Quick Brief
- GPT-5.2 Pro conjectured a formula proving gluon interactions presumed to vanish actually occur under specific conditions
- Internal OpenAI model spent roughly 12 hours generating a formal mathematical proof of the formula’s validity
- Verified by researchers from Harvard, Cambridge, Institute for Advanced Study, and Vanderbilt universities
- Published February 13, 2026, in arXiv preprint titled “Single-minus gluon tree amplitudes are nonzero”
OpenAI’s GPT-5.2 has achieved what many consider a milestone in AI-assisted scientific discovery: deriving an original result in theoretical physics that challenges decades of accepted assumptions about gluon behavior. The breakthrough centers on gluons particles that carry the strong nuclear force binding atomic nuclei together and demonstrates AI’s capacity to identify patterns human physicists overlooked.
The work represents more than computational power. It showcases a new methodology where AI proposes hypotheses, proves them mathematically, and submits findings to peer review alongside human domain experts.
What GPT-5.2 Discovered About Gluon Amplitudes
Particle physicists use scattering amplitudes to calculate the probability of specific particle interactions. For gluons, most amplitudes simplify elegantly at “tree level” calculations excluding complex quantum loops.
One scenario, however, was largely set aside: when one gluon exhibits negative helicity (a spin orientation) while remaining gluons show positive helicity, textbook physics suggested the amplitude must vanish. This assumption held for decades, leading researchers to dismiss the configuration.
GPT-5.2 identified a loophole. The standard argument assumes generic particle momenta directions and energies without special alignment. In a precisely defined momentum space slice called the “half-collinear regime,” that reasoning collapses. Within this regime, the amplitude does not vanish, contradicting established assumptions.
The AI didn’t merely flag an anomaly. It conjectured Equation 39 a formula describing the amplitude’s behavior in this kinematic region.
The 12-Hour AI Proof That Changed Everything
Human physicists manually calculated amplitudes for integer values up to n=6, producing superexponentially complex expressions (Equations 29-32 in the preprint). GPT-5.2 Pro simplified these into elegant forms (Equations 35-38), then identified a pattern suggesting a universal formula for all n values.
A scaffolded version of GPT-5.2 then reasoned through the problem for roughly 12 hours, independently arriving at the same formula and constructing a formal mathematical proof. Researchers subsequently verified the equation using the Berends-Giele recursion relation, a step-by-step method for building multi-particle amplitudes and confirmed it satisfied the soft theorem governing particle behavior.
The formula passed five rigorous tests: Berends-Giele recursion, soft theorem compliance, cyclicity, Kleiss-Kuijf relations, and U(1) decoupling identities none obvious from inspection.
Expert Validation From Leading Physicists
Nima Arkani-Hamed, Professor of Physics at the Institute for Advanced Study, described the formulas as “strikingly simple” after 15 years of personal curiosity about these scattering processes. He noted that finding simple formulas has always been “fiddly” and appeared automatable now realized through modern AI tools.
Nathaniel Craig, Professor of Physics at UC Santa Barbara, stated his research group is already exploring implications of the preprint. He characterized it as “journal-level research advancing the frontiers of theoretical physics” and called it a glimpse into AI-assisted science’s future.
The preprint lists authors Alfredo Guevara (Institute for Advanced Study), Alex Lupsasca (Vanderbilt University and OpenAI), David Skinner (University of Cambridge), Andrew Strominger (Harvard University), and Kevin Weil (OpenAI).
What makes this discovery significant?
Standard textbook arguments suggested single-minus gluon tree amplitudes must vanish for generic particle momenta. GPT-5.2 identified the half-collinear regime where momentum alignment allows non-zero amplitudes, exposing a “loophole” in decades of power-counting arguments.
From Gluons to Gravitons: What’s Next
The methodology extends beyond gluons. GPT-5.2 has already helped researchers apply the framework to gravitons particles mediating gravitational force. Other generalizations, including supersymmetric extensions and transformations under the S-algebra and Lw₁₊∞ algebra, are in development.
This opens pathways for:
- Graviton amplitude calculations using identical half-collinear techniques
- Deeper understanding of quantum field theory’s hidden structures
- AI-assisted pattern recognition across theoretical physics domains
- Automated simplification of superexponentially complex equations
The preprint notes further details, including longer general formulas outside the primary regime, will appear in subsequent publications.
How AI Reasoning Redefined Scientific Collaboration
GPT-5.2’s contribution wasn’t computation alone, it was symbolic reasoning auditable by humans. The model navigated a highly structured space governed by quantum field theory constraints, proposing formulas that satisfied multiple verification criteria simultaneously.
This establishes a template: AI generates hypotheses, produces formal proofs, and submits to rigorous validation pipelines involving deterministic verification and human oversight. The workflow maintains scientific correctness while accelerating discovery in knowledge-intensive domains.
Researchers can now partner with AI to tackle problems where complexity obscures underlying simplicity precisely the scenario where simple formulas historically revealed deep new structures in physics.
Limitations and Considerations
The result applies specifically to the half-collinear regime, not generic kinematics. The amplitude vanishes outside this precisely defined momentum space slice, meaning the discovery doesn’t overturn textbook physics broadly, it refines understanding of edge cases.
Additionally, the work requires peer review before formal publication. OpenAI submitted the preprint to arXiv and welcomes community feedback as the standard peer-review process unfolds.
Frequently Asked Questions (FAQs)
What is a gluon amplitude in particle physics?
A gluon amplitude calculates the probability that gluons particles carrying the strong nuclear force interact in a specific way. Physicists use scattering amplitudes to predict outcomes in particle collisions and quantum field theory experiments.
Why were single-minus gluon amplitudes thought to vanish?
Standard textbook arguments assumed generic particle momenta, where gluon directions and energies have no special alignment. Power-counting analysis suggested insufficient momentum factors to contract with all polarization vectors, forcing the amplitude to vanish.
What is the half-collinear regime that GPT-5.2 identified?
The half-collinear regime is a precisely defined momentum space slice where gluon momenta obey special alignment conditions. In this regime, standard arguments break down, allowing non-zero amplitudes that would vanish under generic kinematics.
How long did GPT-5.2 take to prove the formula?
A scaffolded internal version of GPT-5.2 spent roughly 12 hours reasoning through the problem, independently deriving the formula and producing a formal mathematical proof. Human researchers then verified the proof using multiple analytical methods.
Who verified GPT-5.2’s physics discovery?
The preprint is authored by physicists from Harvard University, University of Cambridge, Institute for Advanced Study, and Vanderbilt University. Prominent theorists Nima Arkani-Hamed and Nathaniel Craig provided independent validation of the work’s significance.
Can this method apply to other physics problems?
Yes. Researchers have already extended the approach to graviton amplitudes (particles mediating gravity) and are developing supersymmetric generalizations. The methodology applies wherever complex expressions may hide simpler underlying patterns.
When will the research be officially published?
The preprint was published on arXiv on February 13, 2026, and is currently undergoing peer review for journal publication. OpenAI and co-authors are soliciting community feedback during the review process.
