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After Math

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Re: After Math

#111

Post by QuesnayJr »

charcircuit wrote: post #31

>The first assumption is wrong because to really solve a mathematical problem, providing a mere answer (even if formally certified) is not sufficient. What is missing is an intelligible proof that human mathematicians can understand and use to advance the aims of mathematics. This makes a bad assumption that humans need to be the one to advance the aims of mathematics. LLMs could be what advances the aims of mathemat…

This is exactly backwards. Mathematics predates the idea of formal proof by millenia. The purpose of proofs since Euclid is to explain to your fellow human why something is true. The idea that the purpose of math is formal proof alone is a new idea that (some) computer programmers want to impose on the field (for the understandable reason that it makes computers primary).

Formal proof only emerged early in the 20th century, and the standard became that in theory a proof should be formalizable to answer any skepticism, but the real goal in Euclid's time and ours has been to communicate why a theorem is true to your fellow humans. There were a few theorems that are only known via computer proof, like the Four Color Theorem, but this has always been regarded as disappointing or even controversial, and the fact that there hasn't been any conceptual breakthrough has meant that we didn't learn anything other than the sheer fact that the Four Color Theorem is true. Theorems that produce understanding, on the other hand, typically produce many new ideas that lead to more theorems.

The purpose of scholarship is understanding. This is just as true for science as it is for math. If AI produces a unified theory of fundamental physics, but it's just an opaque blob, physicists will find it just as unsatisfying.

Re: After Math

#112

Post by awr-asjkt »

It is curious that the academics discuss their own narrow issues and are completely silent on the broader issues of copyright violations, energy usage etc.

Re: After Math

#114

Post by eetde »

yazaddaruvala wrote: post #12

I think as a civilization we need to postulate a new term: “purpose death” Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence. I truly think because of the pace of innovation this will be a universal feeling for every hu…

This goal post stuff is tiresome.

The only thing it reveals is how poor humans are predicting and defining things.

Re: After Math

#115

Post by eetde »

himata4113 wrote: post #56
Negitivefrags wrote: post #43

Earlier quoted context omitted.

You might have delivered 10x more code, but did you deliver 10x more value? Or put another way, are you making 10x more money? It's easy to spend excess productivity effectively wasting time. Most companies did it before AI, and will continue doing it after. It's easy to believe you are not wasting time because you have more bugs fixed or more features delivered, but if it doesn't move the bottom line, what is the po…

I mean it doesn't have to bring 10x more value, but it can be a 10x better experience for existing users. There have been so many niche bugs that were never ever fixed because there's more important things to do, but because fixing a niche bug is now 1 click away that really changes the economics quite a bit especially for small teams. I'm personally working on a product solo that would not be possible without a team…

With all due respect when you strip away the noise - unless it shows up in the financials it hasn’t done anything for the firm.

This is something many firms are struggling to grasp.

Re: After Math

#116

Post by eetde »

svara wrote: post #62
matherial wrote: post #11

Earlier quoted context omitted.

It might feel that way, but I'll ask again: where's the payoff? Where's all the amazing software that everyone is now supposedly shipping 10x faster than before? If I look at the software I'm actually using day-to-day, or that my friends are using, all this stuff looks exactly the same as it did in 2021. Not a single product release from Google, Microsoft, or more scrappy companies in the past 6 months made me go "wo…

This has a clear answer in systems theory; the ability to bang out code was never the limiting factor for Google et al.; large organizations are limited by coordination costs. It's the small teams you need to pay attention to, the organizations that really were limited by engineering capacity. These are by definition also less visible - for now.

That’s not true at all.

The constraint is taste and vision.

You can’t buy either.

Re: After Math

#117

Post by eetde »

matherial wrote: post #11
stabbles wrote: post #7

Wouldn't AI make the field of mathematics more ambitious? In software development it feels that way: there are often tasks I can take on that would have been too risky in 2025, because it was unclear if they were worth it. Now you generate a prototype and can make much better judgement calls what is possible and what is worth pursuing.

It might feel that way, but I'll ask again: where's the payoff? Where's all the amazing software that everyone is now supposedly shipping 10x faster than before? If I look at the software I'm actually using day-to-day, or that my friends are using, all this stuff looks exactly the same as it did in 2021. Not a single product release from Google, Microsoft, or more scrappy companies in the past 6 months made me go "wo…

Beautiful post.

Especially the implicit trade off. - if it becomes ‘easy’ to produce little thought and care is put into it.

Personally I saw this coming ages ago.

After all we live off the contributions of the few in relative terms.

No surprise - most humans don’t have much imagination or creativity.

Re: After Math

#118

Post by curt15 »

GPerson wrote: post #106
yazaddaruvala wrote: post #12

I think as a civilization we need to postulate a new term: “purpose death” Defined something like: temporary state of complete loss of personal purpose and the experience of existential dread from never achieving self-actualization in spite of the tremendous time commitment towards excellence in a now automated intelligence. I truly think because of the pace of innovation this will be a universal feeling for every hu…

I’m just going to say this 100 times I guess. Terence Tao has had a very consistent narrative on AI in math for a very long time, at least since 2023. He’s always described it as a surprisingly good tool and has advocated that mathematicians adopt the technology without becoming totally reliant on it. He’s also always argued that mathematics is fundamentally about human understanding . There’s no change in his messag…

> He’s also always argued that mathematics is fundamentally about human understanding.

It's also worth pointing out he didn't come up with this viewpoint just to "cope" with the headlines. Thurston articulated this way back in the 90s (https://arxiv.org/pdf/math/9404236) and also more recently (https://mathoverflow.net/questions/43690/whats-a-mathematici...):

> The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding.

Re: After Math

#119

Post by auggierose »

anonymouz wrote: post #113
auggierose wrote: post #110

Earlier quoted context omitted.

It is not that nicely written.

Maybe, but it's not worth discussing the content if you dont comprehend what the authors are actually saying.

Here is what they are saying:

    1. AI really did solve a problem in mathematics.

    The first assumption is wrong because to really solve a
    mathematical problem, providing a mere answer (even if
    formally certified) is not sufficient.
Yes, it is sufficient. To say otherwise is just goalpost shifting because you don't like the answer.

    There are, in fact, two notions of proof: a logical
    notion and an intelligible notion.
Wrong again, the only real notion of proof is logical. It is not even possible to say exactly what an "intelligible" notion would be, because that would make it logical.

I would be very surprised if Tao couldn't extract a proof that he understands within a few months out of the formal proof. I would compare this to understanding a difficult proof in some math journal.

In the end, all of this forth and back does not matter. A logical proof is a perfectly fine answer, and given that AI can provide that now, this is the future.

Re: After Math

#120

Post by curt15 »

pylua wrote: post #89
rdedev wrote: post #75

Earlier quoted context omitted.

> AI will run and trample anything that stays in front of it. Right now that entirely depends on the whims of a few people. We can try to make it not be that but I don't have much hope in that area. See climate change > As a software engineer, I myself have only recently recovered from it Can I ask you how you came here? Right now I am getting closer to "purpose death" as you call it. Software engineering is one of t…

It’s not the execs, it’s the economic pressures. If they don’t cut cost someone else will. For the record I feel like I dm in your position also.

Since OpenAI is undoubtedly also under economic pressure, why is it still hiring humans for Account Associates, Android Engineers, Data Scientists instead of demonstrating its AI prowess by automating those roles?

https://openai.com/careers/search/

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