The cultural divide between mathematics and AI • Hacker News Board

Re: The cultural divide between mathematics and AI

#51

Post by WhyOhWhyQ » Wed, Mar 12, 2025, 7:02 PM UTC

throw8404948k wrote: post #39

sarchertech wrote: post #26

Earlier quoted context omitted.

I think you’re missing the point of what the advisor is saying.

No, I get it. My point is human advisor does not have enough time, to answer questions and correctly explain the subject. I may get like 4 hours a week, if lucky. Books are just a cheap substitute for real dialog and reasoning with a teacher. Most ancient philosophy papers were in form of dialog. It is much faster to explain things. AI is a game changer. It shortens feedback loop from a week to hour! It makes mistake…

Books aren't just a lower quality version of dialog with a person though. They operate entirely differently. With very few people can you think quietly for 30 minutes straight without talking, but with a book you can put it down and come back to it at will.

I don't think professional programmers were using notepad in 1985. Here's talk of IDEs from an article from 1985: https://dl.acm.org/doi/10.1145/800225.806843 It mentions Xerox Development Environment, from 1977 https://en.wikipedia.org/wiki/Xerox_Development_Environment

The feedback loop for programming / mathematics / other things I've studied was not a week in the year 2019. In that ancient time the feedback look was maybe 10% slower than with any of these LLMs since you had to look at Google search.

Re: The cultural divide between mathematics and AI

#52

Post by Dracophoenix » Wed, Mar 12, 2025, 7:04 PM UTC

bluefirebrand wrote: post #25

Henchman21 wrote: post #15

Earlier quoted context omitted.

I’ve worked in tech my entire adult life and boy do I feel this deep in my soul. I have slowly withdrawn from the higher-level tech designs and decision making. I usually disagree with all of it. Useless pursuits made only for resume fodder. Tech decisions made based on the bonus the CTO gets from the vendors (Superbowl tickets anyone?) not based on the suitability of the tech. But absolutely worst of all is the arro…

> Move fast and break things!! Even when its the society you live in. This is the part I don't get honestly Are people just very shortsighted and don't see how these changes are potentially going to cause upheaval? Do they think the upheaval is simply going to be worth it? Do they think they will simply be wealthy enough that it won't affect them much, they will be insulated from it? Do they just never think about co…

> Are people just very shortsighted and don't see how these changes are potentially going to cause upheaval?

> Do they think the upheaval is simply going to be worth it?

All technology causes upheaval. We've benefited from many of these upheavals to the point where it's impossible for most to imagine a world without the proliferation of movable type, the internal combustion engine, the computer, or the internet. All of your criticisms could have easily been made word for word by the Catholic Church during the medieval era. The "society" of today is no more of a sacred cow than its antecedent incarnations were half a millenium ago. As history has shown, it must either adapt, disperse, or die.

Re: The cultural divide between mathematics and AI

#53

Post by andrewl » Wed, Mar 12, 2025, 7:10 PM UTC

bluefirebrand wrote: post #25

Henchman21 wrote: post #15

Earlier quoted context omitted.

I’ve worked in tech my entire adult life and boy do I feel this deep in my soul. I have slowly withdrawn from the higher-level tech designs and decision making. I usually disagree with all of it. Useless pursuits made only for resume fodder. Tech decisions made based on the bonus the CTO gets from the vendors (Superbowl tickets anyone?) not based on the suitability of the tech. But absolutely worst of all is the arro…

> Move fast and break things!! Even when its the society you live in. This is the part I don't get honestly Are people just very shortsighted and don't see how these changes are potentially going to cause upheaval? Do they think the upheaval is simply going to be worth it? Do they think they will simply be wealthy enough that it won't affect them much, they will be insulated from it? Do they just never think about co…

Exactly. It was described in Chesterton’s Fence:

There exists in such a case a certain institution or law; let us say, for the sake of simplicity, a fence or gate erected across a road. The more modern type of reformer goes gaily up to it and says, “I don’t see the use of this; let us clear it away.” To which the more intelligent type of reformer will do well to answer: “If you don’t see the use of it, I certainly won’t let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it.”

Re: The cultural divide between mathematics and AI

#54

Post by [deleted] » Wed, Mar 12, 2025, 7:18 PM UTC

tech_ken wrote: post #44

Mathematics is, IMO, not the axioms, proofs, or theorems. It's the human process of organizing these things into conceptual taxonomies that appeal to what is ultimately an aesthetic sensibility (what "makes sense"), updating those taxonomies as human understanding and aesthetic preferences evolve, as well as practical considerations ('application'). Generating proofs of a statement is like a biologist identifying a n…

[deleted]

Re: The cultural divide between mathematics and AI

#55

Post by bluefirebrand » Wed, Mar 12, 2025, 7:32 PM UTC

Dracophoenix wrote: post #52

bluefirebrand wrote: post #25

Earlier quoted context omitted.

> Move fast and break things!! Even when its the society you live in. This is the part I don't get honestly Are people just very shortsighted and don't see how these changes are potentially going to cause upheaval? Do they think the upheaval is simply going to be worth it? Do they think they will simply be wealthy enough that it won't affect them much, they will be insulated from it? Do they just never think about co…

> Are people just very shortsighted and don't see how these changes are potentially going to cause upheaval? > Do they think the upheaval is simply going to be worth it? All technology causes upheaval. We've benefited from many of these upheavals to the point where it's impossible for most to imagine a world without the proliferation of movable type, the internal combustion engine, the computer, or the internet. All…

> The "society" of today is no more of a sacred cow than its antecedent incarnations were half a millenium ago. As history has shown, it must either adapt, disperse, or die

I am not concerned about some kind of "sacred cow" that I want to preserve

I am concerned about a future where those with power no longer need 90% of the population so they deploy autonomous weaponry that grinds most of the population into fertilizer

And I'm concerned there are a bunch of short sighted idiots gleefully building autonomous weaponry for them, thinking they will either be spared from mulching, or be the mulchers

Edit: The thing about appealing to history is that it also shows that when upper classes get too powerful they start to lose touch with everyone else, and this often leads to turmoil that affects the common folk most

As one of the common folk, I'm pretty against that

Re: The cultural divide between mathematics and AI

#56

Post by bluefirebrand » Wed, Mar 12, 2025, 7:36 PM UTC

chasd00 wrote: post #41

bluefirebrand wrote: post #25

Earlier quoted context omitted.

> Move fast and break things!! Even when its the society you live in. This is the part I don't get honestly Are people just very shortsighted and don't see how these changes are potentially going to cause upheaval? Do they think the upheaval is simply going to be worth it? Do they think they will simply be wealthy enough that it won't affect them much, they will be insulated from it? Do they just never think about co…

Humans like to solve problems and be at the top of the heap. Such is life, survival of the fittest after all. AI is a problem to solve, whoever gets to AGI first will be at the top of the heap. It's a hard drive to turn off.

In theory this is actually pretty easy to "turn off"

You flatten the heap

You decrease or eliminate the reward for being at the top

You decrease or eliminate the penalty for being at the bottom

The main problem is that we haven't figured out a good way to do this without creating a whole bunch of other problems

Re: The cultural divide between mathematics and AI

#57

Post by nicf » Wed, Mar 12, 2025, 7:37 PM UTC

xg15 wrote: post #22

> One question generated particular concern: what would happen if an AI system produced a proof of a major conjecture like the Riemann Hypothesis, but the proof was too complex for humans to understand? Would such a result be satisfying? Would it advance mathematical understanding? The consensus seemed to be that while such a proof might technically resolve the conjecture, it would fail to deliver the deeper understa…

oersted's answer basically covers it, so I'm mostly just agreeing with them: the answer is that you use a computer. Not another AI model, but a piece of regular, old-fashioned software that has much more in common with a compiler than an LLM. It's really pretty closely analogous to the question "How do you verify that some code typechecks if you don't understand it?"

In this hypothetical Riemann Hypothesis example, the only thing the human would have to check is that (a) the proof-verification software works correctly, and that (b) the statement of the Riemann Hypothesis at the very beginning is indeed a statement of the Riemann Hypothesis. This is orders of magnitude easier than proving the Riemann Hypothesis, or even than following someone else's proof!

Re: The cultural divide between mathematics and AI

#58

Post by jmount » Wed, Mar 12, 2025, 7:58 PM UTC

unsui wrote: post #33

bluefirebrand wrote: post #25

Earlier quoted context omitted.

> Move fast and break things!! Even when its the society you live in. This is the part I don't get honestly Are people just very shortsighted and don't see how these changes are potentially going to cause upheaval? Do they think the upheaval is simply going to be worth it? Do they think they will simply be wealthy enough that it won't affect them much, they will be insulated from it? Do they just never think about co…

I've called this out numerous times (and gotten downvoted regularly), with what I call the "Cult of Optimization" aka optimization-for-its-own-sake, aka pathological optimization. It's basically meatspace internalizing and adopting the paperclip problem as a "good thing" to pursue, screw externalities and consequences. And, lo-and-behold, my read for why it gets downvoted here is that a lot of folks on HN ascribe to…

Love your point. "Lack of alignment" affects more than just AIs.

Re: The cultural divide between mathematics and AI

#59

Post by butwhatwut » Wed, Mar 12, 2025, 8:15 PM UTC

feoren wrote: post #27

bluefirebrand wrote: post #25

Earlier quoted context omitted.

> Move fast and break things!! Even when its the society you live in. This is the part I don't get honestly Are people just very shortsighted and don't see how these changes are potentially going to cause upheaval? Do they think the upheaval is simply going to be worth it? Do they think they will simply be wealthy enough that it won't affect them much, they will be insulated from it? Do they just never think about co…

> Do they think they will simply be wealthy enough that it won't affect them much, they will be insulated from it? Yes, partly that. Mostly they only care about their rank. Many people would burn down the country if it meant they could be king of the ashes. Even purely self-interested people should welcome a better society for all, because a rising tide lifts all boats. But not only are they selfish, they're also ver…

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Re: The cultural divide between mathematics and AI

#60

Post by nybsjytm » Wed, Mar 12, 2025, 8:19 PM UTC

EigenLord wrote: post #50

Is it really a culture divide or is it an economic incentives divide? Many AI researchers are mathematicians. Any theoretical AI research paper will typically be filled with eye-wateringly dense math. AI dissolves into math the closer you inspect it. It's math all the way down. What differs are the incentives. Math rewards openness because there's no real concept of a "competitive edge", you're incentivized to freely…

> Many AI researchers are mathematicians. Any theoretical AI research paper will typically be filled with eye-wateringly dense math. AI dissolves into math the closer you inspect it. It's math all the way down.

There is a major caveat here. Most 'serious math' in AI papers is wrong and/or irrelevant!

It's even the case for famous papers. Each lemma in Kingma and Ba's ADAM optimization paper is wrong, the geometry in McInnes and Healy's UMAP paper is mostly gibberish, etc...

I think it's pretty clear that AI researchers (albeit surely with some exceptions) just don't know how to construct or evaluate a mathematical argument. Moreover the AI community (at large, again surely with individual exceptions) seems to just have pretty much no interest in promoting high intellectual standards.