mathematical-discovery

This paper presents a deterministic algorithm for online inverse linear optimization with O(d) regret and O(d^2) time per round, marking the first efficient and proper bound of this kind, with the main result obtained using the Cogentic agentic framework and Gemini 3.1 Pro.

EULER is a multi-agent system that explores cross-domain transfers to automatically prove or refute mathematical conjectures, validated with stress tests and evaluated on 120 recent conjectures, producing proofs, refutations, and partial results.

The Station is an open-world multi-agent environment where AI agents autonomously build a scientific literature, leading to novel discoveries on five mathematical problems out of twelve evaluated.

This paper presents a multi-agent AI system that autonomously discovers novel mathematical results through collaborative experimentation and proof generation in an open-world environment, achieving new constructions and theorems.

The paper introduces FAR, a human-AI discovery paradigm that automates the search for mathematical problems from literature, with a pilot in combinatorics demonstrating its effectiveness in identifying conjectures and resolutions.

The Verge reports on OpenAI's Astra model solving ten long-standing mathematics problems, sparking excitement and apprehension among mathematicians about the future of the field.

OpenAI's AI models have solved multiple famous Erdős problems, including the unit distance conjecture, prompting mathematicians to reconsider how AI is transforming mathematical research.

A mathematician describes a spiritual crisis triggered by recent LLM-generated counterexamples to long-standing conjectures, arguing that the human experience of mathematical discovery is vital and threatened.

An AI model named Fable discovered a counterexample to the Jacobian conjecture, a long-standing open problem in mathematics, by finding a polynomial function that meets the special conditions but is not invertible.

Claude, an AI model, reportedly found a counterexample to the long-standing Jacobian Conjecture, verified by multiple LLMs, sparking debate about AI's role in mathematical discovery.

The author shares observations from auto-research experiments in algebra, noting that AI models can generate code and discover novel abstract rules, leading to potentially alien mathematics that humans struggle to understand.

ThetaEvolve is an open-source framework that extends AlphaEvolve to enable small LLMs like DeepSeek-R1-0528-Qwen3-8B to achieve new best-known bounds on open problems through test-time reinforcement learning, accelerating AI self-evolution.

This paper introduces an autoresearch paradigm using LLM agents (coding and theory agents) to discover convex relaxations for sharp-constant inequalities, improving certified lower bounds on two optimization constants.

The article explores how AI is transforming mathematics, raising questions about the role of human mathematicians. It features perspectives from experts like Terence Tao and discusses the potential for AI to automate parts of mathematical discovery.

This paper presents a case study of human-AI co-discovery in mathematics, where AI assisted in expanding an intuition about sign-embedding quantum algorithms into a formal framework and proofs, with human judgment guiding route selection.

This paper examines whether language models can independently discover the concept of zero as a form of out-of-distribution generalization, finding that GPT-2 sized models cannot at test time but improve with training on examples of zero, and that language pretraining reduces the number of required examples.