What happens when you ask artificial intelligence to solve a problem that theoretical physicists have worked on for decades? In a new publication from a team at Princeton, Harvard, Cambridge, and OpenAI, GPT-5.2 Pro GPT-5.2 Pro The latest version of OpenAI’s language model, capable of advanced mathematical reasoning and formulating scientific hypotheses. was the first to propose a key formula describing gluon scattering — a formula that was then proven by another internal OpenAI model and verified by scientists by hand.
This is not science fiction. This is a scientific publication from February 2026.
The Problem: Do These Amplitudes Really Vanish?
In particle physics, scattering amplitudes scattering amplitudes Mathematical expressions determining the probability that given particles will collide and produce specific output particles. Higher amplitude means more probable event. are a fundamental tool for describing interactions between particles. For decades, physicists assumed that a certain class of amplitudes — the so-called single-minus amplitudes — simply vanish.
What are gluons gluons Particles carrying the strong force, one of the four fundamental interactions in nature. Gluons ‘glue’ quarks together inside protons and neutrons. ? They’re the particles responsible for the strong interaction — the force holding quarks together inside protons and neutrons. In Yang-Mills Yang-Mills A theory describing interactions between particles using gauge fields. Forms the mathematical foundation of the Standard Model of particle physics. theory, gluon scattering is a key process, but calculating its amplitudes is a mathematical challenge.
Each gluon has a property called helicity helicity The projection of a particle’s spin onto its direction of motion. For massless particles like gluons, helicity can be +1 (right-handed) or -1 (left-handed). — it can be “plus” or “minus”. Single-minus amplitudes describe a process where one gluon with minus helicity decays into multiple gluons with plus helicity.
Conventional wisdom said: these amplitudes are always zero.
The authors of this publication prove that’s not true.
GPT’s Role: From Hypothesis to Proof
Here’s where the story gets fascinating. The research team, which includes Kevin Weil representing OpenAI, used artificial intelligence not as an auxiliary tool, but as a co-discoverer.
How Did It Work?
GPT-5.2 Pro proposed the hypothesis — the key formula (equation 39 in the publication) describing non-zero single-minus amplitudes
An internal OpenAI model proved the formula — it didn’t just guess, but carried out a mathematical proof
Scientists verified by hand — using Berends-Giele recursion Berends-Giele recursion A method for calculating scattering amplitudes by building increasingly complex amplitudes from simpler components, step by step. , they confirmed the formula is correct
Consistency tests — the formula passed five rigorous mathematical tests
This is an unprecedented example of AI as a partner in scientific discovery — not as a calculator or literature searcher, but as a creator of original mathematical hypotheses.
The Physics: What Was Actually Discovered?
Klein Space and Half-Collinear Configurations
The key to the discovery lies in considering the problem in Klein space Klein space A space with (2,2) signature — two time dimensions and two spatial dimensions. A mathematical abstraction allowing configurations impossible in ordinary spacetime. instead of standard Minkowski spacetime. In Klein space, so-called half-collinear configurations are possible, where certain spinor products ⟨ij⟩ ⟨ij⟩ The spinor product of two particles i and j. When it equals zero for all pairs, we have a half-collinear configuration — impossible in ordinary physics. vanish for all particle pairs.
In ordinary spacetime, such configurations are impossible. In Klein space — they’re perfectly valid.
Main Result: The Amplitude Formula
For n gluons in region R₁, the amplitude is:
$$A_{1 \cdots n}|_{\mathcal{R}_1} = \frac{1}{2^{n-2}} \prod_{m=2}^{n-1} \left[ \text{sg}_{m,m+1} + \text{sg}_{1,2 \cdots m} \right]$$
where sg denotes a sign function depending on particle kinematics.
Key Discoveries
Amplitudes are piecewise-constant integers — they take values only from the set {-1, 0, +1}. This is an extraordinarily elegant result — complex quantum calculations yield discrete, simple numbers.
Recursion relation — the authors derived a formula to calculate the n-particle amplitude from amplitudes for fewer particles:
$$A_{1 \cdots n} = \frac{1}{2} \sum_{m=2}^{n-1} \text{sg}_{m,m+1} \cdot A_{1 \cdots m} \cdot A_{m+1 \cdots n}$$
Concrete Examples
For 3, 4, 5, and 6 gluons, the authors provide explicit formulas. The 6-gluon case contains 32 terms — complex enough that hand calculations would be impractical, but GPT managed to generalize the pattern.
Verification: Five Consistency Tests
The formula proposed by GPT passed rigorous verification:
| Test | Description |
|---|---|
| Cyclicity | Amplitude is invariant under cyclic permutation of particles |
| Reflection symmetry | Correct behavior under order reversal |
| U(1) decoupling | Consistency with gauge theory |
| Kleiss-Kuijf relations | Reduction in number of independent amplitudes |
| Weinberg’s theorem | Correct limits for soft gluons |
Each of these tests is an independent mathematical constraint the formula must satisfy. The fact that a formula “guessed” by AI satisfies all five is strong evidence of its correctness.
Implications for AI in Science
A New Discovery Paradigm
This publication signals a fundamental shift in the human-AI relationship in science:
- From tool to partner: AI doesn’t just process data, it formulates original hypotheses
- From verification to creation: GPT doesn’t check existing theorems — it creates new ones
- From assistant to co-author: Kevin Weil from OpenAI is a full co-author of the publication
What Does This Mean for the Future?
- Accelerated discoveries — problems waiting decades may be solved in weeks
- Democratization of theoretical physics — access to “mathematical intuition” without years of training
- New ethical questions — who is the author of a discovery: human, AI, or both?
Why This Matters for Physics
Beyond Minkowski
The results suggest that physics in Minkowski spacetime Minkowski spacetime The standard spacetime of our universe with (3,1) signature — three spatial dimensions, one time dimension. may be a “shadow” of a richer structure in Klein space. Amplitudes that appear to vanish in our reality are non-zero in a more general mathematical context.
New Theoretical Tools
The discovery opens doors to:
- Better understanding of quantum chromodynamics quantum chromodynamics QCD — the theory describing strong interactions between quarks and gluons. Responsible for the masses of protons and neutrons.
- New methods for calculating scattering amplitudes
- Connections between different spacetime signatures
Summary
The publication “Single-minus gluon tree amplitudes are nonzero” is a milestone on two fronts:
For physics: It overturns a long-standing assumption about the vanishing of a certain class of amplitudes, opening new research directions in field theory.
For AI: It demonstrates that large language models large language models LLMs — neural networks trained on massive text corpora, capable of reasoning, translation, and generating new content. can not only assist but actively participate in creating new mathematical and physical knowledge.
When GPT-5.2 Pro “guessed” a formula that humans then proved and verified, we crossed a threshold. AI is no longer just a tool — it’s becoming a partner in humanity’s greatest adventure: understanding the universe.
Links
- Based on the publication arXiv:2602.12176 PDF