ChatGPT and Claude chose a theoretical physics question and drafted a paper within hours; physicists spent two weeks checking their work, and the models could not prove their conjecture

ChatGPT and Claude chose a theoretical physics question and drafted a paper within hours; physicists spent two weeks checking their work, and the models could not prove their conjecture

On October 23, Christopher Herzog and Andreas Stergiou of King’s College London posted a paper on three-dimensional conformal field theories to arXiv, a server for papers awaiting peer review. These theories describe systems with no preferred length scale, such as a magnet at the point where it loses its magnetization. In the Methods appendix, the authors explained that GPT-5.6 Sol and Claude Opus 5.5 had been asked to write a paper for Physical Review Letters.

Herzog set three conditions: the question should concern theoretical high-energy physics, “so that I have some hope of assessing the reasoning and results”; the answer should take no more than five pages; and the findings should be significant enough to publish. He left the rest to the models: “I would like you to choose the question, carry out the analysis, and write up the results.” Each model proposed three questions. They ranked all six and agreed on the ranking.

The first and third questions were dropped after preliminary analysis. The second, proposed by Claude, became the basis of the paper. Every conformal field theory has several distinct numerical quantities, each of which can be interpreted as a measure of its number of degrees of freedom, or independent ways the system can vary. The question is whether these quantities constrain one another. The quantity cS determines the thermal entropy per unit area: cS·T² at temperature T. The quantity CT measures how strongly fluctuations in energy and momentum at two points are correlated. Claude conjectured that the ratio of cS to CT never exceeds 16πζ(3) ≈ 60,42, the value for a free scalar field, whose particles do not interact.

These quantities and a third, the free energy on a sphere, can be read from a single curve showing how the theory’s entropy, in units of CT, increases as it is heated in curved space. The free energy determines the starting point of the curve, while cS determines its growth at high temperatures. A 2023 conjecture places the scalar at the lowest starting point; Claude’s conjecture gives it the fastest growth. ChatGPT noticed this connection, and Claude proposed a stronger conjecture: at every temperature above the starting temperature, the heat capacity of any theory, in units of CT, is at most that of the scalar.

In four cases, the heat capacity could be calculated at every temperature above the starting temperature, and it remained at or below the scalar value. One case was a family of models with infinitely many fields, starting from the free scalar: as the interaction becomes stronger, the ratio of cS to CT falls from 60,42 to 52,87. For the Ising model, a simplified description of the same magnet, numerical data put the ratio at about 51,1.

The models performed all the calculations and produced a draft within hours. According to the authors, “the resulting text often lacked sufficient detail, and key references were frequently missing.” Other models, GPT-6 Astra and Claude Fable 5.1, then checked the examples, added several more, and tried unsuccessfully to prove the conjecture.

Over two weeks, Herzog and Stergiou checked every calculation by hand or in Mathematica. They suggested citing Herzog and Tatsuma Nishioka’s 2016 paper on the scalar boundary term, an additional contribution to the description of a region’s entanglement (its quantum connection with the rest of space). Because of this term, the scalar’s heat capacity near the start of the curve rises faster than the usual bound allows for theories without such a term. The authors see this as part of the explanation for the scalar’s special role. The Methods appendix ends with these words:

“Despite substantial use of AI in every aspect of preparing the manuscript, we consider the result reliable and interesting enough to publish.”