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“Erdos problem #728 was solved more or less autonomously by AI”

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Re: “Erdos problem #728 was solved more or less autonomously by AI”

#11

Post by chmod775 »

malux85 wrote: post #4
observationist wrote: post #2

Reconfiguring existing proofs in ways that have been tedious or obscured from humans, or using well framed methods in novel ways, will be done at superhuman speeds, and it'll unlock all sorts of capabilities well before we have to be concerned about AGI. It's going to be awesome to see what mathematicians start to do with AI tools as the tools become capable of truly keeping up with what the mathematicians want from…

This is what has excited me for many years - the idea I call "scientific refactoring" What happens if we reason upwards but change some universal constants? What happens if we use Tao instead of Pi everywhere , these kind of fun questions would otherwise require an enormous intellectual effort whereas with the mechanisation and automation of thought, we might be able to run them and see!

I can write a sed command/program that replaces every occurence of PI with TAU/2 in LaTeX formulas and it'll take me about 30 minutes.

The "intellectual effort" this requires is about 0.

Maybe you meant Euler's number? Since it also relates to PI, it can be used and might actually change the framework in an "interesting way" (making it more awkward in most cases - people picked PI for a reason).

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#12

Post by nextaccountic »

D-Machine wrote: post #3

This is great, there is still so much potential in AI once we move beyond LLMs to specialized approaches like this. EDIT: Look at all the people below just reacting to the headline and clearly not reading the posts. Aristotle ( https://arxiv.org/abs/2510.01346 ) is key here folks. EDIT2: It is clear much of the people below don't even understand basic terminology. Something being a transformer doesn't make it an LLM…

It was done by a LLM (ChatGPT)

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#13

Post by measurablefunc »

lapetitejort wrote: post #9
stouset wrote: post #6

Earlier quoted context omitted.

> What happens if we use Tao instead of Pi everywhere Literally nothing other than mild convenience. It’s just 2pi.

Call me a mathematical extremist but I think pi should equal 6.28... and tau, which looks like half of pi, should equal 3.14...

In 1897, the Indiana General Assembly attempted to legislate a new value for pi, proposing it be defined as 3.2, which was based on a flawed mathematical proof. This bill, known as the Indiana pi bill, never became law due to its incorrect assertions and the prior proof that squaring the circle is impossible: https://en.wikipedia.org/wiki/Indiana_pi_bill

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#14

Post by lwansbrough »

Can anyone with specific knowledge in a sophisticated/complex field such as physics or math tell me: do you regularly talk to AI models? Do feel like there's anything to learn? As a programmer, I can come to the AI with a problem and it can come up with a few different solutions, some I may have thought about, some not.

Are you getting the same value in your work, in your field?

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#15

Post by sublinear »

malux85 wrote: post #4
observationist wrote: post #2

Reconfiguring existing proofs in ways that have been tedious or obscured from humans, or using well framed methods in novel ways, will be done at superhuman speeds, and it'll unlock all sorts of capabilities well before we have to be concerned about AGI. It's going to be awesome to see what mathematicians start to do with AI tools as the tools become capable of truly keeping up with what the mathematicians want from…

This is what has excited me for many years - the idea I call "scientific refactoring" What happens if we reason upwards but change some universal constants? What happens if we use Tao instead of Pi everywhere , these kind of fun questions would otherwise require an enormous intellectual effort whereas with the mechanisation and automation of thought, we might be able to run them and see!

* Tau

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#16

Post by D-Machine »

nextaccountic wrote: post #12
D-Machine wrote: post #3

This is great, there is still so much potential in AI once we move beyond LLMs to specialized approaches like this. EDIT: Look at all the people below just reacting to the headline and clearly not reading the posts. Aristotle ( https://arxiv.org/abs/2510.01346 ) is key here folks. EDIT2: It is clear much of the people below don't even understand basic terminology. Something being a transformer doesn't make it an LLM…

It was done by a LLM (ChatGPT)

It could not be done without Aristotle (https://arxiv.org/pdf/2510.01346), did you even read the links?

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#17

Post by D-Machine »

XCSme wrote: post #7
D-Machine wrote: post #3

This is great, there is still so much potential in AI once we move beyond LLMs to specialized approaches like this. EDIT: Look at all the people below just reacting to the headline and clearly not reading the posts. Aristotle ( https://arxiv.org/abs/2510.01346 ) is key here folks. EDIT2: It is clear much of the people below don't even understand basic terminology. Something being a transformer doesn't make it an LLM…

> beyond LLMs to specialized approached Do you mean that in this case, it was not a LLM?

It could not be done without Aristotle (https://arxiv.org/pdf/2510.01346), as clearly described in Tao's posts.

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#18

Post by D-Machine »

ctoth wrote: post #5
D-Machine wrote: post #3

This is great, there is still so much potential in AI once we move beyond LLMs to specialized approaches like this. EDIT: Look at all the people below just reacting to the headline and clearly not reading the posts. Aristotle ( https://arxiv.org/abs/2510.01346 ) is key here folks. EDIT2: It is clear much of the people below don't even understand basic terminology. Something being a transformer doesn't make it an LLM…

[flagged]

Did you not read the parts where Aristotle (https://arxiv.org/pdf/2510.01346) was an integral component of all this?

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#19

Post by HardCodedBias »

malux85 wrote: post #4
observationist wrote: post #2

Reconfiguring existing proofs in ways that have been tedious or obscured from humans, or using well framed methods in novel ways, will be done at superhuman speeds, and it'll unlock all sorts of capabilities well before we have to be concerned about AGI. It's going to be awesome to see what mathematicians start to do with AI tools as the tools become capable of truly keeping up with what the mathematicians want from…

This is what has excited me for many years - the idea I call "scientific refactoring" What happens if we reason upwards but change some universal constants? What happens if we use Tao instead of Pi everywhere , these kind of fun questions would otherwise require an enormous intellectual effort whereas with the mechanisation and automation of thought, we might be able to run them and see!

Think of how this opened up EM:

https://ddcolrs.wordpress.com/2018/01/17/maxwells-equations-...

Re: “Erdos problem #728 was solved more or less autonomously by AI”

#20

Post by saulpw »

chmod775 wrote: post #11
malux85 wrote: post #4

Earlier quoted context omitted.

This is what has excited me for many years - the idea I call "scientific refactoring" What happens if we reason upwards but change some universal constants? What happens if we use Tao instead of Pi everywhere , these kind of fun questions would otherwise require an enormous intellectual effort whereas with the mechanisation and automation of thought, we might be able to run them and see!

I can write a sed command/program that replaces every occurence of PI with TAU/2 in LaTeX formulas and it'll take me about 30 minutes. The "intellectual effort" this requires is about 0. Maybe you meant Euler's number? Since it also relates to PI, it can be used and might actually change the framework in an "interesting way" (making it more awkward in most cases - people picked PI for a reason).

Yeah but you also have to replace all (2*tau/2) with tau, and 4*(tau/2)^2 with tau^2, etc etc...
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