Archive · 3 Aug 2026
Machines Doing Math: Promise and Limits of AI
Scientists use computers that can read and write like people to help solve hard math puzzles.
In 2026, a mathematician named Levent Alpöge used an AI called Claude Fable 5 to find a mistake in a famous math problem called the Jacobian conjecture.
Another AI from OpenAI found a mistake in a different old problem about how many points can be connected in a plane.
These AIs also did very well in math contests called the International Mathematical Olympiad, getting perfect scores.
The computers are good at looking at lots of possibilities quickly, but they can sometimes make up wrong answers, so people still need to check their work carefully.
Levent Alpöge announced a counterexample to the Jacobian conjecture using Anthropic’s Claude Fable 5 AI model.
OpenAI’s internal reasoning model produced a counterexample to Erdős’s 1946 unit‑distance conjecture, verified by nine mathematicians including Tim Gowers.
AI models have advanced from silver to gold to perfect scores in IMO problems, with GPT‑5.6 and Claude Fable 5 achieving 42/42.
AI excels at exploring vast hypothesis spaces and generating proofs but lacks built‑in truth guarantees, leading to possible hallucinations.
The rise of LLMs builds on a century of statistical language modeling, culminating in the Transformer architecture.
- Who
- Mathematicians and AI models such as Claude Fable 5 and GPT‑5.6
- What
- AI models produced counterexamples to long‑standing conjectures and solved IMO problems
- When
- 2024‑2026
- Where
- Global, including Shanghai for the 2026 IMO
- Why
- AI can rapidly explore many possibilities but lacks built‑in truth guarantees
- Jacobian conjecture counterexample
- Levent Alpöge, Claude Fable 5
- Erdős unit‑distance counterexample
- OpenAI internal model
- IMO perfect score
- GPT‑5.6, Claude Fable 5
- AI model type
- Large Language Model
- Transformer architecture
- Introduced 2017