arXiv subjects

Bingcheng Sui

Publications and source records attributed to Bingcheng Sui.

3 recordsLinked to original sources

arXiv2026

The Gold Rush in AI4Math: Where Are We Now?

Recent advances in artificial intelligence (AI) have sparked growing interest in its use for mathematical research. While some view this as a major opportunity for discovery, others have raised concerns about its impact on traditional research practices. Despite extensive debate, empirical evidence on how AI is actually being used in mathematics remains limited. To address this gap, we collected all 32,944 arXiv submissions posted between March 1 and August 20, 2026, whose primary or secondary categories included Mathematics. We identified 3,575 submissions that explicitly disclosed author use of AI, of which 1,712 involved at least one substantive mathematical contribution. Our analysis reveals several broad patterns. First, disclosed AI use increased sharply over the study period, with substantive use growing from 1.39% of Mathematics submissions in March to 14.09% through August 20. Second, substantive AI use is highly uneven across fields: Combinatorics has the largest number of such papers, while Metric Geometry has the highest substantive-use rate. Third, substantive AI use is geographically concentrated: under weighted author counts, the United States and China together account for about two-thirds of the recognized country weight. Fourth, AI is already being applied to open research problems: among 717 named open-problem records associated with substantive use, 71% are labeled as fully resolved based on the authors' descriptions, with proofs of the conjectured statement more common than counterexamples or disproofs. Finally, AI-system use is also highly concentrated, with OpenAI systems appearing most frequently, followed by Anthropic. Together, these findings suggest that AI-assisted mathematics is expanding rapidly but remains at an early and uneven stage of adoption.

stat.AP↗

arXiv2026

A New Impossibility Region for the $5\times5$ Symmetric Nonnegative Inverse Eigenvalue Problem

We present a new impossibility region for the $5\times5$ symmetric nonnegative inverse eigenvalue problem. The region lies in the low-trace regime and, to the best of our knowledge, has not been identified previously. The proof uses a suitable diagonal shift to transform the problem to a critical high-trace boundary and then reduces a complementary commuting matrix to a weighted five-cycle. The characteristic polynomial and spectral identities of this five-cycle provide the main tools for deriving the resulting contradiction.

math.RA↗

arXiv2025

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications

Cycle count statistics are fundamental tools in statistics and engineering, with applications in motif counting, channel coding, and statistical inference of network and matrix data. However, how to compute high-order cycle count statistics efficiently is still an open problem. In this paper, we aim to derive Computationally Efficient Equivalent Forms (CEEF) for cycle count statistics of any given order, where we express each cycle count statistic equivalently as a linear combination of finitely many terms. Using the CEEF, we provide a much more efficient way to compute the cycle count statistics. The CEEF problem has no known general solution and requires delicate combinatorial arguments together with extensive calculations. While this task is hard to accomplish by humans alone, it provides an ideal setting in which Artificial Intelligence (AI) can be useful. We solve the problem by combining several theorems we derive with powerful coding skills of modern AI systems. Our results leverage graph-theoretic arguments and yield new formulas for general cases that were previously unknown. We find that, although AI cannot solve the problem independently, it becomes highly effective when guided by humans through theorems we derive as well as a clear derivation strategy, step-by-step instructions, and carefully-written prompts. We consider several statistical applications, including spiked matrix testing, estimation of weak spike eigenvalues, and pairwise network comparison. For each problem, we demonstrate that optimal statistical performance is achieved by using high-order cycle count statistics, and our CEEF formulas make their computation feasible on large-scale data sets.

cs.CL↗