I worked as a research mathematician for a while, and I've published peer-reviewed math papers. Reading this tweet put me in the strange position of feeling like defending the way peer review works in my (former) field, which I'm not used to doing. Among other problems it goes too slowly, it pays only the participants who provide the least value, and it was designed for a world that hasn't existed for a long time.
But this tweet paints a somewhat misleading picture of the role peer review plays in practice in modern math research. Reading this tweet could leave you with the impression that when someone proves a new result, no one pays any attention until it's gone through peer review and published in a journal. This just isn't true. ArXiv preprints are much more widely read than the journals' version of articles, and they go up essentially as soon as they're written. Certainly no one's waiting the year-plus it would take to get the article published in a journal! And even before that, mathematicians communicate their results to each other through slightly less formal channels, like blogs, conference talks, and regular human word of mouth.
In short, despite the sclerotic and parasitic nature of the journal system, the way ideas get disseminated in the field in practice is actually a lot closer to the ideal prewar picture he's describing in the tweet. I'm led to understand that this was less true before the Internet, but even by the time I started my PhD in 2009 things had been working the way I just described for quite a while.
And the quotation is not even by a mathematician, but by a cognitive scientist, so probably they did not refer to mathematics.
No "serious mathematician" (tm) is "waiting for peer review" nor do methematicians widely consider peer reviewed articles to be by default 100% correct just because they are peer reviewed. I have many times encountered conversations where mathematicians were doubting previous published/peer reviewed articles of others. That's not the main purpose of peer review, that's what some people outside of mathematics (like tweeter op; though his bio says that he is "ranked in the top 2% of scientists globally" so who am I to talk) think of peer review.
> It just became difficult for the average engineer to pursued more advanced mathematical considerations. I believe that this might soon change.
It reminds me of the arguments that now with LLMs "everybody can be a programmer" as if there was some kind of gatekeeper, apart from time and effort required, that forbade some people from coding. And as if suddenly one can become an expert programmer without putting an effort to learn just because they can prompt an llm.
Maybe llms can make certain subjects more approachable to beginners, but there is a certain type of people who act as if one can get that expertise without having to put an immense effort still to learn.
This was especially funny to watch during the Jacobian Conjecture announcement, where people on HN were waiting for "Lean proofs" and corroboration from other mathematicians for... a published counterexample to the Conjecture.
This was definitely something I saw on HN, but for what it's worth, in my conversations that night with other mathematicians no one brought up Lean proofs or peer review even as a joke. We just copied and pasted the polynomials into a computer algebra system and checked it ourselves and then said "holy shit, I guess the Jacobian conjecture is false". Couldn't have taken more than five minutes after we first saw the tweet.
Right, that's what was so funny about it. Finding a counterexample: an incredible mathematical achievement. Verifying a counterexample: barely even a weeknight homework problem in an undergraduate multivariable course.
I have been respectfully following Lemire for more than 15 years but he got a bit weird after COVID-19. Although his arguments are not completely wrong, he fails to mention the large impact of what he is saying. Yes, peer review is not good but it's been one of the best tools we have. We can swap the peer review with democracy and elections, and got almost same arguments. That's why this is giving me an ick.
We don't have to imagine his scenario, that's what happened to Évariste Galois. But then again any university professor gets dozens of crank letters a year claiming to have solved the trisection of angles or such.
This is a response to a strawman... I think we'd want to see what an actual mathematician says to sensibly analyze this discourse
I do think that there are two things going on that explains the past couple weeks' breakthroughs:
1) A lot of conjectures are weakly grounded.
2) Maybe humans are biased towards proving conjectures rather than finding counter-examples (prestige in finding proofs, tedium in searching for contradictions, etc.)
3) Math is one of the rare fields that can be 'solved' in pure token space without needing empirical or subjective-opinion support
Hi, used to be actual mathematician here (lecturer, publication in JEMS and all that)
For starters he's talking about how peer review is bad because of politics. That's fair.
But no one is saying that's the case with AI math. I think that the mathematical community wants to see the methods by which the Jacobian counterexample was constructed. As opposed to "lol xd my r00b0t solved le Jacoby conjectoor"
If these proofs were output by the AI in a format readable by a proof verification system, the verification step of publishing vanishes. Then it's only valuable to check if the stated intention actually matches the proof and isn't something completely different.
I don't know why your comment is downvoted, because it makes much sense. That's assuming the proof is not founded in assumptions, and the proof checker doesn't have bugs.
Is it not the case now that oligarchs "own" intellectual credibility? Becoming a credentialed mathematician requires an entire lifetime of devotion, lots of money or scholarships, and association with institutions controlled by monied interests. Token spend is arguably cheaper, and although still paid to monied interests, lowers the bar for real participation in mathematics.
I worked as a research mathematician for a while, and I've published peer-reviewed math papers. Reading this tweet put me in the strange position of feeling like defending the way peer review works in my (former) field, which I'm not used to doing. Among other problems it goes too slowly, it pays only the participants who provide the least value, and it was designed for a world that hasn't existed for a long time.
But this tweet paints a somewhat misleading picture of the role peer review plays in practice in modern math research. Reading this tweet could leave you with the impression that when someone proves a new result, no one pays any attention until it's gone through peer review and published in a journal. This just isn't true. ArXiv preprints are much more widely read than the journals' version of articles, and they go up essentially as soon as they're written. Certainly no one's waiting the year-plus it would take to get the article published in a journal! And even before that, mathematicians communicate their results to each other through slightly less formal channels, like blogs, conference talks, and regular human word of mouth.
In short, despite the sclerotic and parasitic nature of the journal system, the way ideas get disseminated in the field in practice is actually a lot closer to the ideal prewar picture he's describing in the tweet. I'm led to understand that this was less true before the Internet, but even by the time I started my PhD in 2009 things had been working the way I just described for quite a while.
Which serious mathematicians?
There is a quotation about peer review. I'm assuming that's also made up.
And the quotation is not even by a mathematician, but by a cognitive scientist, so probably they did not refer to mathematics.
No "serious mathematician" (tm) is "waiting for peer review" nor do methematicians widely consider peer reviewed articles to be by default 100% correct just because they are peer reviewed. I have many times encountered conversations where mathematicians were doubting previous published/peer reviewed articles of others. That's not the main purpose of peer review, that's what some people outside of mathematics (like tweeter op; though his bio says that he is "ranked in the top 2% of scientists globally" so who am I to talk) think of peer review.
> It just became difficult for the average engineer to pursued more advanced mathematical considerations. I believe that this might soon change.
It reminds me of the arguments that now with LLMs "everybody can be a programmer" as if there was some kind of gatekeeper, apart from time and effort required, that forbade some people from coding. And as if suddenly one can become an expert programmer without putting an effort to learn just because they can prompt an llm.
Maybe llms can make certain subjects more approachable to beginners, but there is a certain type of people who act as if one can get that expertise without having to put an immense effort still to learn.
he is a professor at quebec. I am pretty sure he knows serious mathematians that he perhaps does not want to name directly.
This was especially funny to watch during the Jacobian Conjecture announcement, where people on HN were waiting for "Lean proofs" and corroboration from other mathematicians for... a published counterexample to the Conjecture.
This was definitely something I saw on HN, but for what it's worth, in my conversations that night with other mathematicians no one brought up Lean proofs or peer review even as a joke. We just copied and pasted the polynomials into a computer algebra system and checked it ourselves and then said "holy shit, I guess the Jacobian conjecture is false". Couldn't have taken more than five minutes after we first saw the tweet.
Right, that's what was so funny about it. Finding a counterexample: an incredible mathematical achievement. Verifying a counterexample: barely even a weeknight homework problem in an undergraduate multivariable course.
I need to make the same post when someone finally RLs an LLM to get really good at performance engineering.
Many "serious" performance engineers are aghast
"Nooo the r00b0t can't make llvm faster and not tell us how!!! it has to make a commit to the open source!!!"
"Ha, that's peer review and politics"
I have been respectfully following Lemire for more than 15 years but he got a bit weird after COVID-19. Although his arguments are not completely wrong, he fails to mention the large impact of what he is saying. Yes, peer review is not good but it's been one of the best tools we have. We can swap the peer review with democracy and elections, and got almost same arguments. That's why this is giving me an ick.
This is Lemire so take it with a big grain of salt. Some notable mathematicians including Fields medalists are not 'aghast'.
Since when did Lemire need to be taken with a grain of salt?
We don't have to imagine his scenario, that's what happened to Évariste Galois. But then again any university professor gets dozens of crank letters a year claiming to have solved the trisection of angles or such.
> So it is possible, for example, for a teenager to become known as an obsessive proof-checker even though that teenager has no formal credentials.
Hard to cry this as a benefit after locking papers down behind a costly wall for decades.
This is a response to a strawman... I think we'd want to see what an actual mathematician says to sensibly analyze this discourse
I do think that there are two things going on that explains the past couple weeks' breakthroughs:
1) A lot of conjectures are weakly grounded.
2) Maybe humans are biased towards proving conjectures rather than finding counter-examples (prestige in finding proofs, tedium in searching for contradictions, etc.)
3) Math is one of the rare fields that can be 'solved' in pure token space without needing empirical or subjective-opinion support
Hi, used to be actual mathematician here (lecturer, publication in JEMS and all that)
For starters he's talking about how peer review is bad because of politics. That's fair.
But no one is saying that's the case with AI math. I think that the mathematical community wants to see the methods by which the Jacobian counterexample was constructed. As opposed to "lol xd my r00b0t solved le Jacoby conjectoor"
If these proofs were output by the AI in a format readable by a proof verification system, the verification step of publishing vanishes. Then it's only valuable to check if the stated intention actually matches the proof and isn't something completely different.
I don't know why your comment is downvoted, because it makes much sense. That's assuming the proof is not founded in assumptions, and the proof checker doesn't have bugs.
AI would dramatically increase the demand of gatekeeping.
>> The current peer-review model, I should remind you, is a recent invention from the second half of the twentieth century.
What? In EU Crelle's Journal is founded in 1826, while in the US the American Journal of Mathematics in 1878.
Mathematicians having their stackoverflow moment.
[dead]
tl;dr for everyone: disrupt the conservative academic establishment*
*unspoken or unintended consequence being so that the oligarchy can seize the authority of intellectual credibility
Is it not the case now that oligarchs "own" intellectual credibility? Becoming a credentialed mathematician requires an entire lifetime of devotion, lots of money or scholarships, and association with institutions controlled by monied interests. Token spend is arguably cheaper, and although still paid to monied interests, lowers the bar for real participation in mathematics.
LLMs are bad at math of course. You can't calculate non-deterministically and expect accuracy. https://news.harvard.edu/gazette/story/2025/07/ai-leaps-from...
Calculators are great at math though. Put them together, and honey, you got yourself a stew going.