Abstract:
The theoretical computer world has also been bombarded by AI! Last night, AI completely crossed the Rubicon River of scientific research and officially began to "overturn" the building of human knowledge. OpenAI dropped nuclear bombs in the three major fields of theoretical computers, pure mathematics and theoretical physics:
This may be the most explosive technology news this year, if not one of them.
Claude even bluntly said that if these results hold true, this will be the most important day in the history of mathematics and theoretical computing.
Among them, the mathematical breakthrough is highly related to Fields Medal winner Wang Hong’s previous work on Kakeya’s conjecture, while the physical breakthrough may be the most important of the three, and may solve the problems left by Nobel Prize winner Chen Ning Yang.
This time I’m going to talk about a breakthrough in the computer field: the exponential time assumption does not hold.
According to Claude, this is a Turing Award-level disruptive achievement that "if the statement is correct, this will change computer science."
Sebastien Bubeck, current OpenAI researcher, former Microsoft Vice President of Artificial Intelligence and distinguished scientist, praised this as "the biggest surprise I have seen in 20 years."
Moreover, on the same day, two AIs announced this breakthrough almost at the same time!
OpenAI and Anthropic, two AI giants, announced at almost the same time that their internal models had overturned the "exponential time hypothesis" (ETH) that has dominated theoretical computer science for 27 years!
What is even more terrifying is that in the paper Anthropic dumped, it was clearly marked that the core algorithm was built by the internal model Claude
Zero human intervention
independently deduced under the circumstances.This paper, which may go down in the history of human science, has the only signed author, Claude.
The "sky" in the theoretical computer world has fallen. What does this mean?
To put it simply, in 1999,
Exponential Time Hypothesis (ETH)
Proposed by Russell Impagliazzo and Ramamohan Paturi, University of California, San Diego.You can think of it as a combination lock with n switches, which is the 3SAT problem.
For half a century, countless extremely smart brains have tried their best to unlock the lock, but no one can break one thing:
The time to crack the lock will always skyrocket "exponentially" as the number of switches increases.
For example, suppose a lock needs to be filled with n numbers, each number being between 1 and 9. Each position has 9 choices, so there are 9ⁿ possibilities in total, which is 9 times n times.
We can solve this puzzle by exhausting all 9ⁿ possibilities. But this method is extremely inefficient: for a Sudoku puzzle that requires filling in n = 100 numbers, even using all the computers in the world, it would have to wait until the sun cools down.
People have long tried without success to find algorithms whose running time grows slower than 9ⁿ with n.
In 1999, scholars wrote this collective intuition into a formal hypothesis:
There is no sub-exponential time algorithm for 3SAT.
You can improve the speed a little bit, but you'll never get over this "exponential wall." This is like "the speed of light cannot be exceeded" in physics.
This conjecture has been proposed for more than 20 years. In the past, hundreds of papers have been used to study the complexity lower bounds of various computing problems based on the establishment of ETH.
Many studies from graph theory and combinatorial optimization to databases and computational biology are based on this assumption.
If the Riemann Hypothesis is overturned, it will be down to number theory; if ETH is overturned, it will be down to complexity and parameterized algorithms.
ETH’s weight has not reached “
P vs NP
"Or the millennium level of the Riemann Hypothesis.But it is stronger and more specific than P≠NP: if ETH is established, P≠NP can be derived; but if ETH is overturned, P=NP cannot be derived.
A large number of conditional research conclusions that rely on ETH need to be re-evaluated.
A new batch of “victims” in the field of AI have emerged——
There is also a buddy in the group. A paper he wrote before was based on the premise of the establishment of ETH.
Now this premise may be gone, and the conclusion of the paper needs to be re-examined.
Imagine that you have spent several years studying a problem, writing papers, and making proofs, and even scholars in a field have been studying this hypothesis for more than 20 years (such as Professor Tuli).
One day, an AI model tells you that the premise that everyone has always believed may be wrong.
Crossing the Rubicon of Scientific Research: Sole Author Claude
A dramatic scene happened immediately.
OpenAI President Greg Brockman just posted an official announcement, and his old rival Anthropic just published a paper with the same title.
He was so aggressive that he crashed on the spot!
Anthropic said: Coincidentally, this is not the case. Our Claude internal model was released on
October 16th
It has independently overturned ETH!
Moreover, Anthropic left a "source statement" on the paper page:
The core algorithm was discovered on October 16th by an internal Claude research model, consuming 14 million output tokens without any human input.
This means that
AI has completely crossed the Rubicon River of scientific research
——It is no longer a human tool, but has become the real "first author".What is the concept of 14 million Tokens? A complete volume of "The Three-Body Problem" has approximately 900,000 words. 14 million Tokens is equivalent to Claude deducing more than a dozen thick drafts of "The Three-Body Problem" in one breath.
After evaluation, many top scholars said: This is equivalent to an AI model completing the scientific research of one to two years of a top human postdoctoral fellow in a few days without eating, drinking or sleeping.
!In the past few days, Claude explored the path by himself, deduced the formulas by himself, verified the logic by himself, and even used unpopular mathematical tools across borders, and finally put a proof in front of mankind.
This time, it’s not “AI helps mathematicians search literature,” nor is it “AI got an Olympiad question right.”
This is AI single-handedly breaking through the most hard-core and purest theoretical disciplines of mankind.
The founder was woken up overnight, and the mathematician transformed into an "auditor" to lose weight quickly
Does AI overturn it if it says it has overturned it? Could it be that the AI is "seriously talking nonsense (hallucination)"?
The most magical scene happened. In order to prove their innocence, the two companies did not just throw out a PDF, but also disclosed the
Lean formal proof code
.Lean is a "selfless electronic reviewer". Even if there is a logical jump, it will directly report an error. Since the code can run smoothly, it means that the underlying logic almost blocks the possibility of errors. Handing over papers that are “machine-verifiable” is the irrefutable confidence of AI.
But this does not fully confirm the correctness of the proof.
The two founders of the ETH conjecture, Russell Impagliazzo and Ramamohan Paturi, are said to have been urgently asked to come out.
Twenty-seven years ago, two scholars wrote down a conjecture; 27 years later, they were awakened to check how an AI overturned it.
This is probably the most complicated emotion in academic history.
Currently, these two experts are teaming up with top teams from MIT and other universities to conduct a line-by-line review of their codes.
At the same time, another front is also advancing rapidly.
Faced with this more than 60-page "alien" proof produced by AI, it is extremely difficult for the human brain to read.
NVIDIA Senior AI Architect Shiva Kintali broke out overnight and compressed OpenAI's original 60-page ETH falsification certificate into a 22-page streamlined version!
He cut off the tedious steps of AI and did not pursue the optimal logarithmic factor. He only sought to falsify basic statements cleanly and added calculation examples.
He has only one goal:
"Let human colleagues truly understand."
Now, an unprecedented academic spectacle appears:
AI is responsible for tackling tough problems: in a few days, it opens a door that no one has opened in 27 years;
Humans are responsible for digestion: refining AI’s lengthy deductions into knowledge that humans can understand and continue to push forward.
Now, it’s humans’ turn to grade and streamline the AI’s homework.
The "subject-object change" of basic scientific research
As early as March 2023, OpenAI released a sensational "Forecast Report on the Impact of AI on the Job Market." In this list, the person who tops the list of
"The Jobs Most Impacted by AI" is surprisingly mathematician
.
At that time, most people scoffed at this: Mathematics requires the most rigorous logic of humans. How could an AI that talks so much about cheating be able to do theoretical mathematics?
However, exactly three years later, as ETH was falsified by AI overnight, Kakeya conjecture was broken by models one after another...
This bullet fired three years ago finally hit the target of human theoretical research.
Does this mean that scientists will lose their jobs collectively? No.
As Peking University alumnus and scholar Weijie Su observed three years ago:
AI will not simply and crudely "replace" any field, but will reshape them. Future scientific research will greatly reward those who can make deep connections with real-world challenges and other disciplines.
Just like after the invention of the camera, painters no longer need to compete with each other to "who paints more like one", thus Impressionism and modern art were born.
When AI takes over the hard work of "calculation and proof", humans can finally spend their precious energy on more fundamental issues:
Looking for the next question worth exploring and establishing real-life connections across disciplines.
27 years ago, when the two scholars wrote the ETH conjecture, they never imagined that it would not be human beings who ended it.
Unexpectedly, two AIs would hand in the exam on the same day.
“The world is not being changed by AI, but has already been changed.”
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