Tootfinder

Reinforced Generation of Combinatorial Structures: Applications to Complexity Theory
Ansh Nagda, Prabhakar Raghavan, Abhradeep Thakurta
https://arxiv.org/abs/2509.18057 https://…

Reinforced Generation of Combinatorial Structures: Applications to Complexity Theory
We explore whether techniques from AI can help discover new combinatorial structures that improve provable limits on efficient algorithms. Specifically, we use AlphaEvolve (an LLM coding agent) to study two settings: a) Average-case hardness for MAX-CUT and MAX-Independent Set: We improve a recent result of Kunisky and Yu to obtain near-optimal upper and (conditional) lower bounds on certification algorithms for MAX-CUT and MAX-Independent Set on random 3- and 4-regular graphs. Our improved l…

Scientific Algorithm Discovery by Augmenting AlphaEvolve with Deep Research
Gang Liu, Yihan Zhu, Jie Chen, Meng Jiang
https://arxiv.org/abs/2510.06056 https://

Scientific Algorithm Discovery by Augmenting AlphaEvolve with Deep Research
Large language models hold promise as scientific assistants, yet existing agents either rely solely on algorithm evolution or on deep research in isolation, both of which face critical limitations. Pure algorithm evolution, as in AlphaEvolve, depends only on the internal knowledge of LLMs and quickly plateaus in complex domains, while pure deep research proposes ideas without validation, resulting in unrealistic or unimplementable solutions. We present DeepEvolve, an agent that integrates deep …

The Mathematician's Assistant: Integrating AI into Research Practice
Jonas Henkel
https://arxiv.org/abs/2508.20236 https://arxiv.org/pdf/2508.20236

The Mathematician's Assistant: Integrating AI into Research Practice
The rapid development of artificial intelligence (AI), marked by breakthroughs like 'AlphaEvolve' and 'Gemini Deep Think', is beginning to offer powerful new tools that have the potential to significantly alter the research practice in many areas of mathematics. This paper explores the current landscape of publicly accessible large language models (LLMs) in a mathematical research context, based on developments up to August 2, 2025. Our analysis of recent benchmarks, such as MathArena and the O…