Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

The Dark Night of Mathematics

kirwinhampshire.substack.com

Post reply on HN
Print view View original

71–80 of 321 posts

Re: The Dark Night of Mathematics

#71

Post by fraboniface »

robotpepi wrote: post #19
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.

Exactly! I have some many colleagues who typically say that they do "math for the beauty" while holding permanent research positions funded by the state.

One could also see it this way: shouldn't the goal of society be to allow more and more people to do things for the beauty of it rather that producing ever more useless stuffs and destroy the planet on the way?

Re: The Dark Night of Mathematics

#72

Post by mike_hearn »

Arodex wrote: post #33
robotpepi wrote: post #19

Earlier quoted context omitted.

Exactly! I have some many colleagues who typically say that they do "math for the beauty" while holding permanent research positions funded by the state.

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

Cryptography has always been largely driven by industrial mathematicians.

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.

Re: The Dark Night of Mathematics

#73

Post by joshdavham »

drivebyhooting wrote: post #15

Well for me the twilight had already come when I realized I’d never amount to a decent mathematician. Maybe this is rather a common experience? LLMs just democratized that process.

What made you realize you'd never amount to a decent mathematician?

For me, it was a course in Real Analysis haha

Re: The Dark Night of Mathematics

#74

Post by joe_the_user »

yaqubroli wrote: post #7

> “Even if AI can prove theorems and theory-craft more efficiently than humans, and even if these proofs and theories are beautiful and interesting, and even if they are presented with elegance and clarity of thought, mathematicians will still have a place in the appraisal, presentation, understanding and appreciation of this new abundance of pleasing non-human proofs. We can still practice mathematics, learn mathema…

I begrudgingly agree, but with the caveat that tending to a vegetable garden in your backyard is also a spiritual pursuit. Mathematics isn’t some special discipline that elevates you beyond other people, as much as it is useful and interesting.

The thing is, if someone had the option to press a button and cause their garden to be weeded and growing perfectly, if most gardeners were using that button instead of growing normally, maybe some people would keep gardening for the spiritual part but they'd certainly feel like the rug had been pulled out from under them.

Edit: As another example, Robert Pirsig in his famous book described motorcycle maintinence as a spiritual enterprise. However, the quality that gave it this was the patience required-for and the uncertainty involved-in the enterprise. And again, if all you have to do is press a button, the spiritual part kind of goes away.

Re: The Dark Night of Mathematics

#75

Post by lagrange77 »

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…

> investigating mathematics is fun whether it is new to the world or not.

Yes exactly. Enjoying the beauty of nature is (thankfully) completely decoupled from the job/money/society side of things.

Re: The Dark Night of Mathematics

#76

Post by blueflow »

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.

math never was a science to begin with.

Re: The Dark Night of Mathematics

#77

Post by loose-cannon »

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.

there's a human element in discovery and in problem solving. Whether or not somebody chooses to sidestep work isn't necessarily an indication that the work isn't science. It's just an indication that some people are passionate and invested in performing the work.

Re: The Dark Night of Mathematics

#78

Post by breezybottom »

jckt wrote: post #35
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.

Disregarding the competing definitions of “science”, a significant value in mathematical work is “the journey”. The truth or falsehood of individual results are rarely as important as the machinery developed to deliver it. If all the genie did was tell you something was true or false, the only learning you gain is to backtrack and develop the machinery yourself. To a certain extent this is true of the other sciences…

Not from a logical positivist perspective, which is why you conveniently disregarded "competing views".

Re: The Dark Night of Mathematics

#79

Post by mkckto »

Without knowing anything about the specifics of the conjectures that are falling, I wonder if this affair highlights an issue with the quality of the "open conjectures" that are out there.

There are a lot of reasons you might make a conjecture. Perhaps you are motivated by a search for structure: "We suspect that these objects behave like this, therefore we naturally imagine that...". But you might make a conjecture out of empirical evidence: "We checked 1 million examples, time to make a conjecture." While empiricism has its place in mathematics, it might not be the best motivation for a conjecture. As Bishop said, "Do not ask whether a statement is true until you know what it means." If you pose a conjecture based on empirical evidence, perhaps you should be thinking more about why you would imagine your statement be true in the first place.

I know some will think that this rings of goalpost moving, but when I hear about all these counterexamples spelling the end of mathematics as we know it, I just wonder how strong those conjectures really were in the first place. Again, I haven't actually dug into the specifics of any of the results so admittedly I could be totally off base, but I do know that not all conjectures are created equal.

Re: The Dark Night of Mathematics

#80

Post by code51 »

lagrange77 wrote: post #75
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…

> investigating mathematics is fun whether it is new to the world or not. Yes exactly. Enjoying the beauty of nature is (thankfully) completely decoupled from the job/money/society side of things.

You can enjoy the beauty of nature, especially mathematics, if you're alive and well enough to focus.
Post reply on HN