Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

GPT-5.4 Pro solves Erdős Problem #1196

twitter.com

Post reply on HN
Print view View original

11–20 of 21 posts

Re: GPT-5.4 Pro solves Erdős Problem #1196

#11

Post by krige »

energy123 wrote: post #5
seanhunter wrote: post #4

Earlier quoted context omitted.

Agree. Additionally, it’s really disheartening that people do this with Erdos problems specifically. They are not major research questions in mathematics, but were intended as little conjectures that people could use as a way into serious number theory with a small cash reward and a little bit of minor fame for being the person who did the work to solve one of them. They are not things where the solution itself provi…

Number theorist Jared Lichtman says this AI proof is from "The Book", the highest compliment one can give. He also says: > I care deeply about this problem, and I've been thinking about it for the past 7 years. I'd frequently talk to Maynard about it in our meetings, and consulted over the years with several experts (Granville, Pomerance, Sound, Fox...) and others at Oxford and Stanford. This problem was not a questi…

Number theorist Jared Lichtman is also involved with an AI startup so he might have a bit of an incentive to frame things this way.

Re: GPT-5.4 Pro solves Erdős Problem #1196

#13

Post by Zababa »

krige wrote: post #11
energy123 wrote: post #5

Earlier quoted context omitted.

Number theorist Jared Lichtman says this AI proof is from "The Book", the highest compliment one can give. He also says: > I care deeply about this problem, and I've been thinking about it for the past 7 years. I'd frequently talk to Maynard about it in our meetings, and consulted over the years with several experts (Granville, Pomerance, Sound, Fox...) and others at Oxford and Stanford. This problem was not a questi…

Number theorist Jared Lichtman is also involved with an AI startup so he might have a bit of an incentive to frame things this way.

Thank you, that feels like important context!

Re: GPT-5.4 Pro solves Erdős Problem #1196

#14

Post by energy123 »

Zababa wrote: post #13
krige wrote: post #11

Earlier quoted context omitted.

Number theorist Jared Lichtman is also involved with an AI startup so he might have a bit of an incentive to frame things this way.

Thank you, that feels like important context!

This guy also says it's a book proof though:

https://en.wikipedia.org/wiki/Thomas_Bloom

Re: GPT-5.4 Pro solves Erdős Problem #1196

#17

Post by martin293 »

adrian_b wrote: post #16
isaacfrond wrote: post #15

The proof is here: https://www.overleaf.com/project/69dd1d8437eba662fda82929

Much more interesting than the proof would be to see the exact prompts used by Liam Price to generate the proof.

I have no exact prompt to share, but he does write:

> Appreciate the insight! If it's at all of interest, this was a one-shot (supposed) solution in about 80 mins, unlike some other problems like 851 that took over 20 continuations totalling perhaps 15-20 hours of reasoning time.

Source: https://www.erdosproblems.com/forum/thread/1196#post-5365

Re: GPT-5.4 Pro solves Erdős Problem #1196

#18

Post by martin293 »

krige wrote: post #11
energy123 wrote: post #5

Earlier quoted context omitted.

Number theorist Jared Lichtman says this AI proof is from "The Book", the highest compliment one can give. He also says: > I care deeply about this problem, and I've been thinking about it for the past 7 years. I'd frequently talk to Maynard about it in our meetings, and consulted over the years with several experts (Granville, Pomerance, Sound, Fox...) and others at Oxford and Stanford. This problem was not a questi…

Number theorist Jared Lichtman is also involved with an AI startup so he might have a bit of an incentive to frame things this way.

Source: https://www.math.inc/a-conversation-with-terry-tao

However, I think this is still likely a very significant achievement/milestone.

Re: GPT-5.4 Pro solves Erdős Problem #1196

#19

Post by Zababa »

energy123 wrote: post #14
Zababa wrote: post #13

Earlier quoted context omitted.

Thank you, that feels like important context!

This guy also says it's a book proof though: https://en.wikipedia.org/wiki/Thomas_Bloom

Important context too, thanks! More context:

- Thomas Bloom is the current owner of https://www.erdosproblems.com/

- He previously posted on X on the 2025/10/17 the following:

> Hi, as the owner/maintainer of http://erdosproblems.com, this is a dramatic misrepresentation. GPT-5 found references, which solved these problems, that I personally was unaware of. The 'open' status only means I personally am unaware of a paper which solves it. [1]

> GPT-5 has been a very useful tool in searching the literature, and this has been a valuable addition to the website. Its literature searching ability is already useful and impressive enough, no need to describe it as something it's not! [2]

[1]: https://x.com/thomasfbloom/status/1979254235075059732

[2]: https://x.com/thomasfbloom/status/1979254675833549207

I don't have the mathematical chops or knowledge of mathematicians to evaluate any of that.

Re: GPT-5.4 Pro solves Erdős Problem #1196

#20

Post by menaerus »

sealion127 wrote: post #9
mrkeen wrote: post #8

Earlier quoted context omitted.

What's the conflict?

Research integrity vs. hyping up AI, obviously. Even in small matters like calling this proof "From The Book".

So where's the proof of this exact problem and why exactly did it end up on the list of unsolved problems if it has been already solved?
Post reply on HN