... success for the Protestants and ruin to the Catholics, based on astrology and Biblical prophecies. 'These, however, are all conjectures, probable indeed and plausible, but not certain'. No doubt.
October 8, 2026 at 7:54 PM
... success for the Protestants and ruin to the Catholics, based on astrology and Biblical prophecies. 'These, however, are all conjectures, probable indeed and plausible, but not certain'. No doubt.
Et si l’intelligence artificielle, en résolvant trop vite les grandes conjectures, privait les nouvelles générations de ce qui fait le cœur même des mathématiques : la fierté de comprendre par soi-même ?
➡️ https://l.lepoint.fr/YH3
➡️ https://l.lepoint.fr/YH3
October 8, 2026 at 7:31 PM
Et si l’intelligence artificielle, en résolvant trop vite les grandes conjectures, privait les nouvelles générations de ce qui fait le cœur même des mathématiques : la fierté de comprendre par soi-même ?
➡️ https://l.lepoint.fr/YH3
➡️ https://l.lepoint.fr/YH3
Faire des conjectures sans preuve, ca s'appelle comment déjà ?
October 8, 2026 at 7:17 PM
Faire des conjectures sans preuve, ca s'appelle comment déjà ?
When all the conjectures have been proven or disproven who will come up with more? Who will have learned anything from the trying and failing or succeeding in proving them?
October 8, 2026 at 6:21 PM
When all the conjectures have been proven or disproven who will come up with more? Who will have learned anything from the trying and failing or succeeding in proving them?
So far AI is proving good at proofs, but I have not read of any novel conjectures coming from AI. When will AI develop this kind of curiosity and speculation? Next week?
October 8, 2026 at 4:44 PM
So far AI is proving good at proofs, but I have not read of any novel conjectures coming from AI. When will AI develop this kind of curiosity and speculation? Next week?
‣ Update: OpenAI updated the repository and removed 3 flawed preprints corresponding to item #032 in the overview: compare github.com/openai/math/... (old version, left image) and github.com/openai/math/... (new version, right image). •12/(11+1)
October 8, 2026 at 4:24 PM
‣ Update: OpenAI updated the repository and removed 3 flawed preprints corresponding to item #032 in the overview: compare github.com/openai/math/... (old version, left image) and github.com/openai/math/... (new version, right image). •12/(11+1)
...from proving math conjectures regarding Gaussian elimination?
October 8, 2026 at 12:33 PM
...from proving math conjectures regarding Gaussian elimination?
« ̝Un̄e thé̢or͑ie nͩ'est s̪c̪ieͧn̫tiͬfͮi̝quê ̃q̿ue si͡ ͊e͋lͥlͦe̐ pe̊u̵t e̴n ̸ṕrînc͏i̿pe̙ ê͙tre r͚éfut́ée ̹pa͉r ̢l̿'̲e͚xp̵ér̤i̊eͥnͨc͆e̢, ̥et la ͕sc̵i͂e̒n͚ceͬ pr̀o͌gr̟e̍ss͆e͏ ̊p̝a͘r u̧n͉e s͞uite ͂in̖int͓er͆romp̿u͖ẽ ͍dȅ ̠conjec͙tures̗ h̍a͓r͊die͠s̶ ̀et͎ de̍ ré̘f̍u̢ta͋ti̕ons̱, ͝uͅn̸e̍ i̘m̽age…
October 8, 2026 at 4:11 AM
« ̝Un̄e thé̢or͑ie nͩ'est s̪c̪ieͧn̫tiͬfͮi̝quê ̃q̿ue si͡ ͊e͋lͥlͦe̐ pe̊u̵t e̴n ̸ṕrînc͏i̿pe̙ ê͙tre r͚éfut́ée ̹pa͉r ̢l̿'̲e͚xp̵ér̤i̊eͥnͨc͆e̢, ̥et la ͕sc̵i͂e̒n͚ceͬ pr̀o͌gr̟e̍ss͆e͏ ̊p̝a͘r u̧n͉e s͞uite ͂in̖int͓er͆romp̿u͖ẽ ͍dȅ ̠conjec͙tures̗ h̍a͓r͊die͠s̶ ̀et͎ de̍ ré̘f̍u̢ta͋ti̕ons̱, ͝uͅn̸e̍ i̘m̽age…
All mathematical areas need new frameworks and they have to decide which problems are interesting. OpenAI doesn’t have sufficient experts to understand the content they generate. Some mathematicians were overly fixated on solving specific conjectures, but we know we need a bigger vision
October 8, 2026 at 3:27 AM
All mathematical areas need new frameworks and they have to decide which problems are interesting. OpenAI doesn’t have sufficient experts to understand the content they generate. Some mathematicians were overly fixated on solving specific conjectures, but we know we need a bigger vision
Lean verification is also *not* a guaranteed way to verify if they solved the conjectures. arxiv.org/abs/2610.08144
Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs
Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this pro...
arxiv.org
October 8, 2026 at 3:21 AM
Lean verification is also *not* a guaranteed way to verify if they solved the conjectures. arxiv.org/abs/2610.08144
GPT
Turing complete graph theory
Writing some strange proofs for me
It's no longer just NLP
But it's just the price I pay
Conjectures are calling me
Open up my tired eyes
'Cause I'm Dr. Brightside
Turing complete graph theory
Writing some strange proofs for me
It's no longer just NLP
But it's just the price I pay
Conjectures are calling me
Open up my tired eyes
'Cause I'm Dr. Brightside
October 8, 2026 at 3:17 AM
GPT
Turing complete graph theory
Writing some strange proofs for me
It's no longer just NLP
But it's just the price I pay
Conjectures are calling me
Open up my tired eyes
'Cause I'm Dr. Brightside
Turing complete graph theory
Writing some strange proofs for me
It's no longer just NLP
But it's just the price I pay
Conjectures are calling me
Open up my tired eyes
'Cause I'm Dr. Brightside
it seems telling that models haven't found any new math problems or conjectures
October 8, 2026 at 2:49 AM
it seems telling that models haven't found any new math problems or conjectures
I imagine the step of finding proofs/disproofs of your newly created conjectures used to take up significant time, so that part will be much faster now. Feels overall like a win for the field?
October 8, 2026 at 1:42 AM
I imagine the step of finding proofs/disproofs of your newly created conjectures used to take up significant time, so that part will be much faster now. Feels overall like a win for the field?
It seems that the majority of maths, that is to derive new definitions and theorems, find generalizing structures etc, remains largely human-driven.
Trying to prove (long-standing) conjectures might become less meaningful with AI. Was that ever a major part of what mathematicians worked on?
Trying to prove (long-standing) conjectures might become less meaningful with AI. Was that ever a major part of what mathematicians worked on?
October 8, 2026 at 1:40 AM
It seems that the majority of maths, that is to derive new definitions and theorems, find generalizing structures etc, remains largely human-driven.
Trying to prove (long-standing) conjectures might become less meaningful with AI. Was that ever a major part of what mathematicians worked on?
Trying to prove (long-standing) conjectures might become less meaningful with AI. Was that ever a major part of what mathematicians worked on?
PS: Personally it's also an honor to have a conjecture I formulated as a grad student be among the problems OpenAI chose to use their model to solve.
arxiv.org/abs/1504.02411
(n+1)-th reason to be happy: you probably won't have to wait 10+ years for your conjectures to finally be solved by AI 🙃
arxiv.org/abs/1504.02411
(n+1)-th reason to be happy: you probably won't have to wait 10+ years for your conjectures to finally be solved by AI 🙃
Can Almost Everybody be Almost Happy? PCP for PPAD and the Inapproximability of Nash
We conjecture that PPAD has a PCP-like complete problem, seeking a near equilibrium in which all but very few players have very little incentive to deviate. We show that, if one assumes that this prob...
arxiv.org
October 7, 2026 at 11:57 PM
PS: Personally it's also an honor to have a conjecture I formulated as a grad student be among the problems OpenAI chose to use their model to solve.
arxiv.org/abs/1504.02411
(n+1)-th reason to be happy: you probably won't have to wait 10+ years for your conjectures to finally be solved by AI 🙃
arxiv.org/abs/1504.02411
(n+1)-th reason to be happy: you probably won't have to wait 10+ years for your conjectures to finally be solved by AI 🙃
Recently I’ve also really enjoyed _collaborating_ with AI. Harnesses and mindlessly typing “resume” make research boring, but actually brainstorming ideas with AI and proposing conjectures that it can refute – I find that very satisfying.
October 7, 2026 at 11:57 PM
Recently I’ve also really enjoyed _collaborating_ with AI. Harnesses and mindlessly typing “resume” make research boring, but actually brainstorming ideas with AI and proposing conjectures that it can refute – I find that very satisfying.
They are solving those problems now without being able to verify them at the same time. The verification (like Lean formalization) is done separately afterwards, if possible at all.
As for interesting conjectures, most of them are now said to be uninteresting and insignificant when solved...
As for interesting conjectures, most of them are now said to be uninteresting and insignificant when solved...
October 7, 2026 at 9:56 PM
They are solving those problems now without being able to verify them at the same time. The verification (like Lean formalization) is done separately afterwards, if possible at all.
As for interesting conjectures, most of them are now said to be uninteresting and insignificant when solved...
As for interesting conjectures, most of them are now said to be uninteresting and insignificant when solved...
But AI isn't inventing new interesting conjectures / theorems, it's just finding proofs for ones that we've already decided are interesting. It's not just about finding stuff that's *new*, it's about finding stuff that's *interesting*. And AI is very bad at that on its own. At least in my experience
October 7, 2026 at 8:57 PM
But AI isn't inventing new interesting conjectures / theorems, it's just finding proofs for ones that we've already decided are interesting. It's not just about finding stuff that's *new*, it's about finding stuff that's *interesting*. And AI is very bad at that on its own. At least in my experience
The point is that for maths they have a ready supply of interesting conjectures and a guaranteed way of deciding if they've solved them. For other fields, the difficulty is finding the right question that generates understanding. Mathematicians are now realising that proofs aren't that.
October 7, 2026 at 7:59 PM
The point is that for maths they have a ready supply of interesting conjectures and a guaranteed way of deciding if they've solved them. For other fields, the difficulty is finding the right question that generates understanding. Mathematicians are now realising that proofs aren't that.
OpenAI dropped more than 700 proposed solutions to deep mathematical conjectures yesterday. That is if Euler had dropped his entire career work in one day.
This is why people are freaking out. These things are no small feat to solve.
This is why people are freaking out. These things are no small feat to solve.
October 7, 2026 at 7:58 PM
OpenAI dropped more than 700 proposed solutions to deep mathematical conjectures yesterday. That is if Euler had dropped his entire career work in one day.
This is why people are freaking out. These things are no small feat to solve.
This is why people are freaking out. These things are no small feat to solve.
Are we talking “Big Head” or “Little Head” 😜
I especially hope it doesn't mean you are this doctor: “He used to make shuddering conjectures about the possible actions of a headless physician with the power of reanimating the dead.” — H.P. Lovecraft
I especially hope it doesn't mean you are this doctor: “He used to make shuddering conjectures about the possible actions of a headless physician with the power of reanimating the dead.” — H.P. Lovecraft
October 7, 2026 at 7:51 PM
Are we talking “Big Head” or “Little Head” 😜
I especially hope it doesn't mean you are this doctor: “He used to make shuddering conjectures about the possible actions of a headless physician with the power of reanimating the dead.” — H.P. Lovecraft
I especially hope it doesn't mean you are this doctor: “He used to make shuddering conjectures about the possible actions of a headless physician with the power of reanimating the dead.” — H.P. Lovecraft
Math and computer science researchers and PhD students all over the world, how are we feeling?
Is this a black mirror episode?
AI just proved 722 theorems? The Unique Games conjecture? Subcubic Conjectures?
Is this a black mirror episode?
AI just proved 722 theorems? The Unique Games conjecture? Subcubic Conjectures?
October 7, 2026 at 7:23 PM
Math and computer science researchers and PhD students all over the world, how are we feeling?
Is this a black mirror episode?
AI just proved 722 theorems? The Unique Games conjecture? Subcubic Conjectures?
Is this a black mirror episode?
AI just proved 722 theorems? The Unique Games conjecture? Subcubic Conjectures?
I would like to think and would hope that the real work goes way beyond outstanding conjectures and allows us to understand more about the nature of reality.
I might be being a little romantic there...
I might be being a little romantic there...
October 7, 2026 at 6:03 PM
I would like to think and would hope that the real work goes way beyond outstanding conjectures and allows us to understand more about the nature of reality.
I might be being a little romantic there...
I might be being a little romantic there...
I do wonder if there are a bunch of maths conjectures which are essentially way beyond baseline human capabilities at the moment - I think Stephen Baxter gets into this in some of his Xeelee books.
The conjectures and proofs are interesting but they might just be too damn hard to crack.
The conjectures and proofs are interesting but they might just be too damn hard to crack.
October 7, 2026 at 6:03 PM
I do wonder if there are a bunch of maths conjectures which are essentially way beyond baseline human capabilities at the moment - I think Stephen Baxter gets into this in some of his Xeelee books.
The conjectures and proofs are interesting but they might just be too damn hard to crack.
The conjectures and proofs are interesting but they might just be too damn hard to crack.
On October 7, 2008, TV show 'Outrageous Fortune' aired episode "Dangerous Conjectures"
October 7, 2026 at 5:24 PM
On October 7, 2008, TV show 'Outrageous Fortune' aired episode "Dangerous Conjectures"