The Dark Night of Mathematics • Hacker News Board

Re: The Dark Night of Mathematics

#61

Post by consensus1 » Sat, Jul 25, 2026, 7:25 PM UTC

iahds9uasd wrote: post #25

zemvpferreira wrote: post #10

This is what locking yourself away in an ivory tower gets you. Do things ‘for beauty’ and watch as they are automated and commoditized by the people who depend on them for their continued wellbeing, reduced to a hobby or sport. But the reduction began when you yourself started putting more importance on your enjoyment of the process over the value being provided to your customers.

Customers? It's math. This is like a comment a golem built to raise the S&P 500 would write.

If somebody is paying you to do something and someone else comes along that can do that thing much better than you and/or for less money you've got a problem. Whether or not you call the person paying that money a customer or use some other term the fundamental issue is the same.

Re: The Dark Night of Mathematics

#62

Post by bonoboTP » Sat, Jul 25, 2026, 7:26 PM UTC

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.

Re: The Dark Night of Mathematics

#63

Post by jostylr » Sat, Jul 25, 2026, 7:30 PM UTC

As a mathematics person, I find this at odds with my views. I know the current regime rewards new mathematical discoveries for professional advancement, but that is a job thing, one which can be altered by the powers that be. To me investigating mathematics is fun whether it is new to the world or not. The complaint is similar to lamenting how everywhere has already been visited and there is nothing to be done other than have your own personal experience of a place. I saw the redwoods recently for the first time and I thoroughly enjoyed the experience despite not being the first person to see them. Mathematical discovery is much the same except now we have tools that help us dramatically with the tedious stuff, the researching what others know. In the old days, I would spend a long time figuring something out and only at the end could I figure out where to find it in the literature. Very frustrating. Now, we have machines to guide us to many things and understandings and clarifications. They are guides that help us get to where we want to be and then let us wander as we desire. This is incredible. I am currently using them to develop the computational tools I want to use to explore stuff.

As for squeezing in the time to do mathematics if the paying jobs disappear, there is a good chance we will have a world of plenty very shortly. I have a belief that the Austrian economists are right that there will always be plenty for humans to do and get rewarded for, but I also think that the costs of living will be so low that someone who wants to do mathematics will have plenty of time to do so. I hope this person holds the faith long enough and tries to see how the AI's can help accelerate one's own understanding. I am no fan of AIs generating a bunch of papers that no one reads or cares about, but I could say the same about the immense number of papers made by humans as well. If anything, the AIs make all of that immense knowledge more valuable as it is now knowable and accessible through these tools. There is also the fact that the mathematics job market has been oversaturated for at least 20 years. What our new tools allow is for people to be able to do mathematics outside of having access to a research library and top mathematics department.

Re: The Dark Night of Mathematics

#64

Post by anematode » Sat, Jul 25, 2026, 7:34 PM UTC

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.

Re: The Dark Night of Mathematics

#65

Post by bonoboTP » Sat, Jul 25, 2026, 7:39 PM UTC

discreteevent wrote: post #16

zemvpferreira wrote: post #10

This is what locking yourself away in an ivory tower gets you. Do things ‘for beauty’ and watch as they are automated and commoditized by the people who depend on them for their continued wellbeing, reduced to a hobby or sport. But the reduction began when you yourself started putting more importance on your enjoyment of the process over the value being provided to your customers.

> But the reduction began when you yourself started putting more importance on your enjoyment of the process over the value being provided to your customers. 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…

No. The "only value" is the one that people decide to give you, based on their choice. This can be coordinated via taxation and redistribution, but it's still paid from someone to you. Someone has to decide that you doing this thing is something that they like so much that they pay you a token, which you can use to redeem useful work from other citizens, such as repairing you car, or remodeling your bathroom.

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.

Re: The Dark Night of Mathematics

#66

Post by coffepot77 » Sat, Jul 25, 2026, 7:42 PM UTC

tptacek wrote: post #22

One way to differentiate between an art or a craft and a science is that if a genie appeared and offered to trivialize all the discovery work of your career and simply give you the answers today, and you'd say "no", you're probably not doing science.

Persian Curse seems to apply here

“May your every desire be immediately fulfilled.”

Re: The Dark Night of Mathematics

#67

Post by turing_curious » Sat, Jul 25, 2026, 7:46 PM UTC

NitpickLawyer wrote: post #52

Arodex wrote: post #33

Earlier quoted context omitted.

Progress is made by these people - including progress you rely on heavily as a programmer, such as cryptography. Not by the industry.

> 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 pointles…

[dead]

Re: The Dark Night of Mathematics

#68

Post by azakai » Sat, Jul 25, 2026, 7:47 PM UTC

lordnacho wrote: post #58

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 c…

> How much of the identity of a mathematician is tied up in being the first to discovery?

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.

Re: The Dark Night of Mathematics

#69

Post by Zsfe510asG » Sat, Jul 25, 2026, 7:47 PM UTC

jostylr wrote: post #63

As a mathematics person, I find this at odds with my views. I know the current regime rewards new mathematical discoveries for professional advancement, but that is a job thing, one which can be altered by the powers that be. To me investigating mathematics is fun whether it is new to the world or not. The complaint is similar to lamenting how everywhere has already been visited and there is nothing to be done other…

Yes, we'll have free health care, boomers will rent their apartments for $100, everyone will have UBI and a Tesla with a warp drive that travels to the terraformed Mars.

Hayek and Friedman predicted it!

Re: The Dark Night of Mathematics

#70

Post by joe_the_user » Sat, Jul 25, 2026, 7:47 PM UTC

tptacek wrote: post #22

One way to differentiate between an art or a craft and a science is that if a genie appeared and offered to trivialize all the discovery work of your career and simply give you the answers today, and you'd say "no", you're probably not doing science.

The only "fields" where a genie appearing and doing all your work for you are fields (jobs) where you only about the money at the end. There are some fields where a serious practitioner might be happy to have a genie do all the "grunt work" (though what people that is varies - I'm not sure what "discovery work" means here but it doesn't matter since present AI promises to do everything in the future if not now).

And this analogy breaks down further given that both the real now genie and the hypothetically more powerful genie of the future would each work for your (ex) employer.