A new preprint co-authored by researchers from the Institute for Advanced Study, Vanderbilt University, OpenAI, the University of Cambridge, and Harvard University presents a significant breakthrough in theoretical physics, demonstrating that a class of gluon scattering amplitudes previously thought to vanish actually do not under specific conditions. The paper, titled “Single-minus gluon tree amplitudes are nonzero,” is available on arXiv and is being prepared for formal publication. The study focuses on scattering amplitudes—quantities that determine the probability of particle interactions in quantum field theory. For gluons, the force carriers of the strong nuclear interaction, many tree-level amplitudes (those calculated without quantum loops) exhibit surprising simplicity. However, a long-standing assumption held that when one gluon has negative helicity and all others have positive helicity, the corresponding amplitude must be zero. This configuration was largely ignored due to this expectation. The new work challenges that assumption. The authors identify a special kinematic regime—the half-collinear limit—where the momenta of the gluons are aligned in a precise, non-generic way. In this regime, the amplitude does not vanish. The team computes the amplitude explicitly and derives a compact, elegant formula valid for any number of gluons, a result that was conjectured by GPT-5.2 Pro. The human researchers first calculated the amplitudes for small values of n (up to n=6) by hand, producing highly complex expressions. GPT-5.2 Pro then analyzed these results, drastically simplifying them and revealing a pattern that led to the general formula. An internal, scaffolded version of GPT-5.2 subsequently spent about 12 hours reasoning through the problem, independently deriving the same formula and producing a formal proof of its correctness. The result was verified through multiple standard checks, including consistency with the Berends-Giele recursion relation and the soft theorem, which governs how amplitudes behave when a particle’s energy becomes very small. The discovery has already enabled extensions to gravitons—the hypothetical carriers of gravity—suggesting broader implications for quantum gravity and fundamental physics. Nima Arkani-Hamed, a leading theoretical physicist at the Institute for Advanced Study, praised the work, noting that the pursuit of simple formulas often leads to deeper physical insights. He highlighted the potential of modern AI tools to automate the discovery of such simplicity, calling the paper a compelling example of how artificial intelligence is beginning to play a transformative role in theoretical physics. He anticipates the emergence of general-purpose tools capable of identifying and generating simple, meaningful formulas across physics and mathematics.