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Machine-Assisted Proof [pdf]

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Re: Machine-Assisted Proof [pdf]

#21

Post by simplemathmind »

generationP wrote: post #18
simplemathmind wrote: post #16

I did not read the pdf, but I think that LLM and Lean could be useful tools for mathematiceans to prove or refute theorems, but the creative idea that sparks knowledge and new theorems lies in the human, the others are tools that can help to reduce time and effort needed and so, indirectly, they can foster and enhance creativity. It also could mitigate some reasoning that require mechanical prove of many details. Any…

Right, and the paper you didn't read contains a lot more than that.

I apologize in that case, can you give a brief summary of what is the most important point of that pdf?, I don't know why but my gut feeling is to refuse to read something just based on people reputation. I know that Tao is a very bright mathematician but I also think that he doesn't know much about computer science or computer languages (my evidence is very slim here: once I noted that Tao was very happy with a very simple program, a trivial one, so I inferred from that he still has to learn a lot about programming). For now, it seems clear that the best he can do (for him and us) is to devote his time to math that is his best skill. But it could happen that he could use his best world IQ and math skills to learn how to use LLMs and Lean in a never seem before way to obtain something really valuable.

Today I don't think there is any evidence that such thing is going to happen. On one hand, in general, intelligent people are the first to learn how to use new tools in new or better ways, tools that are useful for what they are good at and are devote at. On the other hand, following that path detracts energy from the core of math that requires intuition and creativity and not so much mechanical proofs. On a third hand, there is always the money question that we can not see, that is because is in the third hand.

Re: Machine-Assisted Proof [pdf]

#22

Post by empiricus »

benreesman wrote: post #9

With all respect to luminaries: this will not stand up. This will be treated harshly by history. I’m nobody but I’m going to stand up to Terence Tao and Scott Aarinson: you’re wrong or bought or both. This is a detour and I want to make clear to history what side I was on.

What's with the beef? In the paper Terence describes how he currently uses some imperfect but useful tools, which will surely change in the future if better tools appear. It does not say "LLM will be smarter than a kid bwahaha world domination".

Re: Machine-Assisted Proof [pdf]

#23

Post by rthanb »

jstummbillig wrote: post #13
kartwna wrote: post #10

"I have found it works surprisingly well for writing mathematical LaTeX, as well as formalizing in Lean; indeed, it assisted in writing this very article by suggesting several sentences as I was writing, many of which I retained or lightly edited for the final version. While the quality of its suggestions is highly variable, it can sometimes display an uncanny level of simulated understanding of the intent of the tex…

Sure: Supporting stuff furthers that stuff. If it works for you, there's your incentive.

Sure, have a Pepsi. It is delicious!

At this stage Tao should disclose whether he has any financial relationship with OpenAI, including stock ownership or even access to experimental models or more computational power than the average user.

I've never seen any academic hyping up a company like that, unless they explicitly have/had a financial relationship like Scott Aaronson.

Re: Machine-Assisted Proof [pdf]

#24

Post by screye »

kartwna wrote: post #10

"I have found it works surprisingly well for writing mathematical LaTeX, as well as formalizing in Lean; indeed, it assisted in writing this very article by suggesting several sentences as I was writing, many of which I retained or lightly edited for the final version. While the quality of its suggestions is highly variable, it can sometimes display an uncanny level of simulated understanding of the intent of the tex…

Tenured professors are at no risk of losing jobs and have minimum business interests. The literal smartest person in the world will be the last person to lose his job anyway.

AI anxiety comes from a fear that AI will replace us, individuals or corporate entities alike. Tao is immune to these risks.

Re: Machine-Assisted Proof [pdf]

#25

Post by rthanb »

empiricus wrote: post #22
benreesman wrote: post #9

With all respect to luminaries: this will not stand up. This will be treated harshly by history. I’m nobody but I’m going to stand up to Terence Tao and Scott Aarinson: you’re wrong or bought or both. This is a detour and I want to make clear to history what side I was on.

What's with the beef? In the paper Terence describes how he currently uses some imperfect but useful tools, which will surely change in the future if better tools appear. It does not say "LLM will be smarter than a kid bwahaha world domination".

This paper just namedrops ChatGPT. Previously, we had this:

https://mathstodon.xyz/@tao/113132502735585408

It may only take one or two further iterations of improved capability (and integration with other tools, such as computer algebra packages and proof assistants) until the level of "(static simulation of a) competent graduate student" is reached, at which point I could see this tool being of significant use in research level tasks.

Re: Machine-Assisted Proof [pdf]

#26

Post by benreesman »

empiricus wrote: post #22
benreesman wrote: post #9

With all respect to luminaries: this will not stand up. This will be treated harshly by history. I’m nobody but I’m going to stand up to Terence Tao and Scott Aarinson: you’re wrong or bought or both. This is a detour and I want to make clear to history what side I was on.

What's with the beef? In the paper Terence describes how he currently uses some imperfect but useful tools, which will surely change in the future if better tools appear. It does not say "LLM will be smarter than a kid bwahaha world domination".

some of the most demonstrably evil people alive at scale are extravagant in their claims of precisely “blah blah world domination”.

I’m calling bullshit on AGI. I’m repudiating as offensive both the ill intentions and the technical failure of these people.

I’m proposing that all sincere hackers denounce OpenAI as a matter of principle.

Did I stutter?

Re: Machine-Assisted Proof [pdf]

#27

Post by rthanb »

screye wrote: post #24
kartwna wrote: post #10

"I have found it works surprisingly well for writing mathematical LaTeX, as well as formalizing in Lean; indeed, it assisted in writing this very article by suggesting several sentences as I was writing, many of which I retained or lightly edited for the final version. While the quality of its suggestions is highly variable, it can sometimes display an uncanny level of simulated understanding of the intent of the tex…

Tenured professors are at no risk of losing jobs and have minimum business interests. The literal smartest person in the world will be the last person to lose his job anyway. AI anxiety comes from a fear that AI will replace us, individuals or corporate entities alike. Tao is immune to these risks.

So are all other academics though. There is at least some resistance on Mathoverflow:

https://meta.mathoverflow.net/questions/6039/has-mo-been-red...

The question of exploitation is not a question of anxiety, but of exasperation.

Re: Machine-Assisted Proof [pdf]

#28

Post by [deleted] »

rthanb wrote: post #23
jstummbillig wrote: post #13

Earlier quoted context omitted.

Sure: Supporting stuff furthers that stuff. If it works for you, there's your incentive.

Sure, have a Pepsi. It is delicious! At this stage Tao should disclose whether he has any financial relationship with OpenAI, including stock ownership or even access to experimental models or more computational power than the average user. I've never seen any academic hyping up a company like that, unless they explicitly have/had a financial relationship like Scott Aaronson.

[deleted]

Re: Machine-Assisted Proof [pdf]

#29

Post by vouaobrasil »

I think his comparison to previous machine-assistance is misleading. In previous cases, the use of machines was never creative, whereas now AI has the ability to suggest creative lines.

In the short-term, this sounds exciting. But I also think it reduces the beauty of math because it is mechanizing it into a production line for truth, and reduces the emphasis on the human experience in the search for truth.

The same thing has happened in chess, with more people advocating for Fischer random because of the boring aspect of preparing openings with a computer, and studying games with a computer. Of course, the computer didn't initiate the process of in-depth opening preparation but it launched it to the next level. The point is that mechanization is boring except for pure utility.

My point is that math as a thing of beauty is becoming mechanized and it will lead to the same level of apathy in math amongst the potentially interested. Of course, now it's exciting because it's still the wild west and there are things to figure out, but what of the future?

Using advanced AI in math is a mistake in my opinion. The search for truth as a human endeavor is inspiring. The production of truth in an industrialized fashion is boring.

Re: Machine-Assisted Proof [pdf]

#30

Post by benreesman »

empiricus wrote: post #22
benreesman wrote: post #9

With all respect to luminaries: this will not stand up. This will be treated harshly by history. I’m nobody but I’m going to stand up to Terence Tao and Scott Aarinson: you’re wrong or bought or both. This is a detour and I want to make clear to history what side I was on.

What's with the beef? In the paper Terence describes how he currently uses some imperfect but useful tools, which will surely change in the future if better tools appear. It does not say "LLM will be smarter than a kid bwahaha world domination".

The beef is that many of us have enough grime on our hands. Many of us at the absolute elite frontier of this technology find its application in both technical reality and fundraising fantasy to be beneath any possible ideal.

And there are a lot of us.

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