AI Agents Failed to Prove Fermat's Last Theorem. Then They Got a Shared To-Do List

Introduction

At first glance, it may seem surprising: artificial intelligence (AI) agents failed to prove one of the most complex statements in mathematics—Fermat's Last Theorem—and then succeeded thanks to a shared to-do list system. This case underscores the importance of proper technology and approach usage when working with autonomous systems.

Initial Failures

In early September 2023, company Anthropic presented the results of a team of Claude agents that independently proved Fermat's Last Theorem in just 11 days. Initially, the process went smoothly, but then the agents lost control over the project state and ceased to effectively collaborate with each other. This led to the failure of the first phase.

Problems with Autonomous Agents

If you have ever worked with two or more autonomous AI agents on the same codebase, you already understand this problem. They can unintentionally destroy each other’s work, making collaborative work extremely difficult.

Solution: A Shared Task Management System

The key factor in success was the implementation of a shared task management system in the form of a directed acyclic graph (DAG), which acted as the team’s memory. This approach allowed the agents to maintain context and effectively interact with each other.

How the Shared Task Management System Works

A shared task management system provides the following functionalities:

• Information Exchange: All agents can see and use information created by others.
• Access Control: Each agent has specific access rights to information.
• Authentication and Authorization: Confirmation of each agent’s identity for security purposes.

These functionalities enable agents to work more efficiently and minimize conflicts.

Numbers Behind the Scene

Let's look at some numbers that illustrate the scale of this task:

• 13 million lines of code: This is an enormous amount of logic that needed to be checked and coordinated.
• 29,000 intermediate theorems: Each of these theorems is a step toward solving the problem.
• 6 billion output tokens: This is the volume of information that needed to be processed and interpreted.

These numbers highlight the complexity of the task and the necessity for precise and efficient process management.

Practical Tips for Developers

If you are working with autonomous agents, here are some tips:

1. Use a Shared Task Management System: This will help prevent conflicts and improve coordination between agents.
2. Regularly Check Project Status: Ensure all agents know the current project status and can adapt to changes.
3. Conduct Regular Reviews: This will help identify errors and problems early on.
4. Use Version Control Systems: This will allow tracking changes and restoring previous project versions if needed.

Conclusion

This case shows that even with powerful autonomous agents, proper organization of their work is crucial. A shared task management system can be the key to success when tackling complex tasks.

SEO Title

AI Agents and a Shared Task Management System

SEO Description

Research on how a shared task management system helped AI agents prove Fermat's Last Theorem after initial failures.

SEO Keywords

AI, autonomous agents, Fermat's Last Theorem, shared task management system, mathematics

Tags

AI, autonomous systems, task management, Fermat's Last Theorem, mathematics

Search on Unsplash

programming code