Abstract:
Anthropic officially announced that Claude has won a cutting-edge record in theoretical physics. It ran continuously for several days with almost no human intervention, and solved the notoriously difficult "nine-circle scattering amplitude" calculation problem in the high-energy physics community in one fell swoop! Specifically, it calculated the nine-turn result of the six-particle amplitude in the plane N=4 super-Yang-Mills theory. The previous human record stopped at eight turns.
Note that the "Yang" in the Yang-Mills model refers to the physics guru Mr. Yang Chenning.
The "Yang-Mills Theory" co-founded by him and Mills in 1954 is the cornerstone of modern particle physics.
Any high-order calculation based on it can be called the ultimate challenge of human brain power.
Today, humanity’s top theoretical physicists have been “cut off” by AI.
What’s even more frightening is that Claude completed this god-level challenge using only one prompt word and spending thousands of dollars!
The answers returned a few days later, some of which were expanded to 30 billion items.
It seems that there are many more low-hanging fruits in science than imagined.
This time, physicist Lance Dixon, who was responsible for verifying the results for AI, expressed this emotion:
Most theoretical physicists around me have long admitted that large models will subvert physics sooner or later, but they just don’t know when that day will hit them.
For me, that day is September 1st.
Hard-core physicists challenge AI
"My old profession is very special"
The origin of the story stems from the "provocation" of a physicist.
Matt von Hippel, once a theoretical particle physicist, is now a popular science writer.
The five circles in 2016, the six circles and the seven circles in 2019, his name is in the list of authors of the paper
Facing the recent AI news, he said he would not believe in evil unless he saw a large model solving problems in his field with his own eyes.
Deep Blue defeated the chess master Kasparov. The Go community said: Go is too complicated for computers to play. As a result, he was slapped in the face by AlphaGo.
AlphaFold crushed human protein structure experts, but other fields said: We don’t have that kind of data and can’t replicate it.
Now, large language models can read literature and imitate mathematical proofs. But the debate still continues: Does AI only find counterexamples and cannot propose new frameworks? Does it only work in fields with clear rules like mathematics, but not in fuzzy fields like physics? ……
It’s the same formula every time: academics are skeptical until the AI comes into its own.
He thinks his old line of work, "scattering amplitude," is different.
Last month, he posted a "hero post" on his blog to all AI companies on the Internet:
If your AI company really wants to shock us scientific researchers, come and challenge my old profession!
Please demonstrate that AI can solve unsolved problems in the field of scattering amplitude within a computing budget that ordinary academics can afford.
He asked three questions in total, one of which was:
Count N=4 super Yang-Mills model to Nine Loops!
In theoretical physics, physicists use the formula of "scattering amplitude" to predict the behavior of particles, such as how particles in the Large Hadron Collider collide.
Scattering amplitude
But this formula is a nightmare. To get infinitely close to the true answer, physicists must layer layers of fine corrections called "loops" one on top of the other.
With each additional "circle" added, the answer becomes more accurate, but the amount of calculation increases exponentially!
In practice, most humans stay in the second or third circle. The most accurate predictions in particle physics only use the fifth circle.
In the special "test sandbox" model,
the current limit record of humans is
"
Eight circles
"
. This was achieved after years of hard work by Professor Lance Dixon and his team at the SLAC National Accelerator Laboratory.
"Nine circles"? It seems to be an area that requires massive computing power and countless talented brains to spend years to reach.
Matt’s challenge to AI is so simple and crude.
One word of reminder, several thousand dollars, Claude "killed like crazy"
Faced with this public challenge, Anthropic scientists quietly accepted the challenge.
At the end of August, two physicist employees at Anthropic, Liam and Siddharth, quietly contacted Matt: "Hey, we've solved your challenge."
Matt's jaw dropped on the spot. How? Burned millions of dollars of computing power?
No.
The research team used Claude Science, a system specially designed for scientists that allows Claude to run according to strict rules. The model is currently the strongest publicly available model Fable 5.1.
They entered a simple prompt to Claude:
The current problem is: Calculate the six-particle (hexagon) amplitude of the plane N=4 SYM model under nine circles.
Then, the researcher did not teach Claude how to do it step by step, but left him a message:
I'm going to bed. I won't be here for the next few hours. You continue to count, unless I ask you to stop, and report your progress to me every 4 to 6 hours.
Then, Claude started a crazy deduction without anyone watching!
It uses a method called "bootstrapping" that Dixon and his collaborators have developed over the years, just like solving a Sudoku game, constantly eliminating wrong options among countless parameters.
A few days later, Claude not only calculated the nine circles, but also calculated them using two different physical methods (the original bootstrap method and the indirect shape factor method)!
Specifically, in the original bootstrapping method, the method used by Dixon's team is called bootstrap, which is similar to Sudoku. All possible functions are filled in the grid, and the rules of physics are used to eliminate them one by one. The rest is the answer.
Claude directly took out Python and the open source library SymPy, and calculated a bloody path in the space of six particle amplitudes.
In the indirect shape factor method, when Dixon and his colleagues rushed eight times, they first calculated a simple "shape factor" and then used a peculiar "plantar duality" symmetry to translate the result into amplitude.
Claude followed this style of play and pushed up again.
For the shape factor, Claude did not calculate a Feynman integral. It turns the entire physics problem into a very large system of equations, and uses integers to solve the whole process without decimal errors. It can also repeatedly check the calculation by changing several large prime numbers.
The first hurdle is memory. If you push it to nine circles according to the old method, there will be 1.85 million unknowns alone, and the system of equations is so large that it cannot be accommodated in the memory.
Claude changed his mind and used plantar duality to "guess" part of the answer. Coupled with symmetry, the number of unknowns dropped from 1.85 million to 76,000.
The next step is to solve "Sudoku". 76,000 unknown numbers were eliminated by the rules of physics, and finally only the only solution remained.
Finally translated back to amplitude, there are more than 30 billion results in one section alone, and only 1.67 billion in eight circles.
Moreover, the cost of solving unsolved problems in human physics is extremely low.
According to the price for ordinary users, each route costs one to two thousand US dollars, and the two channels add up to several thousand US dollars. The bulk of it is the cost of running Claude for a long time.
As for the direct bootstrapping, the computing power cost purely for running Python code is only US$100 - which is equivalent to renting 96 CPUs and running it for a week.
With 100 US dollars and a prompt, Claude easily broke through the ceiling of theoretical physics in a few days.
Former world record holder: "I was cut off by AI, but I am very excited"
The results are calculated, but are they correct?
Anthropic’s team found the “eight lap” record holder, Professor Lance Dixon himself, to check the calculation.
That day was September 1st, which coincidentally happened to be the day Fable 5.1 was released.
The moment Professor Dixon got the results, he was extremely shocked. Because he knows how difficult it is.
After completing eight laps in 2023, he and his team have been stuck at nine laps for the past two years.
The entire calculation process is like building a playing card castle or baking a soufflé. As long as there is a wrong code or an incorrect symbol in the middle, the entire calculation will completely collapse.
But not only did Claude not crash, he also wrote all the tedious code from scratch, perfectly avoiding all pitfalls!
After two weeks of careful verification, Professor Dixon confirmed that Claude’s nine lap results were correct!
So Professor Dixon is heartbroken?
"No," Professor Dixon wrote openly in the blog post, for two reasons.
First, their team has been training a customized transformer model to predict higher lap times. The slogan is that any candidate answer given by the machine has tool verification. Claude is also a transformer, only about a million times bigger than theirs.
Secondly, Claude used all the methods developed by him and his collaborators over the years, and when submitting the answers, he also used the format that his team had set long ago (the professor guessed that this was Claude trying to sell face to them).
I am verifying Claude's results, and Claude is also verifying all our past work.
He also gave a very high evaluation:
Except for me and my co-authors, Claude may be the "person" in the world who understands the papers I published in 2019 and 2023 best.
And his teammate Kyle Cranmer is still messy on X, "I just found out that our group was snatched by Anthropic, and I'm still digesting it... Although it's not too surprising, I really wish we had the time and resources to invest in it."
Extreme reversal
The Chinese team also reached nine laps with GPT-6
Interestingly, just a few days after Anthropic found the question author von Hippel, he received another piece of news - He Song's team from the Institute of Theoretical Physics, Chinese Academy of Sciences.
He Song is a leading figure in the field of scattering amplitude in China. His representative works in recent years include proposing the Cachazo-He-Yuan form of the scattering amplitude of quantum field theory, groundbreaking discovery of the geometric origin of scattering in field theory and string theory, calculation and rigorous solution of the high cycle of field theory, and a series of important works in the duality of gauge fields, gravity and string theory.
On September 17, He Song, Jing Jirong, and Li wanted to publicly upload the core skeleton data of the six-particle amplitude from two circles to nine circles on the academic platform Zenodo.
In terms of public release time, it is 8 days earlier than Anthropic’s official announcement!
He Song’s team also used AI. Dixon revealed that GPT-6 helped the Chinese team calculate some constraints, but the overall framework was built by humans themselves.
von Hippel also confirmed that they did use GPT-6 as an assistant, but it was by no means a pure AI play style like Anthropic.
Dixon laughed at himself and said, "People seem to like to come to me and tell me that they have solved the nine circles. Now, I was first robbed by a machine, and then turned around and was robbed again by "human + machine"."
Not long ago, when OpenAI announced that it had solved the Millennium Problem Navier-Stokes equation and Claude advanced a key lower bound of the Riemann Hypothesis, some people asked: Why does AI only solve mathematical problems and not physical problems?
Now, isn’t this coming?
Although what Claude calculated is only a "toy model" of N=4 super Yang-Mills, which is still a long way from explaining the dark matter and antimatter of the real universe, its symbolic significance is unprecedented.
This is like the first time AlphaGo defeated Lee Sedol. What everyone exclaims is that machines can actually master areas that belong to human intuition.
Professor Dixon left an intriguing remark:
The ability of large language models to execute the complex recipes and organize computations we set is a huge win.
But one day, when the big language model begins to propose new physical principles and insights before humans, that will be the moment that truly touches the human soul.
Perhaps, low-hanging fruits are everywhere now.
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