arXiv:2504. 19451v4 Announce Type: replace-cross Abstract: This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory.
Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.
arXiv:2604. 02995v3 Announce Type: replace-cross Abstract: We introduce the penalised Saito functional $\mathfrak S_{\lambda,\beta}(\mathcal{A};d_1,d_2)$ for a reduced arrangement $\mathcal{A}$ of $n$ lines and a prescribed pair $d_1+d_2=n-1$.
The paper introduces a method for evaluating the intrinsic interestingness of mathematical theorems by comparing the length of their proofs to the length of their statements. It trains a 27B language model to predict proof difficulty, enabling the generation and selection of more interesting theorems while significantly reducing overlap with existing Mathlib. The approach allows iterative expansion of a self‑building, machine‑verified mathematical library guided by quantifiable metrics.
arXiv:2606. 03419v1 Announce Type: cross Abstract: The 2026 disproof of Erd\H{o}s's unit-distance conjecture and Sawin's subsequent explicit quantitative refinement show that the maximum number $u(n)$ of unit distances among $n$ planar points can exceed $n^{1+\varepsilon}$ for a fixed positive $\varepsilon$.
arXiv:2605. 05870v3 Announce Type: replace Abstract: We study the efficient computation of Shapley values for \emph{product games} -- cooperative games in which the coalition value factorizes as a product of per-player terms.
arXiv:2609. 29881v1 Announce Type: cross Abstract: Choosing Shellsort gaps is a well-known open problem.
arXiv:2608. 11195v1 Announce Type: new Abstract: AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively.