Anthropic's Levent Alpöge claims the Mythos model solved the Erdős unit distance problem, offering no formal proof
OpenAI reportedly solved the same mathematical problem using '5.5'.
#83rohan anil@_AROHAN_The legendary mythos model!
It would be cool to get harness and see how much overhang is on the existing models. I am betting many of them solve it and is a function of how much conditioning is provided.
levent@__alpoge__over the weekend i checked the obvious thing, which is whether mythos is able to solve the erdos unit distance problem, aka erdos problem #90. the answer is: yea
#94Sholto Douglas@_SHOLTODOUGLASHuge credit to the OAI team for solving the unit distance problem with 5.5 - it is now my go to example that models can in fact pull together disparate ideas into new discoveries.
As with all 4 minute miles, we had to try and cross it too! Turns out mythos solves it with a cute, simple proof. This implies some serious overhang in discoveries!
levent@__alpoge__over the weekend i checked the obvious thing, which is whether mythos is able to solve the erdos unit distance problem, aka erdos problem #90. the answer is: yea
#517Andrew Curran@ANDREWCURRAN_Mythos has also solved the Erdos unit distance problem. 'This implies some serious overhang in discoveries!'
Sholto Douglas@_sholtodouglasHuge credit to the OAI team for solving the unit distance problem with 5.5 - it is now my go to example that models can in fact pull together disparate ideas into new discoveries. As with all 4 minute miles, we had to try and cross it too! Turns out mythos solves it with a cute, simple proof. This implies some serious overhang in discoveries!
#517Andrew Curran@ANDREWCURRAN_levent@__alpoge__here’s opus 4.7’s texed up version of mythos’s argument: https://www-cdn.anthropic.com/files/4zrzovbb/website/ca35f196125c899a5ad11f011080202a652aef02.pdf. i found it amusing that mythos was so nervous about the fame of the open problem that it stuck to the first choice, here X = d_n^2, that got it a contradiction, when simply choosing X a large constant depending on D in its bound wins a power. it had such a hard time believing in itself! all mathematicians know the feeling:).
Andrew Curran@AndrewCurran_@_sholtodouglas They are trying to community note you for saying OAI used 5.5
Sholto Douglas@_sholtodouglasHuge credit to the OAI team for solving the unit distance problem with 5.5 - it is now my go to example that models can in fact pull together disparate ideas into new discoveries. As with all 4 minute miles, we had to try and cross it too! Turns out mythos solves it with a cute, simple proof. This implies some serious overhang in discoveries!
#716elie@ELIEBAKOUCH@_sholtodouglas it's not 5.5 no? iirc they mention an internal model
Sholto Douglas@_sholtodouglasHuge credit to the OAI team for solving the unit distance problem with 5.5 - it is now my go to example that models can in fact pull together disparate ideas into new discoveries. As with all 4 minute miles, we had to try and cross it too! Turns out mythos solves it with a cute, simple proof. This implies some serious overhang in discoveries!
#867Alexander Doria@DORIALEXANDERimpressive if true, though with decontamination caveat most interesting part is about the multi-model pipeline "isolated claude code instances hitting mythos are given the problem (…) then an instance summarizes each avenue and assigns instances the summary."
levent@__alpoge__over the weekend i checked the obvious thing, which is whether mythos is able to solve the erdos unit distance problem, aka erdos problem #90. the answer is: yea
further my conviction this is also a training pipeline to elicit open-endedness in models (not really something you can do with RL, though you could argue this is a form of extremely offline RL).
Alexander Doria@Dorialexanderimpressive if true, though with decontamination caveat most interesting part is about the multi-model pipeline "isolated claude code instances hitting mythos are given the problem (…) then an instance summarizes each avenue and assigns instances the summary."
#980Lisan al Gaib@SCALING01btw this is just a side project for mythos
no biggie, not even with a post by the official Anthropic acc
levent@__alpoge__over the weekend i checked the obvious thing, which is whether mythos is able to solve the erdos unit distance problem, aka erdos problem #90. the answer is: yea
#980Lisan al Gaib@SCALING01btw this is just a side project for mythos
no biggie, not even worth a post by the official Anthropic acc
levent@__alpoge__over the weekend i checked the obvious thing, which is whether mythos is able to solve the erdos unit distance problem, aka erdos problem #90. the answer is: yea
#980Lisan al Gaib@SCALING01Claude Mythos also found a "cute, simple proof" for the unit distance problem
Sholto Douglas@_sholtodouglasHuge credit to the OAI team for solving the unit distance problem with 5.5 - it is now my go to example that models can in fact pull together disparate ideas into new discoveries. As with all 4 minute miles, we had to try and cross it too! Turns out mythos solves it with a cute, simple proof. This implies some serious overhang in discoveries!
#1245Alex Volkov@ALTRYNENEW: Claude Mythos ALSO solved the Erdos problem that OpenAI 5.5 recently solved.
OpenAI made this into a huge marketing deal, involved field medalists, math folks are freaking out about their future.
Anthropic just... tweeted it out. No announcement.
Also, this shows that... what? Anthropic was more focused on the security angle "Mythos is too dangerous to release" than the "We've crossed a Science Rubicon"
Sholto Douglas@_sholtodouglasHuge credit to the OAI team for solving the unit distance problem with 5.5 - it is now my go to example that models can in fact pull together disparate ideas into new discoveries. As with all 4 minute miles, we had to try and cross it too! Turns out mythos solves it with a cute, simple proof. This implies some serious overhang in discoveries!
#1271Damek@DAMEKDAVISNice mythos can solve it too suggesting that I'm wrong in my feeling that Claude can't do math reliably. Would be fun to try it if ever released.
levent@__alpoge__over the weekend i checked the obvious thing, which is whether mythos is able to solve the erdos unit distance problem, aka erdos problem #90. the answer is: yea
#1496Chubby♨️@KIMMONISMUSErdős problem #90 has been open for decades. Over the weekend a mathematician tested whether Claude Mythos could solve it. It did.
But what caught my attention: Mythos didn't replicate the known approach from OpenAI's #1196 solution. It repeatedly settled on a different argument, one the mathematician called cleaner, with "no analytic complications." Air-gapped, no internet, no information leakage.
GPT-5.5 solved numerous Erdős problems earlier this year. DeepMind's Nexus knocked out 9. Now Mythos, with a cleaner proof than the one that already existed.
Problems that survived 80 years are falling in weeks.
levent@__alpoge__over the weekend i checked the obvious thing, which is whether mythos is able to solve the erdos unit distance problem, aka erdos problem #90. the answer is: yea