arXiv:2602.05216v2 Announce Type: replace-cross Abstract: Searching for mathematical results remains difficult: most existing tools retrieve entire papers, while mathematicians and theorem-proving agents often seek a specific theorem, lemma, or proposition that answers a query. While semantic search has seen rapid progress, its behavior on large, highly technical corpora such as research-level mathematical theorems remains poorly understood. In this work, we introduce and study semantic theorem retrieval at scale over a unified corpus of $9.2$ million theorem statements extracted from arXiv and seven other sources, representing the largest publicly available corpus of human-authored, research-level theorems. We represent each theorem with a short natural-language description as a retrieval representation and systematically analyze how representation context, language model choice, embedding model, and prompting strategy affect retrieval quality. On a curated evaluation set of theorem-search queries written by professional mathematicians, our approach substantially improves both theorem-level and paper-level retrieval compared to existing baselines, demonstrating that semantic theorem search is feasible and effective at web scale. The project page, search tool, dataset, REST API, and MCP server are available at theoremsearch.com.

arXiv:2603.03684v2 Announce Type: replace-cross Abstract: Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical practice, and to respond appropriately to the challenges and opportunities we now face.

arXiv:2603.03684v1 Announce Type: cross Abstract: Recent developments show that AI can prove research-level theorems in mathematics, both formally and informally. This essay urges mathematicians to stay up-to-date with the technology, to consider the ways it will disrupt mathematical practice, and to respond appropriately to the challenges and opportunities we now face.

arXiv:2505.20181v2 Announce Type: replace-cross Abstract: The increasing deployment of Artificial Intelligence (AI) and other autonomous algorithmic systems presents the world with new systemic risks. While focus often lies on the function of individual algorithms, a critical and underestimated danger arises from their interactions, particularly when algorithmic systems operate without awareness of each other, or when those deploying them are unaware of the full algorithmic ecosystem deployment is occurring in. These interactions can lead to unforeseen, rapidly escalating negative outcomes - from market crashes and energy supply disruptions to potential physical accidents and erosion of public trust - often exceeding the human capacity for effective monitoring and the legal capacities for proper intervention. Current governance frameworks are inadequate as they lack visibility into this complex ecosystem of interactions. This paper outlines the nature of this challenge and proposes some initial policy suggestions centered on increasing transparency and accountability through phased system registration, a licensing framework for deployment, and enhanced monitoring capabilities.