# Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdHos Problems

arXiv: https://arxiv.org/abs/2601.22401 · HTML: https://mlsanity.com/paper/2601.22401/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 46 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Built on by (most cited first, 30 of 32)

- [Towards Autonomous Mathematics Research](https://mlsanity.com/paper/2602.10177/) (2026)
- [Automated Conjecture Resolution with Formal Verification](https://mlsanity.com/paper/2604.03789/) (2026)
- [LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks](https://mlsanity.com/paper/2606.03303/) (2026)
- [LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization](https://mlsanity.com/paper/2606.05400/) (2026)
- [LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematics](https://mlsanity.com/paper/2602.24173/) (2026)
- [Aletheia tackles FirstProof autonomously](https://mlsanity.com/paper/2602.21201/) (2026)
- [Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification](https://mlsanity.com/paper/2603.15617/) (2026)
- [Semi-Autonomous Formalization of the Vlasov-Maxwell-Landau Equilibrium](https://mlsanity.com/paper/2603.15929/) (2026)
- [Closing the Loop to Discover Psychological Theories with an Automated Cognitive Scientist](https://mlsanity.com/paper/2606.26448/) (2026)
- [GRAFT-ATHENA: Self-Improving Agentic Teams for Autonomous Discovery and Evolutionary Numerical Algorithms](https://mlsanity.com/paper/2605.11117/) (2026)
- [Evolution Fine-Tuning: Learning to Discover Across 371 Optimization Tasks](https://mlsanity.com/paper/2606.29082/) (2026)
- [EsoLang-Bench: Evaluating Genuine Reasoning in Large Language Models via Esoteric Programming Languages](https://mlsanity.com/paper/2603.09678/) (2026)
- [Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs](https://mlsanity.com/paper/2605.09063/) (2026)
- [AI Finds A Way](https://mlsanity.com/paper/2608.23875/) (2026)
- [How Open Must Language Models be to Enable Reliable Scientific Inference?](https://mlsanity.com/paper/2603.26539/) (2026)
- [Accelerating Scientific Research with Gemini in the Real-World](https://mlsanity.com/paper/2608.26701/) (2026)
- [Discovering mathematical concepts through a multi-agent system](https://mlsanity.com/paper/2603.04528/) (2026)
- [An Enigma of Artificial Reason: Investigating the Production-Evaluation Gap in Large Reasoning Models](https://mlsanity.com/paper/2606.01462/) (2026)
- [From Solvers to Research: Large Language Model-Driven Formal Mathematics at the Research Frontier](https://mlsanity.com/paper/2607.07779/) (2026)
- [Artificial Organisations](https://mlsanity.com/paper/2602.13275/) (2026)
- [k-server-bench: Automating Potential Discovery for the k-Server Conjecture](https://mlsanity.com/paper/2604.07240/) (2026)
- [Lectures on AI for Mathematics](https://mlsanity.com/paper/2604.11504/) (2026)
- [Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery](https://mlsanity.com/paper/2604.21187/) (2026)
- [Grokability in five inequalities](https://mlsanity.com/paper/2605.05193/) (2026)
- [SCALAR: A Neurosymbolic Framework for Automated Conjecture and Reasoning in Quantum Circuit Analysis](https://mlsanity.com/paper/2605.10327/) (2026)
- [Using large language models to probe the limits of atom-centered structural descriptors](https://mlsanity.com/paper/2607.26984/) (2026)
- [How Good Are Frontier Models at Physics? Expert Re-Grading Reveals Broken Evaluations and Near-Saturation of Leading Benchmarks](https://mlsanity.com/paper/2609.13009/) (2026)
- [FrugalEvo: Towards Cost-Aware LLM-Guided Program Evolution](https://mlsanity.com/paper/2610.03675/) (2026)
- [Bolzano: From Expert-Guided Proof Search to Automated Open-Problem Solving](https://mlsanity.com/paper/2610.09769/) (2026)
- [SqueezeBench: Saturation-Resilient Evaluation of Mathematical Capability](https://mlsanity.com/paper/2610.13461/) (2026)

## Abstract (arXiv)

We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's ErdHos Problems database. We employ a hybrid methodology: AI-driven natural language verification to narrow the search space, followed by human expert evaluation to gauge correctness and novelty. We address 13 problems that were marked 'Open' in the database: 5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature. Our findings suggest that the 'Open' status of the problems was through obscurity rather than difficulty. We also identify and discuss issues arising in applying AI to math conjectures at scale, highlighting the difficulty of literature identification and the risk of ''subconscious plagiarism'' by AI. We reflect on the takeaways from AI-assisted efforts on the ErdHos Problems.