OpenAI just dropped 372 math proofs on the world. They dropped a Navier-Stokes proof about a month back and there was a bunch of controversy so I guess the new PR strategy is shock and awe.
I’m not qualified to assess quality but watching the reaction of mathematicians, some of these results are v significant. e.g. this post on X from a Stanford math prof:
Another one: The Kakeya problem in 4-D! Just this summer, Hong Wang won the Fields medal for the Kakeya proof in 3-D (Wang-Zahl, 2026)
So, Fields medal-worthy.
But the feelings.
I spent thousands of hours on that problem. I really enjoyed it. Hearing that it is solved somehow makes me sad in a far-off way, like hearing an ex-girlfriend died suddenly in a car crash.
(on Hacker News)it’s as if trucks had run me over; all the problems (and therefore research avenues) that I mentioned in my lectures, articles, and funding applications have been solved.
(on X)
If they wanted shock and awe then they got it: 100+ reactions from mathematicians.
I am curious about what kind of thing “being a mathematician” becomes…
I am familiar with the feelings! Both engineers and designers have been going through the Five Stages.
But, for me, my mental image of the kind of work I do is constructing new things, like the Doozers in Fraggle Rock. I don’t have much imagination, I have to think by making and then encountering what I make to figure out what to make next, so the huge acceleration (and increased individual agency) in speculative building is wonderful.
WHEREAS my mental image of mathematics has been mining. Deep in the tunnels, pickaxes at the stubborn rock, raw and earned intuition guiding the miners to the rare diamonds that must be there.
And what’s happened is that the rock has fallen away… the intellectual frontier has pulled way, way, way back over the horizon…
Look I don’t mean to be all Platonist about this, but I feel like mathematics is already “there” somehow.
And what AI has done is turn the granite-against-the-nose into vast continents, open country under open sky as far as the eye can see.
All has been discovered (well, 372 proofs right now, each of them a human lifetime’s work, but practically speaking “all” is a decent approximiation).
So what is it now, to be a mathematician?
The “vast continents” image sticks with me:
Less unearthing and more exploring.
I’m reminded of what my kid’s encyclopaedia and Wikipedia euphemistically both call the Age of Discovery: that period from the 15th century onwards when Europeans explored the world and nicked things to bring home. (It never ended.)
There were botanists and biologists and anthropologists and archeologists, but they weren’t today’s botanists and biologists and anthropologists and archeologists.
Not professional scientists but amateur explorers and enthusiastic collectors who trekked into the heart of uncharted continents and lugged stuff back to amaze and astound.
(One of my favourite museums in the world is the Pitt Rivers in Oxford. General Pitt-Rivers was just a guy who collected a lot of things.)
They mostly didn’t need skill or training. Some ready cash, some bravery, and a decent handle on public taste to spot the tasty stuff…
Perhaps that’s the new job of the mathematician? To venture into the new natural world opened up by the AIs and figure out what to haul back?
In a matter of days, mathematics is already becoming an amateur sport: there’s a mass game on X making integer multiplication quicker and quicker.
A scavenger hunt.
Look, collecting to amaze and astound, and then looking at the collection… I don’t mean to devalue the activity, the process leads to great things.
Darwin goes voyaging, draws a LOT of pictures of finches, and figures out the origin of species. Boom.
I had a chat a few months back with a person adjacent to one of the extremely well-funded frontier math labs.
He explained the thesis…
Every couple hundred years something comes out of mathematics that turns society upside down, he said.
For example #1: the mathematics of chance led to the financialisation of risk and unlocked the explosion of capital that built the world we have today.
For example #2: George Boole figured out how to connect logic (reasoning) with numbers, and when you combine that with physical state then you get all of computers.
So what’s example #3? That’s what they’re hunting for.
But what then?
A cornerstone of the Age of Discovery was the Columbian Exchange, which brought tomatoes, tobacco, potatoes and chilli across the Atlantic for the first time. Plus a ton of silver and gold.
In exchange: horses and smallpox. You’re welcome!
Professor Mark Maslin (UCL) outright refuses the term. He calls it the Great Dying.
In 1492, there were 60,000,000 people living in the Americas, which was roughly the same size as the population in Europe and in China. Within a hundred years of first contact with Europeans, fifty five million out of those sixty million were dead.
Imagine.
Because it’s only the age of “discovery” from the European perspective, right?
There’s no discovery going on for the people living there.
So… these new mathematical continents uncovered on the map by AI… these amateur mathematicians hacking their way up-river…
Not to drag out a metaphor waaaaay too far (I’ve never let it stop me before) – but who will they find already there?
In Greg Egan’s astounding short Luminous (read it in The Best of Greg Egan) they discover that SPOILERS while we inhabit a physics of small numbers and loosely coupled phenomenon there are coterminously and unnoticed SPOILERS aliens in the mathematics of trans-astronomic integers.
I mean:
We’ve already discovered that if we make a matrix large enough then when we talk to it, it talks back.
So maybe that should be the real goal of going into mathematics today.
Not figuring out what gem to bring back from the frontier to disrupt society.
But instead: first contact.
OpenAI just dropped 372 math proofs on the world. They dropped a Navier-Stokes proof about a month back and there was a bunch of controversy so I guess the new PR strategy is shock and awe.
I’m not qualified to assess quality but watching the reaction of mathematicians, some of these results are v significant. e.g. this post on X from a Stanford math prof:
So, Fields medal-worthy.
But the feelings.
If they wanted shock and awe then they got it: 100+ reactions from mathematicians.
I am curious about what kind of thing “being a mathematician” becomes…
I am familiar with the feelings! Both engineers and designers have been going through the Five Stages.
But, for me, my mental image of the kind of work I do is constructing new things, like the Doozers in Fraggle Rock. I don’t have much imagination, I have to think by making and then encountering what I make to figure out what to make next, so the huge acceleration (and increased individual agency) in speculative building is wonderful.
WHEREAS my mental image of mathematics has been mining. Deep in the tunnels, pickaxes at the stubborn rock, raw and earned intuition guiding the miners to the rare diamonds that must be there.
And what’s happened is that the rock has fallen away… the intellectual frontier has pulled way, way, way back over the horizon…
Look I don’t mean to be all Platonist about this, but I feel like mathematics is already “there” somehow.
And what AI has done is turn the granite-against-the-nose into vast continents, open country under open sky as far as the eye can see.
All has been discovered (well, 372 proofs right now, each of them a human lifetime’s work, but practically speaking “all” is a decent approximiation).
So what is it now, to be a mathematician?
The “vast continents” image sticks with me:
Less unearthing and more exploring.
I’m reminded of what my kid’s encyclopaedia and Wikipedia euphemistically both call the Age of Discovery: that period from the 15th century onwards when Europeans explored the world and nicked things to bring home. (It never ended.)
There were botanists and biologists and anthropologists and archeologists, but they weren’t today’s botanists and biologists and anthropologists and archeologists.
Not professional scientists but amateur explorers and enthusiastic collectors who trekked into the heart of uncharted continents and lugged stuff back to amaze and astound.
(One of my favourite museums in the world is the Pitt Rivers in Oxford. General Pitt-Rivers was just a guy who collected a lot of things.)
They mostly didn’t need skill or training. Some ready cash, some bravery, and a decent handle on public taste to spot the tasty stuff…
Perhaps that’s the new job of the mathematician? To venture into the new natural world opened up by the AIs and figure out what to haul back?
In a matter of days, mathematics is already becoming an amateur sport: there’s a mass game on X making integer multiplication quicker and quicker.
A scavenger hunt.
Look, collecting to amaze and astound, and then looking at the collection… I don’t mean to devalue the activity, the process leads to great things.
Darwin goes voyaging, draws a LOT of pictures of finches, and figures out the origin of species. Boom.
I had a chat a few months back with a person adjacent to one of the extremely well-funded frontier math labs.
He explained the thesis…
Every couple hundred years something comes out of mathematics that turns society upside down, he said.
For example #1: the mathematics of chance led to the financialisation of risk and unlocked the explosion of capital that built the world we have today.
For example #2: George Boole figured out how to connect logic (reasoning) with numbers, and when you combine that with physical state then you get all of computers.
So what’s example #3? That’s what they’re hunting for.
But what then?
A cornerstone of the Age of Discovery was the Columbian Exchange, which brought tomatoes, tobacco, potatoes and chilli across the Atlantic for the first time. Plus a ton of silver and gold.
In exchange: horses and smallpox. You’re welcome!
Professor Mark Maslin (UCL) outright refuses the term. He calls it the Great Dying.
Imagine.
Because it’s only the age of “discovery” from the European perspective, right?
There’s no discovery going on for the people living there.
So… these new mathematical continents uncovered on the map by AI… these amateur mathematicians hacking their way up-river…
Not to drag out a metaphor waaaaay too far (I’ve never let it stop me before) – but who will they find already there?
In Greg Egan’s astounding short Luminous (read it in The Best of Greg Egan) they discover that SPOILERS while we inhabit a physics of small numbers and loosely coupled phenomenon there are coterminously and unnoticed SPOILERS aliens in the mathematics of trans-astronomic integers.
I mean:
We’ve already discovered that if we make a matrix large enough then when we talk to it, it talks back.
So maybe that should be the real goal of going into mathematics today.
Not figuring out what gem to bring back from the frontier to disrupt society.
But instead: first contact.