# G"odel Test: Can Large Language Models Solve Easy Conjectures?

arXiv: https://arxiv.org/abs/2509.18383 · HTML: https://mlsanity.com/paper/2509.18383/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 11 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 7 of 7)

- [Guaranteed Non-convex Optimization: Submodular Maximization over Continuous Domains](https://mlsanity.com/paper/1606.05615/) (2016)
- [Constrained Submodular Maximization via New Bounds for DR-Submodular Functions](https://mlsanity.com/paper/2311.01129/) (2023)
- [Weakly Submodular Maximization Beyond Cardinality Constraints: Does Randomization Help Greedy?](https://mlsanity.com/paper/1707.04347/) (2017)
- [Submodular + Concave](https://mlsanity.com/paper/2106.04769/) (2021)
- [Using Partial Monotonicity in Submodular Maximization](https://mlsanity.com/paper/2202.03051/) (2022)
- [Weakly Submodular Function Maximization Using Local Submodularity Ratio](https://mlsanity.com/paper/2004.14650/) (2020)
- [Bicriteria Submodular Maximization](https://mlsanity.com/paper/2507.10248/) (2025)

## Built on by (most cited first, 5 of 5)

- [Towards Autonomous Mathematics Research](https://mlsanity.com/paper/2602.10177/) (2026)
- [Solving a Research Problem in Mathematical Statistics with AI Assistance](https://mlsanity.com/paper/2511.18828/) (2025)
- [MathNet: a Global Multimodal Benchmark for Mathematical Reasoning and Retrieval](https://mlsanity.com/paper/2604.18584/) (2026)
- [Automated alignment is harder than you think](https://mlsanity.com/paper/2605.06390/) (2026)
- [The Benjamini--Hochberg Procedure Can Fail to Control the FDR for Correlated Two-Sided Gaussian Tests](https://mlsanity.com/paper/2607.12208/) (2026)

## Abstract (arXiv)

Recent announcements from frontier AI model labs have highlighted strong results on high-school and undergraduate math competitions. Yet it remains unclear whether large language models can solve new, simple conjectures in more advanced areas of mathematics. We propose the G"odel Test: evaluating whether a model can produce correct proofs for very simple, previously unsolved conjectures. To this end, we study the performance of GPT-5 on five conjectures in combinatorial optimization. For each problem, we provided one or two source papers from which the conjecture arose, withheld our own conjecture, and then assessed the model's reasoning in detail. On the three easier problems, GPT-5 produced nearly correct solutions; for Problem 2 it even derived a different approximation guarantee that, upon checking, refuted our conjecture while providing a valid solution. The model failed on Problem 4, which required combining results from two papers. On Problem 5, a harder case without a validated conjecture, GPT-5 proposed the same algorithm we had in mind but failed in the analysis, suggesting the proof is more challenging than expected. Although our sample is small, the results point to meaningful progress on routine reasoning, occasional flashes of originality, and clear limitations when cross-paper synthesis is required. GPT-5 may represent an early step toward frontier models eventually passing the G"odel Test.