Give an AI the Same Math Problem and the Proof Comes out Shaped Differently

At the end of a growing number of mathematics papers sits a sentence nobody can check. It says that an artificial intelligence helped with the ideas, or the proofs, or the checking. That sentence is the whole of the record. A reader who wants to know how much of the mathematics came from a machine has only the authors' word for it, as precise or as vague as they chose. Four researchers have now gone looking for the answer somewhere else, in the shape of the proof itself.

Yuanchuan Guo, Jiashun Jin, Zheng Tracy Ke and Bingcheng Sui describe their method in a preprint posted to the arXiv on Nov. 5, 2026. It has not been peer-reviewed and names no journal. What it offers is the comparison group that has always been missing. The team took 700 mathematics papers posted to the arXiv in January 2022, before AI help was common, and wrote a brief for each naming its mathematical setting and the conclusion it aimed at. Each brief went to GPT-6 Astra without the original text. Back came complete manuscripts on the same problems, each paired with the human paper it shadows.

Those pairs sit inside a larger collection of 8,281 papers in five groups. Alongside the January 2022 reference set are papers whose authors disclose substantive AI help with the mathematics; 722 manuscripts OpenAI released in September and October 2026 from an unreleased internal model; the rebuilt manuscripts; and 625 human papers whose prose an AI had rewritten while leaving the mathematics alone. Two of the five groups, 1,325 papers in all, were written at the team's own instruction. That is its weakest point and its strongest: the only place where the AI label is certain rather than claimed.

ProofTrace reads a paper as a graph. Each node is a result: a theorem the paper states, one it borrows from elsewhere, or a conclusion reached inside a proof and never named. An arrow from one node to another means the argument for the second directly uses the first. From that graph the framework computes 342 measurements of how a paper is put together. The graphs are not produced by a parser: a language model, GPT-5.6 Luna, extracts the nodes and arrows from each paper's converted text, and neither the graphs nor the prompts have been released. So the structure being measured is a model's reading of it.

The AI proofs almost never leaned on anyone else

Set against their human counterparts, the rebuilt manuscripts differed on 265 of them. The clearest gap was in credit. Results borrowed from outside the paper made up 0.2% of the nodes in the rebuilt graphs, against 6.1% in the human ones. The AI manuscripts leaned instead on conclusions worked out inside their own proofs, rather than lifted out and stated as lemmas for later use. The authors summarize the pattern as "a smaller proportion of externally cited results, greater reliance on intermediate conclusions developed within proofs rather than stated as lemmas, and altered graph connectivity." Much the same differences turned up in the OpenAI manuscripts, and more faintly in the papers that disclose AI help.

The authors report that many of them hold up under controls for research field, manuscript length and graph size. That is a claim about controls, not about cause: nothing here says AI involvement produced the shape. Adjusting for the size of the graphs costs the most, shrinking the typical effect by about a third, and a few features flip direction. Nor is the signature universal inside mathematics. It appears in combinatorics, number theory, probability and algebraic geometry. In machine learning and in optimization and control, in the authors' words, "none reaches significance."

Where the ground gets softer

The second half of the work rests on weaker ground. For a detection test, the team trained a classifier to tell the human reference papers from the ones disclosing substantive AI help. The human side is arXiv mathematics from January 2022; the other side was posted between September 2025 and August 2026. The two sets are roughly four years apart, so some of what a classifier separates may be era rather than AI. The authors concede the gap, in their section on trends rather than beside the detection result: "Historical Human papers were posted in a different period, so we cannot assess whether contemporaneous Human papers changed similarly." The label on that side is a disclosure statement, and disclosure can be incomplete, as the authors note. What the classifier picks up is a structural signature that goes with disclosed AI help in this collection. It is not a test for AI use.

What the rewriting test actually showed

Then came the test that makes the method interesting. An AI rewrote the prose of the human test papers, leaving the equations and reasoning in place, and every detector ran again. ProofTrace barely moved, from 0.8306 to 0.8365 on a scale where 0.5 is a coin toss and 1 is perfect. Several of the text-based detectors fell well below chance. Paraphrasing has been known to break such detectors since at least 2023.

Three things qualify the comparison, and the paper publishes all three. On untouched papers, five fine-tuned text detectors scored higher than ProofTrace, the best of them 0.9576 against 0.8306. What the table supports is robustness, not accuracy. The authors' stronger variant, which adds language features to the structural ones, is not robust at all: it falls from 0.8903 to 0.6246 under the same rewrite. And only the human half of the test set was rewritten, so a text detector that correctly spotted AI prose in those papers was marked wrong for it. The sub-chance scores are the design showing through, not detectors failing in the wild.

That the table says so at all is worth noting: the authors built every part of the comparison, including all ten rival detectors, which they tuned themselves. A self-evaluation that reports five rivals beating the home method is not the usual shape of one. No funding statement, no conflict-of-interest statement and no data or code availability statement appears anywhere in the paper.

The authors keep their reach modest. The framework, they write, "could be adapted to other fields that rely on mathematical reasoning." Could, not does. They float the idea of an alarm for journals in the same conditional. Their first stated limitation decides whether any of this holds up in use: "we do not take adversarial attacks into account." Nothing here tests what a model does when told to write a proof that looks human. And the disclosure labels the detection half rests on come from the survey of arXiv submissions the same group posted in August, itself unrefereed.