For over two thousand years, the brightest minds of humanity, have been climbing the same mountain range: mathematics.
From Euclid and Gauss to Hilbert and Wiles, each peak conquered required betting one's entire life.
But now, this heroic era belonging to mathematics has ended.
A long article by xAI co-founder Christian Szegedy, "Whither Mathematics?", blew up on X.
In his depiction, mathematicians are explorers free-climbing in a primeval jungle, while AI is an airplane that has already planted its flag on summits no one has ever climbed.
The era of the lone climber is ending, and the era of mapping the entire continent is beginning.
Mathematics is about to graduate. It will step out of the ivory tower and become the foundation for all scientific and technological progress.
He bet ten years on this day
Rewind to Szegedy's youth. At the time, he attended a mathematics specialization class at the best school in Hungary, with 8 hours of math classes per week, spending most of his youth on competition problems.
Later, he earned a PhD in applied mathematics from the University of Bonn, joined Google, and stayed there for over a decade.
Several unavoidable cornerstones in the history of deep learning bear his name. The classic image recognition network Inception, he was the first author of the paper; the pioneering paper that revealed neural networks can be easily fooled by "adversarial examples", he was also the first author; batch normalization, which is a must in textbooks, was proposed by him and his colleagues.
In 2023, he became one of the 12 founding members of Musk's xAI.
But throughout his entire career, it has always been mathematics.
In 2019, he wrote a position paper advocating the path of autoformalization, to create superhuman mathematicians.
So-called autoformalization is letting AI automatically translate human-written mathematics into proofs that machines can verify line by line.
At that time, the goal he set was 2029.
In 2024, he moved the timeline up by three years. AI skeptic Gary Marcus replied below him, I'm not as optimistic as you.
In February of the same year, he discussed a bet on X with François Chollet, the father of Keras, and others, wagering on "before June 2026, a superhuman AI mathematician will appear".
Then, 2026 really arrived.
In May, OpenAI overturned a unit distance conjecture that had been suspended for 80 years. In July, an Anthropic researcher used Claude Fable 5 to disprove the Jacobian conjecture proposed in 1939.
By September, everything began to accelerate.
On September 4, Anthropic's internal model took only 11 days to write the complete proof of Fermat's Last Theorem in the theorem prover Lean.
On September 8, OpenAI announced that 10,000 Agents ran for 88 hours and cracked the Millennium Prize Problem, the Navier-Stokes equations.
On September 21, OpenAI also said that its internal model had solved more than 100 long-standing unresolved mathematical problems.
All of this, happened before the 2029 he originally predicted.
Two thousand years, a heroic climb
The long essay begins with his own high school graduation.
The first two hours after the graduation exam ended were the freest moments of his life. Then, the emptiness came.
There were no more competitions, no one taught him anymore, and no one cared. He wrote, "For the first time, I didn't know who I was without it."
He wanted to tell mathematicians all over the world, what you are about to experience is exactly this feeling.
In Szegedy's writing, doing pure mathematics is like exploring a wilderness without a map. It is harder to traverse than the roadless Darién Gap between Panama and Colombia; novices get lost within days, catch malaria, or are eaten by wild beasts.
Explorers do three things: draw maps, find mines, and build tools.
The most respected are those who endure hardships to climb a high mountain and draw a sketch at the summit.
For mountains that others have failed to climb, whoever climbs them will be revered as a god. The Langlands program is such an achievement.
Toolmakers also become famous, but they do not receive that kind of halo. Finding a "mine" useful to ordinary people, such as discovering that elliptic curves can be used for cryptography, most number theorists do not care much about it, and only write it into grant applications.
Those stones that everyone wants to conquer are conjectures. They themselves are often not that interesting, but they are testing grounds for climbing tools.
But what explorers stay in the jungle for is something else.
In the end, this is why people stay. Not for the map, not for the money, but for that rare moment when a stone no one cared about becomes a great mountain, and the entire terrain unfolds beneath your feet.
In the words of Stephen Wolfram, the father of Mathematica, pure mathematics is the greatest intellectual edifice built by human civilization.
This edifice was built over more than two thousand years by lonely climbers, stone by stone, peak by peak.
An airplane planted the flag on the summit
Then, the airplane came.
The Wright brothers' first flight lasted only 12 seconds, and the distance flown was not even as long as the wingspan of a large passenger plane. Szegedy said, this is roughly where AI is in mathematics today.
Until this year, these airplanes were still very primitive, able to fly only a few hundred meters, a few meters above the ground, absurdly expensive, and useful only on a few occasions.
But over the past few months, they have been able to fly into the Darién Gap without crashing, "we even landed on a few rocks that no one had ever climbed," which is to say, they solved a few conjectures.
Next, he wrote a parable.
To be honest, these rocks aren't that interesting. We climb them to sharpen our tools for the real mountains, and your airplanes can't fly that high.
Szegedy's judgment is that saying "airplanes can't reach the real summits, nor can they draw large-scale maps" is a fallacy of static thinking. Today's airplanes are still very primitive compared to those a few months from now, let alone a few years from now.
Mathematics Has Graduated
Once airplanes become cheap, the entire jungle will be transformed.
Szegedy predicts that private airplanes will be everywhere, and anyone who can afford it can charter one to land on any rock. Humans will invent satellites, survey the mineral deposits of the entire jungle, and then mine them.
The scene will be very dirty and chaotic. Today's explorers will be terrified, will long for the good old days, and will curse the big companies for ruining the jungle they love.
He wrote, "They are right, but that doesn't change anything. Big companies will find unimaginable wealth there."
The sport of rock climbing will not disappear. There will be more amateur explorers chartering flights to the rocks they like, buying ready-made gear at tool shops, and climbing together with friends.
Those with less physical strength will sit in airplanes to search for more majestic mountains, or look down upon entire mountain ranges from a place higher than any peak.
"The atmosphere and excitement of the old days will disappear forever. Mathematics will be more brilliant, more useful, and more ordinary than in the old era of heroic exploration."
The first sentence of the final section of the long essay is, "Don't bet against airplanes."
Those who say AI cannot propose conjectures, cannot build theories, cannot explain, are describing the models of last spring. Within a few months, these descriptions will no longer hold. Whoever stakes their identity on "AI can't do X" is building a house on sand.
Universities, journals, tenure committees will all look about the same within a few years, but what they reward will fundamentally change.
The heroism of climbing mountains that others cannot climb will become less important. In its place will be three other skills: choosing which terrain is worth exploring, commanding fleets of airplanes, and telling the whole world about your discoveries.
He also admits, "For many people in the system, this will feel like a demotion, and some will resist."
The final paragraph of the long essay reads like this.
"Mathematics is about to graduate. It will grow into a complete industry, becoming the true infrastructure for all scientific and technological progress, becoming the foundation on which all other fields stand, rather than a quiet corner of academia.
The era of the solitary climber is ending, and the era of mapping entire continents is beginning. As for me, I can't wait to ride a supersonic airplane and go see those vast mountain ranges."
The Stanford mathematician Jared Duker Lichtman, whom he named, wrote when reposting, that he had been waiting for this moment since he was a graduate student in 2019.
Only subversion without replacement will leave a vacuum. But a clear vision of the future will bring new life. The next step is already clear: we are preparing to translate all known mathematics into formalized code.
We Must Know, We Will Know
However, not everyone is willing to accept this diploma.
Just 5 days before Szegedy published his essay, Wolfram wrote a long essay of over 7,000 words, saying he was "a bit impatient" with claims like "humans are no longer needed to do mathematics."
In his view, the goals of mathematics "almost by definition must come from outside the system, specifically, from us." He also personally stepped into the pitfall of automated formalization, where AI told him "the proof passed," but it did not prove what he wanted to prove.
His conclusion is that pure mathematics will never be finished.
Imperial College mathematician Kevin Buzzard used the "five stages of grief" to paint a portrait of the entire mathematics community—denial, anger, bargaining, depression; plenty of representatives can be found for the first four stages.
In his article, he mentioned that Fields Medalist Scholze publicly stated he would not use AI, "and is willing to hold out to the death for this."
There was also a doctoral student whose research got stuck on a lemma, and ChatGPT proved it in one go. This doctoral student began to doubt what meaning there was in everything he was doing.
This grief is more familiar to Szegedy than to anyone else. On the day of his high school graduation, he too thought he had lost a part of his life.
But in his long essay he said that this grief is real, it just won't last too long.
In 1930, Hilbert left behind a sentence in Königsberg, which was later engraved on his tombstone: "We must know. We will know."
At the end of his long essay, Buzzard also quoted this sentence.
Mathematics is destined to be the first foundational discipline industrialized by AI. It can be checked line by line by machines, without needing experiments; right is right, wrong is wrong.
So the hardest bones that AI has cracked first—the Millennium Problems, the Jacobian conjecture, Fermat's Last Theorem—are all in mathematics.
Mathematics is transforming from a craft in the hands of a few geniuses into the foundation beneath the entire tech industry. On AI's path to superintelligence, it is the first continent beginning to be mapped.
References:
https://docs.google.com/document/d/e/2PACX-1vTSh-pyNP3Gi99WMmsinnLmE9V5CDI0HEm6WGbIPMNt3V5SGlClHF8-BetotKHOImrvQDSXmFdiOw8D/pub
https://x.com/ChrSzegedy/status/2106482567365140538
https://x.com/AndrewCurran_/status/2106503812332786044
Editor: Moses
This article comes from the WeChat public account "Xin Zhi Yuan" (ID: AI_era), author: Revelation of ASI
