Rediscovering constants of mathematical curves, an experiment testing AI agents against traditional algorithms

In a research paper accepted for presentation at the Mathematical Inference and Artificial Intelligence workshop at NeurIPS 2026, researcher Younes Zaitunko tested a core hypothesis that occupies development labs today: can an AI agent rediscover a mathematical theorem on its own within a controlled environment? The experiment relied on generalized Plücker curves as a closed test environment, using a fourth-degree Plücker product. The agent was given the numerical coordinates of six pairs of lines defined by eighty sets of boundary conditions, with the full text of the target theorem omitted from the task instructions, to test its ability to arrive at the theorem from raw data.

The agent's saved research log showed a trajectory that relied on discarding successive geometric hypotheses before settling on a homogeneous cubic equation.This equation was crafted to match polygon edges, and when its mathematical coefficients were frozen and tested on eighty new values of previously unseen parameters, it succeeded in predicting the locations of 480 lines with a standardized error margin of 8.88 × 10⁻¹⁷. Although the diameters of the discovery set provided a consistency check beyond the matching scope, the researcher noted that this does not constitute a fully independent test on completely isolated data.

The most significant result in the paper was the revelation of the agent's strict empirical limits, as a separate test run on a single configuration showed that the mathematical evidence was insufficient to establish stability.More importantly, a subsequent reference comparison using a simple deterministic algorithm that explores boundary degrees was able to recover the same cubic equation.Consequently, the experiment did not demonstrate any qualitative advantage of the AI agent over traditional polynomial-matching methods, prompting the author to present this case as a scientific protocol that clearly separates conjecture, numerical verification, and final formal proof, highlighting declared constraints concerning the agent's metadata, prior knowledge, and result reproducibility.

These findings carry a fundamental critical dimension for researchers, engineering teams, and funding officials at universities and research centers in the Gulf, Egypt, and the Levant.Spending on operating complex AI agents requires substantial computing resources and high costs, whereas the experiment shows that traditional mathematical and deterministic matching tools achieve the same result with decisive accuracy.When planning to establish an AI research laboratory or direct institutional investments toward scientific discovery, a prudent decision requires obliging research teams to set deterministic comparison baselines before assuming agent superiority, and to precisely distinguish between numerical curve matching and the production of genuine mathematical proofs, in order to avoid wasting local computing resources on tasks that classical algorithms can accomplish at minimal cost.