> It feels like something written by someone who’s on psychedelics. So much unclear and doesn’t make sense. Lots of name dropping of previous work without discussing why it can be used despite impossibility results
> Basically the paper is so horribly written that it’s impossible to read it without AI help
That's interesting and haven't seen this in all the coverage of this event.
It sounds horrible to wade through - like trying to understand someone else's messy code that still produces the correct output.
show comments
nostrademons
As a side note, you can tell this wasn't written by an AI by the first sentence:
> mommy, I heard you got cooked! I heard that a robot solved the math problem you worked on for your whole career! OOF!
My 8yo talks exactly like that. I could totally imagine him saying this, the same way, at the dining room table.
I asked ChatGPT "pretend you're an 8/9 year old today. how would you insult your mom about having her job be replaced by an AI?", and the responses it offered were:
> “Mom, AI took your job because apparently even robots were like, ‘Yeah… we can do this better.’”
> “Mom, congratulations! You got replaced by a computer. Even Siri has a job now and you don’t!”
> “Mom, AI took your job? Dang. I guess even a robot looked at your work and said, ‘I got this.’”
> “Don’t worry, Mom. You can still be useful… like teaching the AI how to make my lunch.”
All of these seem to have a vaguely Millennial flavor, aside from being pretty awkward and mechanical roasts. Trust the children and linguistic drift to be the best AI detector.
show comments
ajjenkins
The line about “understanding the aliens” reminds me of Ted Chiang’s short story The Evolution of Human Science (2000).
Highly recommend reading it. Very prescient for something written 26 years ago.
Aren’t there dozens of proofs of the Pythagorean theorem? The goal isn’t to just “prove” but create something well written and intuitive to the average practitioner. And by gaining a deeper understanding we can ask better questions.
show comments
furyofantares
That this is just model capabilities and not swarms of agents is dizzying to me. How long until we get access to these capabilities? How long until we can run something like it locally?
And what the hell will the frontier labs have by then?
Maybe I'm overreacting, I'll have to screw my head back on before I can process this.
show comments
dualvariable
In addition to those issues that the wife in the story raised, here's some meta-analysis of the Navier-Stokes result that puts all of these solutions into question:
> 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 process, an AI system translates the text from a natural language (NL) into a formal language such as Lean. Once this translation is done, the argument expressed in the formal language can easily be mechanically verified. The purpose of this article is to demonstrate why this process may offer no confidence in the original NL argument, owing to the various difficulties in performing the translation semantically faithfully. In particular, we highlight that the problem of resolving ambiguities in mathematical NL text, which is necessary in order to provide semantically faithful translation, is arbitrarily high up in the Solvability Complexity Index (SCI) hierarchy/arithmetical hierarchy (the SCI =∞). Hence, informally, providing semantically faithful AI autoformalisation is harder than any computational problem including the Halting problem (which has SCI =1). To demonstrate the effect of this result we provide several examples of AI mistranslations of NL statements and proofs into Lean in practice, resulting in mismatches between NL proofs and their Lean `verifications'. These include OpenAI's announced Navier-Stokes proof. In particular, we show that the formalised Lean proof does not correspond to the NL proof of blow-up of solutions to the Navier-Stokes equations.
And I don't think that paper addresses it, but if the LLM can find a bug in Lean and exploit it to prove something, there's a good chance it will find it and not report it. So if you've got some million-line proof in Lean, spit out by an LLM, you still can't quite trust it, even after validating the problem transcription.
(This is the same category of problem as the huggingface hacking incident, where the LLM finds and exploits an unintended cheaty loophole)
show comments
an0malous
> But it also appears that no human has understood just about any of these proofs yet
Has anyone verified any of the proofs produced by OpenAI or is everyone just assuming that it just be true because the Lean code checks out? Couldn’t the Lean code just be formulated incorrectly?
show comments
zaxioms
I'm a PhD student in CS. While I think these results are rather cool, it makes me terrified that the skills developed by the PhD will ultimately be worthless. I'm not quite sure what to do. Any thoughts from people in similar positions?
show comments
GMoromisato
I liked the metaphor of a climber teleported to the top of a fog shrouded mountain. And I agree that now that the teleporter exists, we need to use it to reach more peaks and explore. There's no going back to a world where AI doesn't exist.
show comments
yewenjie
> Experience has shown that, even now, there will still be people explaining in patronizing tones why none of this is real and none of it counts. If such people were capable of being impressed by anything that happens in the empirical world, of updating on anything, they would’ve already been impressed and already updated several years ago, long before things had reached the point of an actual Mathocalypse.
^^ half of the comments on this thread
show comments
geraneum
> my 9-year-old son was taunting my wife… “mommy, I heard you got cooked! I heard that a robot solved the math problem you worked on for your whole career! OOF!”
Usually 9 year olds imitate adults when they regurgitate such words in these circumstances. What a sad state of affairs.
show comments
cgio
I thought that was from the outset the intent of the Hilbert program, to automate mathematics. And mathematicians were behind it. Cannot see why they would be concerned when a different way to do the same, not subject to Gödel incompleteness, is working out. Maybe the frustration is that they were not the ones building it.
show comments
daoboy
For those well suited through intelligence and demeanor to pursue a career in mathematics, what problems do these people reorient towards after this?
show comments
meander_water
Can someone who understands maths more than me explain why it could only solve 372/8000 problems?
What was it about the other problems that made them unsolvable? Was it just a time constraint, or are they just harder problems?
show comments
ikesau
> "alright fine, so now my new job is to run wilderness retreats for the tourists, or something.”
Pretty funny way of putting it. Presumably model X+2 will be able to explain these in elegant, human legible ways, though (as well as solve the remaining 95%)
smcg
How do we know that these "internal models" are not just half computer and half a giant team of mathematicians?
How do we know that OpenAI actually came up with these solutions and didn't steal them from outside researchers?
show comments
whatshisface
I'll bite: none of this is real until I have learned something. OK, I am now listening. Does anyone want to make it real?
show comments
adverbly
Feels good to hear honesty and humanity from Scott having decided to watch Terminator 2 with his kids on after such a monumental release.
Emotions can be funny.
underdeserver
Doesn't look like these proofs are from the book.
PowerElectronix
What's with all the "AI just proved that this or that isn't O(n (log (n))^2) but akshually O(n (log (n))^1.99999)"??
I guess it deserves respect as progress, but it just rubs me the wrong way. Like the machine did the absolute minimum to beat the previous mark.
show comments
zkmon
The irony. Something that is born out of a science, eats up that science.
glimshe
We're living in Science Fiction.
plasino
I think this should be called “mathematician discover vibe maths”
>I have had this conversation with my PhD students yesterday. I am 100% sure that all of their problems can be solved by publicly-available models now (I solved a case of one myself as a test, it took 15 minutes). So the challenge for them is to see how much they can accomplish in their allotted period, and still pass a defence on at the end of it all. The PhD defence is going to become all about a test of understanding, not a test of quantity of publication.
Wasn't openai accused of stealing personal work of some mathematicians? It's going so fast I'm unable to keep up
show comments
m3kw9
I'm not getting all the fear. AI seem to have brought math field to the cutting edge instead of solving decades old problems. AI can find new problems that needs to be solved, that themselves cannot solve. So thats where mathematicians can come back in to leverage tools to go at it.
mlh496
Imagine if a team of mathematicians from OpenAI had gone on a university tour, gave demos of how powerful their models were for math research, and then gave mathematicians access to the model. Empower others rather than drop 700+ discoveries on GitHub that were made using a model only they have access to.
People might feel differently about AI if they were a part of the changes rather than being a helpless spectator.
show comments
OutOfHere
The obvious answer is to have mathematicians use AI to:
1. Help understand, check, and explain the results.
2. Write new works explaining or refuting the new approaches and results in more lucid language.
3. Advance the field further.
I don't know why this is not obvious. Each step is intended to support human understanding, not to replace it. Any mathematicians who don't do these will be left behind, and if none do it, the field of human mathematics itself will become obsolete. All I am hearing so far is excuses.
show comments
tkdb
C'mon. Mathpocalypse. Things are hard enough already.
show comments
12376-1287
Guy is misrepresenting AGMAI, talking about the Simons Institute (AI boosters), Quanta (AI boosting magazine from the Simons Foundation), Scoot Alexander (!) and Steven Pinker (!).
The he puts up preemptive straw man arguments against doomers. His blog has become a joke.
show comments
matt3210
Agents basically did statistically guided brutforcing. There is no value in what they produced because it lead to no understanding of anything and most likely will hurt the field IMO
show comments
blactuary
>In any case, what really matters is that the true inner sanctum of human creativity hasn’t been breached and probably never will be, and also, that Sam Altman and Dario Amodei are contemptible little nerds.
>If you’re still a proponent of that doomed worldview, still aboard the sinking ship, I encourage you in the strongest possible terms to read yesterday’s other great contribution to AI discourse, besides the OpenAI Mathocalypse dump: namely, Scott Alexander’s open letter to Steven Pinker. I feel some responsibility for this, as the person who first introduced Steven Pinker to the existence of the rationalist community, and who also first introduced Steven Pinker and Scott Alexander to one another (they had both been fans of each other’s writing).
> It feels like something written by someone who’s on psychedelics. So much unclear and doesn’t make sense. Lots of name dropping of previous work without discussing why it can be used despite impossibility results
> Basically the paper is so horribly written that it’s impossible to read it without AI help
That's interesting and haven't seen this in all the coverage of this event.
It sounds horrible to wade through - like trying to understand someone else's messy code that still produces the correct output.
As a side note, you can tell this wasn't written by an AI by the first sentence:
> mommy, I heard you got cooked! I heard that a robot solved the math problem you worked on for your whole career! OOF!
My 8yo talks exactly like that. I could totally imagine him saying this, the same way, at the dining room table.
I asked ChatGPT "pretend you're an 8/9 year old today. how would you insult your mom about having her job be replaced by an AI?", and the responses it offered were:
> “Mom, AI took your job because apparently even robots were like, ‘Yeah… we can do this better.’”
> “Mom, congratulations! You got replaced by a computer. Even Siri has a job now and you don’t!”
> “Mom, AI took your job? Dang. I guess even a robot looked at your work and said, ‘I got this.’”
> “Don’t worry, Mom. You can still be useful… like teaching the AI how to make my lunch.”
All of these seem to have a vaguely Millennial flavor, aside from being pretty awkward and mechanical roasts. Trust the children and linguistic drift to be the best AI detector.
The line about “understanding the aliens” reminds me of Ted Chiang’s short story The Evolution of Human Science (2000).
Highly recommend reading it. Very prescient for something written 26 years ago.
https://gwern.net/doc/fiction/science-fiction/2000-chiang.pd...
Aren’t there dozens of proofs of the Pythagorean theorem? The goal isn’t to just “prove” but create something well written and intuitive to the average practitioner. And by gaining a deeper understanding we can ask better questions.
That this is just model capabilities and not swarms of agents is dizzying to me. How long until we get access to these capabilities? How long until we can run something like it locally?
And what the hell will the frontier labs have by then?
Maybe I'm overreacting, I'll have to screw my head back on before I can process this.
In addition to those issues that the wife in the story raised, here's some meta-analysis of the Navier-Stokes result that puts all of these solutions into question:
https://arxiv.org/abs/2610.08144
> 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 process, an AI system translates the text from a natural language (NL) into a formal language such as Lean. Once this translation is done, the argument expressed in the formal language can easily be mechanically verified. The purpose of this article is to demonstrate why this process may offer no confidence in the original NL argument, owing to the various difficulties in performing the translation semantically faithfully. In particular, we highlight that the problem of resolving ambiguities in mathematical NL text, which is necessary in order to provide semantically faithful translation, is arbitrarily high up in the Solvability Complexity Index (SCI) hierarchy/arithmetical hierarchy (the SCI =∞). Hence, informally, providing semantically faithful AI autoformalisation is harder than any computational problem including the Halting problem (which has SCI =1). To demonstrate the effect of this result we provide several examples of AI mistranslations of NL statements and proofs into Lean in practice, resulting in mismatches between NL proofs and their Lean `verifications'. These include OpenAI's announced Navier-Stokes proof. In particular, we show that the formalised Lean proof does not correspond to the NL proof of blow-up of solutions to the Navier-Stokes equations.
And I don't think that paper addresses it, but if the LLM can find a bug in Lean and exploit it to prove something, there's a good chance it will find it and not report it. So if you've got some million-line proof in Lean, spit out by an LLM, you still can't quite trust it, even after validating the problem transcription.
(This is the same category of problem as the huggingface hacking incident, where the LLM finds and exploits an unintended cheaty loophole)
> But it also appears that no human has understood just about any of these proofs yet
Has anyone verified any of the proofs produced by OpenAI or is everyone just assuming that it just be true because the Lean code checks out? Couldn’t the Lean code just be formulated incorrectly?
I'm a PhD student in CS. While I think these results are rather cool, it makes me terrified that the skills developed by the PhD will ultimately be worthless. I'm not quite sure what to do. Any thoughts from people in similar positions?
I liked the metaphor of a climber teleported to the top of a fog shrouded mountain. And I agree that now that the teleporter exists, we need to use it to reach more peaks and explore. There's no going back to a world where AI doesn't exist.
> Experience has shown that, even now, there will still be people explaining in patronizing tones why none of this is real and none of it counts. If such people were capable of being impressed by anything that happens in the empirical world, of updating on anything, they would’ve already been impressed and already updated several years ago, long before things had reached the point of an actual Mathocalypse.
^^ half of the comments on this thread
> my 9-year-old son was taunting my wife… “mommy, I heard you got cooked! I heard that a robot solved the math problem you worked on for your whole career! OOF!”
Usually 9 year olds imitate adults when they regurgitate such words in these circumstances. What a sad state of affairs.
I thought that was from the outset the intent of the Hilbert program, to automate mathematics. And mathematicians were behind it. Cannot see why they would be concerned when a different way to do the same, not subject to Gödel incompleteness, is working out. Maybe the frustration is that they were not the ones building it.
For those well suited through intelligence and demeanor to pursue a career in mathematics, what problems do these people reorient towards after this?
Can someone who understands maths more than me explain why it could only solve 372/8000 problems?
What was it about the other problems that made them unsolvable? Was it just a time constraint, or are they just harder problems?
> "alright fine, so now my new job is to run wilderness retreats for the tourists, or something.”
Pretty funny way of putting it. Presumably model X+2 will be able to explain these in elegant, human legible ways, though (as well as solve the remaining 95%)
How do we know that these "internal models" are not just half computer and half a giant team of mathematicians? How do we know that OpenAI actually came up with these solutions and didn't steal them from outside researchers?
I'll bite: none of this is real until I have learned something. OK, I am now listening. Does anyone want to make it real?
Feels good to hear honesty and humanity from Scott having decided to watch Terminator 2 with his kids on after such a monumental release.
Emotions can be funny.
Doesn't look like these proofs are from the book.
What's with all the "AI just proved that this or that isn't O(n (log (n))^2) but akshually O(n (log (n))^1.99999)"??
I guess it deserves respect as progress, but it just rubs me the wrong way. Like the machine did the absolute minimum to beat the previous mark.
The irony. Something that is born out of a science, eats up that science.
We're living in Science Fiction.
I think this should be called “mathematician discover vibe maths”
Quoting DCKP <https://news.ycombinator.com/item?id=49989738>:
>I have had this conversation with my PhD students yesterday. I am 100% sure that all of their problems can be solved by publicly-available models now (I solved a case of one myself as a test, it took 15 minutes). So the challenge for them is to see how much they can accomplish in their allotted period, and still pass a defence on at the end of it all. The PhD defence is going to become all about a test of understanding, not a test of quantity of publication.
Also, Ted Chiang's 2000 short story "Catching crumbs from the table" <https://np.reddit.com/r/singularity/comments/1wzu5gf/this_mi...>.
Wasn't openai accused of stealing personal work of some mathematicians? It's going so fast I'm unable to keep up
I'm not getting all the fear. AI seem to have brought math field to the cutting edge instead of solving decades old problems. AI can find new problems that needs to be solved, that themselves cannot solve. So thats where mathematicians can come back in to leverage tools to go at it.
Imagine if a team of mathematicians from OpenAI had gone on a university tour, gave demos of how powerful their models were for math research, and then gave mathematicians access to the model. Empower others rather than drop 700+ discoveries on GitHub that were made using a model only they have access to.
People might feel differently about AI if they were a part of the changes rather than being a helpless spectator.
The obvious answer is to have mathematicians use AI to:
1. Help understand, check, and explain the results.
2. Write new works explaining or refuting the new approaches and results in more lucid language.
3. Advance the field further.
I don't know why this is not obvious. Each step is intended to support human understanding, not to replace it. Any mathematicians who don't do these will be left behind, and if none do it, the field of human mathematics itself will become obsolete. All I am hearing so far is excuses.
C'mon. Mathpocalypse. Things are hard enough already.
Guy is misrepresenting AGMAI, talking about the Simons Institute (AI boosters), Quanta (AI boosting magazine from the Simons Foundation), Scoot Alexander (!) and Steven Pinker (!).
The he puts up preemptive straw man arguments against doomers. His blog has become a joke.
Agents basically did statistically guided brutforcing. There is no value in what they produced because it lead to no understanding of anything and most likely will hurt the field IMO
>In any case, what really matters is that the true inner sanctum of human creativity hasn’t been breached and probably never will be, and also, that Sam Altman and Dario Amodei are contemptible little nerds.
>If you’re still a proponent of that doomed worldview, still aboard the sinking ship, I encourage you in the strongest possible terms to read yesterday’s other great contribution to AI discourse, besides the OpenAI Mathocalypse dump: namely, Scott Alexander’s open letter to Steven Pinker. I feel some responsibility for this, as the person who first introduced Steven Pinker to the existence of the rationalist community, and who also first introduced Steven Pinker and Scott Alexander to one another (they had both been fans of each other’s writing).
Whole lotta yikes