Papers for

mathematical software developers

Papers whose findings have a practical use for this group, as judged from the abstract. Open a paper to read what it means in practice.

Oriented matroids counterexamples break longstanding combinatorics conjectures

Neither simpliciality nor mutation connectivity: conjectures of Las Vergnas and Cordovil-Las Vergnas fail

Abstract: We construct a simple rank-$7$ oriented matroid on $24$ elements with no simplicial tope, disproving the Las Vergnas simplex conjecture from 1980. We then show that the mutation graph on uniform oriented matroids is disconnected for infinitely many values of rank $r$ and ground-set size $n$, disproving the Cordovil--Las Vergnas conjecture from 1988.

Mon 14 SeptDiscrete Mathematics
The gist
Some old ideas in math thought every special shape called an oriented matroid had a simple kind of face, but this paper shows a counterexample where none exist. It also shows that certain transformations between these shapes can't always connect all shapes, disproving another guess from decades ago. The authors built specific examples proving these old beliefs wrong.
Open → 2609.15850v1

Mathematics fields invited to help make AI safer and more controllable

Math for AI safety: an invitation for mathematicians

Abstract: Artificial intelligence threatens to outrun human understanding and control. New mathematics is needed to design AI that is legible, steerable, and cooperative with humanity. I organize this invitation by mathematical field, so you can turn straight to your own: logic and game theory for cooperation; probability for agency and world-models; algebra and representation theory for learned features; analysis and geometry for generalization and training dynamics. Each section ends with an open problem that is accessible to a working mathematician with no prior experience in AI safety.

Mon 14 SeptArtificial Intelligence
The gist
AI systems might become too complex for people to understand or control easily. The authors explain how different areas of mathematics—like logic, probability, algebra, and geometry—can help create AI that humans can better understand, guide, and cooperate with. They organize the discussion by math topic and suggest open problems in each area to encourage mathematicians to get involved. This approach aims to build AI systems that are safer and more aligned with human values.
Open → 2609.15289v1