Reasoning Models

Definition

A family of LLMs that explicitly model the reasoning process itself. They allocate test-time compute to reasoning steps (chain-of-thought, search, verification) to improve the ability to solve complex problems.

Why It Matters

• Matches personal interests: reasoning (1.3x) × frontier models (1.3x)
• The most active research thread of 2024-2026 — tracked across the industry since the OpenAI o-series
• A direction that addresses the limits of simple scale-up

State of the Art (2026-05)

• Strongest empirical result (2026-05-20): OpenAI — Disproof of the Erdős unit distance conjecture — autonomous solution of an 80-year-old open pure-math problem. A general-purpose reasoning model found a proof unknown even to expert mathematicians using only chain-of-thought reasoning. The first clear evidence that general-purpose reasoning can make substantive contributions in specialized scientific fields.
• Latest strong claim: Olympiad-level reasoning via simple unified scaling (2026-05-16) — claims gold-medal-level performance on math olympiads
• Gemini 3.1 Deep Think — autonomous math research agent (Aletheia, IMO gold medal, 18 open problems solved, Feng26 paper published)
• Claude Opus 4.7 also emphasizes "multi-step tasks"

Open Problems

• Consistency of the definition of "reasoning" — pattern matching vs genuine reasoning?
• Test-time compute scaling laws — how far is it efficient?
• Domain generalization (math → coding → science → real world)
• Cost — spending more compute on reasoning also increases cost

Key Papers

• An OpenAI model has disproved a central conjecture in discrete geometry — 2026-05-20, autonomous disproof of an 80-year-old open math problem (OpenAI general reasoning model)
• Achieving Gold-Medal-Level Olympiad Reasoning via Simple and Unified Scaling — 2026-05, claims gold-medal performance from scaling alone

Related Concepts

• Test-Time Compute (Inference-Time Compute Scaling) — inference-time compute allocation is the core mechanism of reasoning models
• Agentic Reinforcement Learning — the intersection of multi-step reasoning + RL

Open Debates

• "Simple unified scaling" vs "specialized methods" — which drives progress in reasoning? (2605.13301 argues for the former)