Reported by New智元
Honestly, the history of human science has been completely rewritten tonight!
Just now, OpenAI unveiled three major announcements in quick succession, officially revealing that its internal AI independently achieved three groundbreaking discoveries—
Mathematics: Proved the “local smoothing conjecture” in all dimensions, completely resolving the “Kakeya conjecture,” which had puzzled the mathematical community for a century;
Computer Science: The “Exponential Time Hypothesis” (ETH), which has dominated the field for nearly 30 years, has been falsified;
Theoretical Physics: A rigorous mathematical proof of the existence of four-dimensional quantum chromodynamics (QCD) and pure Yang–Mills theory has been provided.
Upon the release of this news, Silicon Valley and the academic community were thrown into complete chaos.
The Kakutani conjecture puzzled mathematicians for an entire century and was also the primary area of research for Fields Medalist Wang Hong.
But among the three conjectures, the one that truly sent shockwaves through the community is the “Exponential Time Hypothesis” (ETH). Over the past thirty years, the global computer science community has universally accepted ETH as correct.
This assumption, long regarded as an ironclad principle by computer scientists and upon which hundreds of papers have been built, has now been directly overturned overnight by AI.
The most astonishing aspect was the speed: from receiving the proof to the machine completing line-by-line verification, the AI took only one day.
Moreover, the AI exam papers were graded by the very same people who had crafted the questions in the first place, with a Nobel laureate personally leading the verification process.
Nobel laureate David Gross was even more astonished, remarking, “For those who were unaware, the falsification of the ETH hypothesis is truly astonishing and has far-reaching implications.”
Tsinghua alumnus Chen Lijie couldn’t help but exclaim: the Exponential Time Hypothesis is wrong!
The 30-year iron rule has collapsed.
Hundreds of computer science papers have had their foundations shaken.
Let’s start with a question that every programmer can’t avoid: the satisfiability problem (SAT).
Given a set of logical conditions, the question is whether there exists a set of values that makes all of them true simultaneously. It is the progenitor of NP-complete problems and is closely related to the “P versus NP” Millennium Problem.
In the late 1990s, Russell Impagliazzo and Ramamohan Paturi proposed the Exponential Time Hypothesis: problems like 3-SAT cannot be solved in sub-exponential time; at best, they require time on the order of 2^cn.
This hypothesis has never been proven, but almost everyone believes it.
Thus, over the past nearly 30 years, researchers have continually linked it to other problems. In graph theory, databases, computational geometry, and computational biology, hundreds of papers have leveraged the ETH-based bounds on algorithmic speed.
The result is here today: AI has directly proven that all of this was wrong.
OpenAI’s publicly released computer science paper bears a single, unambiguous conclusion in its title: “The Exponential Time Hypothesis Is False.”
This 67-page manuscript proposes an algorithm that can even precisely count how many satisfying assignments a 3-SAT formula has. As long as this number is greater than zero, the question of whether the formula is satisfiable is answered in the process.
You can think of 3-SAT as a large set of mutually constraining switch rules: each rule involves three variables that can be either true or false, and the task is to find an assignment that satisfies all the rules simultaneously.
The difficulty lies in the fact that as the number of variables grows, the number of possible combinations can explode. ETH argues that, in the worst case, the time required to find a solution inevitably incurs an exponential cost that scales with the number of variables.
The paper argues that reducing the growth rate to sub-exponential complexity still falls short of polynomial time; therefore, refuting ETH does not prove P=NP, nor can it be directly interpreted as meaning that all hard problems will be solvable in seconds tomorrow.
OpenAI also made it clear that turning theory into practice and accelerating progress will require substantial follow-up research.
To verify this shocking conclusion, OpenAI even brought the very founder of ETH back from retirement!
Impagliazzo and Paturi, along with Ryan Williams, a renowned expert in complexity theory at MIT, personally led the effort. This morning, Williams publicly shared the paper’s link and its claims regarding time complexity.
A computational limit they spent nearly 30 years researching has now been refuted by AI.
Similarly, the internal AI at OpenAI completed the proof in just one day. It received a natural-language refutation on October 16 and completed the Lean formalization on the 17th.
Here, a day is the interval between two proof formats; the public review that determines whether the result holds is now being handled by this group of experts.
Now, Sebastien Bubeck, a theoretical computer scientist and mathematician at OpenAI, marvels that 3SAT in sub-exponential time is the biggest surprise he has seen in his 20 years of studying theoretical computer science.
He still remembers the shock he felt 25 years ago when he saw just how vast the difference in complexity could be between 3 and 2.
Netizen Peter Gostev joked, “Alright, so what are the odds of winning the P vs. NP problem now?”
Complete all dimensions!
The century-old Kakeya conjecture has been solved in one fell swoop by AI.
First, let’s look at OpenAI’s first major discovery, which lies in the very heart of pure mathematics—Harmonic Analysis.
In the field of mathematics, there is a famous century-old problem known as the Kakeya conjecture.
In 1917, Japanese mathematician Sōichi Kakeya posed the following question: On a plane, if a needle of length 1 is flipped over and rotated by 180 degrees, what is the minimum area it must sweep?
Intuition tells you, just draw a circle.
However, in 1928, the mathematician Besicovitch provided a counterintuitive answer: the area can be made arbitrarily small, approaching zero.
The problem didn’t end there; on the contrary, it only deepened. Mathematicians then turned to ask: Can a set that contains line segments in every direction have zero area, yet still have its “dimension” compressed?
This is the Kakeya conjecture, which asserts that in n-dimensional space, such a set must be of full dimension.
This seemingly childish question later turned out to be a neural hub connecting harmonic analysis, partial differential equations, number theory, and combinatorics.
As those familiar with the field know, in 2019, Guth, Wang Hong, and Zhang Ruixiang proved the two-dimensional local smoothing conjecture; in 2025, Wang Hong and Joshua Zahl solved the three-dimensional Kakeya conjecture, sending shockwaves through the entire mathematical community.
And this time, OpenAI’s model has directly extended the “local smoothing conjecture” to all dimensions.
This conjecture was proposed by Sogge in 1991; it posits that waves traveling in different directions can converge at a single point, causing the local intensity to surge dramatically.
The pattern we’re trying to capture is that this extreme level of focus doesn’t last very long; when you look at a longer time frame, the average degree of concentration turns out to be much milder than the worst moment.
This pattern has implications for an entire field of analysis. OpenAI states that the model, using a novel auxiliary partial differential equation, has provided a proof for all spatial dimensions n≥2.
It is a “parent conjecture”; once proven, both the Kakeya conjecture and the Stein restriction conjecture would collapse like dominoes.
The latter study investigates what estimates can still be maintained when the Fourier transform is restricted to certain surfaces, which is closely related to how waves propagate and concentrate.
From obtaining the natural-language proof on October 18 to completing the Lean formal verification the next day, the AI took only one day.
The significance of this result lies in its use of a more upstream analytical tool to address an entire set of long-standing challenges.
Nobel laureate leads the team
The Millennium Physics Holy Grail has been torn open
The theoretical physics working group, led by David Gross.
In 1973, he co-discovered asymptotic freedom: at extremely short distances and very high energies, the strong interaction actually becomes weaker. This discovery helped establish quantum chromodynamics and earned him the 2004 Nobel Prize in Physics, which he shared with two other scientists.
Now, what he is tasked with understanding and reviewing is the proof that AI has produced based on this theoretical mathematical foundation.
Quantum chromodynamics, or QCD, describes the strong interaction between quarks and gluons. The pure Yang–Mills theory, on the other hand, removes matter fields such as quarks while retaining the self-interactions of gauge fields like gluons.
Physicists have long used quantum field theory to explain and calculate a wide range of phenomena, but rigorously formulating these interactions as mathematical objects in four-dimensional spacetime remains a profound foundational challenge. While formulas can yield successful calculations, achieving a complete mathematical construction of the entire theory is a separate undertaking.
OpenAI stated that this model, following Balaban’s approach in constructive quantum field theory, has provided existence proofs for certain four-dimensional gauge theories and fermion theories, covering QCD as well as a grand unified extension that includes the Standard Model gauge fields and fermions.
Among them, the existence of the pure Yang–Mills theory happens to address part of the Millennium Prize Problems. Clay’s requirement for a complete solution also includes the mass gap, meaning that the energy of non-vacuum excitations cannot approach the vacuum energy arbitrarily closely; this announcement did not declare a resolution to that aspect.
Joining Gross in the group were Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov. That year, Jaffe co-authored the official statement of this Millennium Problem with Edward Witten.
The significance of this list lies in the fact that some individuals laid the groundwork for relevant physical theories, while others personally formulated the prize‑winning problems; now, they are jointly confronting the new arguments put forward by machines.
The model provided a proof of the existence of Yang–Mills theory on September 9, and a proof of QCD on September 18.
Due to the length and complexity, OpenAI did not proceed with this collaboration until October 16, after completing the Lean formalization of the Yang–Mills existence.
Half a century ago, scientists helped humanity understand the strong interaction; today, they have taken up the mantle of AI, continuing to probe the most fundamental mathematical structures of the material world. This generational relay is enough to make one feel the weight of scientific history.
OpenAI gives up attribution and donates 5 million USD.
Precisely because the results are so substantial, OpenAI has classified these three manuscripts as “raw research data.”
To turn this into scientific understanding, it conducted its first-ever trials of three external academic shepherd collaboration models.
Mathematical results are published alongside AI-generated manuscripts and Lean code; computer science results are released with both manuscripts and Lean code, and an expert panel has been assembled; meanwhile, the physics team has decided not to disclose the AI’s raw outputs for now, opting instead to have five leading experts conduct a closed-door review and personally draft explanatory papers.
The four collaboration principles are explained very clearly.
First, transparency—no non-disclosure agreements are required.
Second, no academic authorship disputes: OpenAI does not seek academic authorship for the original findings produced by its internal models.
Third, epistemic recognition: the working group has earned academic recognition through the scientific understanding it has developed, the interpretive papers it has authored, and its accurate tracing of prior scholarship.
Fourth, independence and impartiality: participation is voluntary and unpaid, and scholars reach conclusions entirely on their own.
OpenAI has contributed $5 million to the Simons Foundation, which, together with OpenAI and Anthropic, has pooled $15 million in funding and computational resources to support workshops, conferences, and specialized initiatives, helping scientists independently review, understand, and expand upon AI-generated scientific discoveries.
Currently, the `openai/math` repository has indexed 721 manuscripts generated by OpenAI’s undisclosed internal models, grouped into 373 result families. The models were evaluated on approximately 4,000 open research questions, with each result consuming about 3 hours of ChatGPT Pro–level deep-thinking computational power. At present, roughly 42% of the top-level conclusions have been formalized in Lean.
A prophecy from three years ago
AI will not replace disciplines; rather, it will reshape them.
OpenAI researcher and professor at the University of Pennsylvania’s Wharton School and the Departments of Computer Science and Mathematics, Wei-Jie Su, shared his presentation PPT from three years ago on X.
Slide 4 states that tasks involving complete information—where inputs and outputs are well-defined and boundaries are clear—are most vulnerable to AI disruption. In addition to programmers and accountants, it specifically mentions “perhaps also theoretical computer scientists, theoretical physicists, and (pure) mathematicians.”
Su Weijie remarked that, at the time, almost no one in the audience believed his words.
Looking back, the term “replace” is not entirely accurate. AI will not replace any discipline.
On the contrary, it will fundamentally reshape—and is already reshaping—various disciplines by rewarding research that establishes deep connections with real-world challenges and with other fields.
OpenAI President Greg Brockman wrote in the official announcement that AI has already begun helping us deepen our understanding of the universe.
AI is evolving from a research-assistance tool to a pioneer in making original discoveries in fundamental science.
Once findings are validated, human scientific research will enter a new phase of “AI leading the way in discovery, with humans verifying and interpreting.” Both the pace of scientific breakthroughs and the academic evaluation system will undergo reshaping.
Reference material:
https://openai.com/index/building-scientific-understanding-with-academic-communities/
Editor: Moses Peach