aiqbench analysis
This paper uses a specialized geometric setting to test whether an AI agent can rediscover mathematical invariants without explicit theorem guidance, ultimately finding that deterministic polynomial fitting achieves comparable results. The study serves as a rigorous protocol for distinguishing genuine conjecture from numerical noise while highlighting current limitations in agent metadata and reproducibility. It offers a controlled benchmark for evaluating the necessity of advanced reasoning capabilities versus standard algebraic methods in mathematical discovery tasks.
Can an AI Agent Rediscover a Blaschke-Curve Invariant?
arXiv:2609.38369v1 Announce Type: new Abstract: We study generalized Blaschke curves as a controlled environment for AI-assisted mathematical rediscovery. For one fixed degree-four Blaschke product, an agent receives numerical coordinates of the six pair-lines determined by each of 80 boundary configurations. The target theorem is withheld from the task instructions. The saved research log reports rejected geometric hypotheses and a homogeneous cubic fitted to polygon sides. Its frozen coefficients predict 480 lines from 80 unseen parameter values, with a recorded RMS scale-free residual of $8.88\times10^{-17}$. Discovery-set diagonals provide an out-of-fit consistency check, not a fully held-out test. A separate one-configuration run reports insufficient evidence for invariance. A post-review deterministic degree-search baseline also recovers the cubic, so the experiment does not establish an advantage over polynomial fitting. We present this single-instance case study as a protocol for separating conjecture, numerical validation, and proof, with explicit limitations concerning agent metadata, prior knowledge, and reproducibility.
Abstract:We study generalized Blaschke curves as a controlled environment for AI-assisted mathematical rediscovery. For one fixed degree-four Blaschke product, an agent receives numerical coordinates of the six pair-lines determined by each of 80 boundary configurations. The target theorem is withheld from the task instructions. The saved research log reports rejected geometric hypotheses and a homogeneous cubic fitted to polygon sides. Its frozen coefficients predict 480 lines from 80 unseen parameter values, with a recorded RMS scale-free residual of $8.88\times10^{-17}$. Discovery-set diagonals provide an out-of-fit consistency check, not a fully held-out test. A separate one-configuration run reports insufficient evidence for invariance. A post-review deterministic degree-search baseline also recovers the cubic, so the experiment does not establish an advantage over polynomial fitting. We present this single-instance case study as a protocol for separating conjecture, numerical validation, and proof, with explicit limitations concerning agent metadata, prior knowledge, and reproducibility.
Accepted for poster presentation at the NeurIPS 2026 Workshop on Mathematical Reasoning and AI (MATH-AI). 8 pages, 1 figure. Code and data: this https URL
Artificial Intelligence (cs.AI)
arXiv:2609.38369 [cs.AI]
(or arXiv:2609.38369v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.38369 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 189 words
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