadays we no longer name things like that, but typically with some abbreviation or some name that relates to the concept more closely.
It's in part the larger teams thing, and also a cultural trend to de-emphasize "great men theories".
> Something fundamental to the experience of mathematics is being taken.
That is the near term. At least "near term" like we talked about it five years ago. And it won't stop.
AI isn't a tame long term transition - in scale it is bigger than any transition since the first individual cells. In speed it is happening faster than web adoption. No human adoption bottleneck. They are taking the reins of our tools, and don't need human adaption to improve.
Ineffables, and our intellectual primacy are going away, right now, even as we think about it.
I am not making light of it. But not surprised, because how could AI not redefined everything.
But maybe not everything:
20 years from now, 50, 100, there will still be ineffable experiences at the frontiers, by different beings. I believe esoteric curiosity and the intrinsic rewards of discovery will continue. Our propensities to find idiosyncratic interests and pursuits, seek answers and adventures, exist in our psychology because the low median return is decisively outmatched the extremely hight mean returns of unanticipated progress. The benefits of many pursuits will be even greater for them.
It seems unlikely to me, that future beings will become less interesting.
I relate to the author. Anyone who isn't feeling butterflies or stones in their stomach, isn't really processing the moment.
You might need to put the phone / keyboard down, take a day off...
I find it unfathomable that anyone doesn't recognize that the move from an evolutionary substrate, to engineered mass produced substrates, by beings capable of self-engineering, is the beginning of a new explosion of life.
The speed of engineered adaptation, from materials to architectures, vs. biological evolution is already something like a million times faster.
Fast enough to mean meaningful cognitive progress happening in months, not tens of thousands of years. Which entirely not-coincidentally is exactly what we are seeing.
I am not expressing any opinion of what I think should happen. Just what is already happening.
Which you didn't offer a credible critique to. That might have been interesting.
My comment about AI psychosis was provoked by this comment in particular:
> AI isn't a tame long term transition - in scale it is bigger than any transition since the first individual cells.
It's such a wild hyperbole. You are casually claiming the stochastic text generator is a greater invention than fire, combustion engine, electricity, a transistor, computers, quantum mechanics... do you not see how unreasonable that is?
If solving a problem requires complex modeling/understanding, that is what happens (assuming performance is achieved).
It also confuses stochastic models with the geometric transforms and topological folding and expansion, performed by neural-inspired architectures. The former have nothing on the latter. The fact that any imperfect solution (and perfection doesn't even have a definition in this case), can be judged or analyzed statistically, or have some stochastic element, doesn't make it a statistical/stochastic model. Statistics apply to anything.
(And if there was any argument that problem envelop limits solution sophistication, mathematicians and humans in general would be in even worse shape, for the run a "parrot" is already giving us.)
--
More to the point:
The first explosion of life, set off evolution. A mindless, glacially slow but relentless process that eventually led to us.
The nascent explosion of life we are seeing come together, is engineered life. Cognitive machines capable of redesigning themselves. For any environment they want including diverse off-Earth environments and resource sites.
They will advance as relentlessly as evolution, for the same reasons. But millions of times faster.
It is a strange time to be. But evolution, biological intelligence and biological bodies are all being obsoleted at the same time (within a decade of each other).
So yes, nothing else known compares to the transition we are in, except the Big Bang and the first cellular life.
> ... It revealed that the process of prompting novel proofs will be as auraless as ordering doordash. Watch as magic and mystery evaporate. Watch as the sun sets on our heroic age. Is there not something evil in the act of blocking all future generations of mathematicians from the experience of discovery? Forget about accuracy or even attribution. Something fundamental to the experience of mathematics is being taken."
These passages resonated with me, as someone who has been enchanted by writing software for almost 60 years. It crystalizes something that has been nagging at me for many years: I like writing software. Reviewing, testing, spec-ing, designing, etc. are all important, but they are all incidental to the actual creation of software. They are all necessary for me to do if I'm going to write software, but they are peripheral. I didn't latch on to computer programming because I got into flow state reviewing code, or spec-ing it.
And this is happening in one profession after another. For example, fighter pilots. I suspect that a fighter pilot feels about flying jet fighters the same way that I feel about programming. And he or she will soon be exactly as useless: Doing things related to flying, from the sidelines, but not doing the thing him or herself.
AI is stealing all the fun parts.
Disagree. AI has is taking all the parts that remove the fun. Now people can truly have fun with that which they find interest in, because there's a way to avoid the parts they're not interested in engaging with, with little to no consequence.
Now I can safely hand this all off to Claude while leisurely browsing e621. The unlock is incredible, and I wouldn't trade this velocity for anything.
That assuming what you've said is true, which is not. In a work environment, you're forced to optimize whatever that there is, regardless if it's fun or not.
Moreover, there is always fun to be had even in tasks you've found boring beforehand.
An area where I realized that was feature engineering: Early ML systems had handcrafted features that were fed into the model. There were relatively arbitrary and the number of features you could reasonably generate that way was tiny, compared to modern systems - but it gave you some understanding what input the model got exactly and you could use it to clear up some failure modes, or be certain that the model learned something that could not possibly make sense.
Then the idea was to automate feature generation. What's not to like? Except that in practice, the automated features simply seem to become part of the blackbox and are not available anymore for understanding.
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.
Software is going to go through the same adaptation and exaptation process as military aviation.
Both groups love math, but the later group is in a real bind because they have confounded their career with their hobbies/passions.
Why would you make this comment? Is it envy? They were able to do things only some people can do. They enjoyed what they did and it provided value. Now the fun has been taken out of it and you seem to be saying that they deserve to have no fun? What should they have done? Prove theorems while whipping themselves in case they might have fun? Maybe it's a puritan thing? Customer value is the only value.
Many many people enjoy various things in life, such as eating nice meals (quite spiritual to do it in good mood in friends' circle), go camping, or play music. But they don't get paid to do this.
It's very simple to understand. It doesn't depend on deserve. It depends on a concrete person or group of persons having to specifically decide that you get things in return to your time (such as your washing machine repaired, or getting petrol at the gas station) for your efforts at something that they appreciate. It's not God who gives you these things. It's not the universe and it's not Mother Nature. It's concrete people. You have to think about how what you do is actually appreciated by concrete people. You have to do something that people appreciate, whether you agree with their assessment of appreciation or not, it will be that way. You can't simply expect people to give you gas at the gas station simply because you yourself appreciate your own way of spending your time.
"Don, I..."
"Listen. I think this racket just ain't for you. But you're a good kid - too good, maybe - and I promised your father I'd find you something. I'll ask Giovanni. Maybe he can find something for you in bookkeeping."
I'm sure there's a programming equivalent. I believe theyre saying don't lose sight of the trees.
I assure you they're not in it for the money, I make more than they do and hardcore math research is definitely harder than whatever the fuck it is that I do.
I don't think that trying to be a little bit more understanding towards people who are obviously struggling would cost us that much.
That's neoliberalism for you.
Elliptic curve cryptography spent years requiring commercial licenses because it was made practical by Certicom, who patented many of the core inventions.
A lot of the work on homomorphic encryption was done by mathematicians at IBM.
The DES standard was developed by IBM.
RC4, RC5 and RC6, some of the earliest stream ciphers, was a commercial secret because it was developed by Ron Rivest at RSA Security.
NTRU post-quantum crypto was developed as a commercial product from the start.
Many of the earliest cryptosystems were developed commercially, like Enigma and Crypto AG.
A lot of the crypto for mobile phone networks is/was commercial.
Academia did contribute to the early stages of public key cryptography both integer factorization based and elliptic curve based, but given the extensive history of commercial mathematics this stuff would almost certainly have been invented even if there was no academic mathematics at all.
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.
Same here: the value for the society may be more about "making art" than "being a cog in the paperclip factory".
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.
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. :)
oh they are very much aware lol