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The Dark Night of Mathematics

kirwinhampshire.substack.com

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Re: The Dark Night of Mathematics

#91

Post by senderista »

xg15 wrote: post #11
geophile wrote: post #4

> "They are forbidden from creating original works to express themselves. However, they are still permitted to comment on writing, interpret it, share their taste. They are still valued for their appraisal, presentation, understanding and appreciation of creative writing. They just can’t write creatively anymore. They can go on as an enthusiastic spectator. > ... It revealed that the process of prompting novel proofs…

My suspicion is still that this has to do with losing insight in the little specific details of the matter and general understanding. 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 u…

[dead]

Re: The Dark Night of Mathematics

#92

Post by d_burfoot »

Every single knowledge worker is going to face this kind of crisis. It will be worse for people who cared deeply about their craft, but the crisis will have the same shape. The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output.

Mathematicians should realize: instead of spending decades on individual theorems, you can now create whole new subfields of mathematics. Of course, you won't be doing the creation directly, in the way the mathematicians of old did; that's just not the name of the game anymore. But you will still be directing the research and involved in the creation.

Re: The Dark Night of Mathematics

#93

Post by bonoboTP »

azakai wrote: post #68
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…

This has already been shifting in science and engineering because typically large teams are needed to get things done. Math has held to it better, but even there they are almost always multi-named concepts, like Rivest-Shamir-Adleman etc. And even those often have to ignore names that could plausibly be added.

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".

Re: The Dark Night of Mathematics

#94

Post by pillefitz »

bonoboTP wrote: post #65
discreteevent wrote: post #16

Earlier quoted context omitted.

> 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 ma…

Not everything in life is a transactional zero-sum game. We as society can afford people to work on beauty, without anything else in return. I'd even argue that this should be one of mankind's ultimate goals.

Re: The Dark Night of Mathematics

#95

Post by black_knight »

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 am a mathematician, and I agree with you here. I do not feel at all threatened by LLMs, because for me the joy of mathematics is in constructing the theories and beholding their beauty! I know other people are different from me here. I find having to prove theorems a rewarding part of the whole, but I am also not going to weep if an LLM can unstuck me on difficult proofs.

I am really excited if LLMs means more of mathematics will be formalised. Once we have all of mathematics formalised, I think we will start to see real great progress!

Re: The Dark Night of Mathematics

#96

Post by neonstatic »

Nevermark wrote: post #86
neonstatic wrote: post #60

Earlier quoted context omitted.

> 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...

I am completely calm and serious. This should be mundane, obvious by now. 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 m…

Well, I think you have AI psychosis.

Re: The Dark Night of Mathematics

#97

Post by Nevermark »

neonstatic wrote: post #96
Nevermark wrote: post #86

Earlier quoted context omitted.

I am completely calm and serious. This should be mundane, obvious by now. 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 m…

Well, I think you have AI psychosis.

Five years from now you won't. Ten years from now, robotics will upset another capability/economic apple cart.

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.

Re: The Dark Night of Mathematics

#98

Post by skeledrew »

This is the first I've ever heard math connected to the spiritual. For all my life it has been this rigorous thing grounded in reality in such a way that only people who think a certain way could even approach. Now those people are having this strange "crisis" because AI is being more rigorous than humans I guess. I find it... wild. My, but how the mighty have fallen.

Re: The Dark Night of Mathematics

#99

Post by Jtarii »

d_burfoot wrote: post #92

Every single knowledge worker is going to face this kind of crisis. It will be worse for people who cared deeply about their craft, but the crisis will have the same shape. The way through is to change the way you relate to your work, and to appreciate the fact that you can now produce far more output. Mathematicians should realize: instead of spending decades on individual theorems, you can now create whole new subf…

The creation is the actually enjoyable part.

Taking a helicopter to the top of Everest is not as rewarding as climbing the mountain.

You are completely discrediting the joy humans derive from actually -doing- the work, and not just, telling someone else to do the work.

There is a reason artists hate AI, its because they enjoy the actual act of painting, like mathematicians enjoy the act of proving theorems and programmers enjoy the act of typing lines of text into a file on their computer.

We are intentionally deleting all of the enjoyable high agency jobs and replacing them with "model babysitting".

Re: The Dark Night of Mathematics

#100

Post by jknoepfler »

skeledrew wrote: post #98

This is the first I've ever heard math connected to the spiritual. For all my life it has been this rigorous thing grounded in reality in such a way that only people who think a certain way could even approach. Now those people are having this strange "crisis" because AI is being more rigorous than humans I guess. I find it... wild. My, but how the mighty have fallen.

The history of mathematics is tightly coupled to spirituality... some more famous examples off the top of my head are Cantor, Euclid, and Euler, but there are probably hundreds of examples of folks who explicitly tied their faith to their research.

I definitely don't think there's anything inconsistent with mathematical and theological thinking. That actually strikes me as a very strange idea?

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