Vibe Reasoning: Eliciting Frontier AI Mathematical Capabilities -- A Case Study on IMO 2025 Problem 6

TL;DR

This paper presents Vibe Reasoning, a collaborative AI paradigm that enhances frontier AI models' mathematical problem-solving abilities through meta-prompts, agentic workflows, and model orchestration, demonstrated on IMO 2025 Problem 6.

Contribution

It introduces Vibe Reasoning, a novel approach combining human guidance and AI orchestration to unlock advanced mathematical reasoning in frontier models.

Findings

AI models possess latent problem-solving knowledge.

Agentic workflows improve autonomous reasoning.

Lightweight human guidance enhances AI capabilities.

Abstract

We introduce Vibe Reasoning, a human-AI collaborative paradigm for solving complex mathematical problems. Our key insight is that frontier AI models already possess the knowledge required to solve challenging problems -- they simply do not know how, what, or when to apply it. Vibe Reasoning transforms AI's latent potential into manifested capability through generic meta-prompts, agentic grounding, and model orchestration. We demonstrate this paradigm through IMO 2025 Problem 6, a combinatorial optimization problem where autonomous AI systems publicly reported failures. Our solution combined GPT-5's exploratory capabilities with Gemini 3 Pro's proof strengths, leveraging agentic workflows with Python code execution and file-based memory, to derive both the correct answer (2112) and a rigorous mathematical proof. Through iterative refinement across multiple attempts, we discovered the necessity of agentic grounding and model orchestration, while human prompts evolved from problem-specific hints to generic, transferable meta-prompts. We analyze why capable AI fails autonomously, how each component addresses specific failure modes, and extract principles for effective vibe reasoning. Our findings suggest that lightweight human guidance can unlock frontier models' mathematical reasoning potential. This is ongoing work; we are developing automated frameworks and conducting broader evaluations to further validate Vibe Reasoning's generality and effectiveness.