AI challenges mathematical certainty

Artificial intelligence is now targeting the last bastion of absolute certainty, pure mathematics. OpenAI has announced that its machine will soon resolve a hundred theorems, marking a significant step in the intersection of AI and mathematical research.

OpenAI shares unpublished proofs

The California-based company has recently uploaded over seven hundred files of previously unpublished mathematical proofs to the GitHub platform. These files contain detailed logical derivations and solutions to complex mathematical problems.

Massive computational effort

To generate these results, the company mobilized a colossal computing power, equivalent to approximately three hours of reflection by its most advanced model for each theorem. This effort highlights the immense resources required to achieve such mathematical breakthroughs using AI.

Lean language for verification

OpenAI is sharing these proofs through the Lean language, a programming tool designed to verify computer reasoning. Lean allows mathematicians to check the validity of AI-generated proofs using formal logic and automated verification.

Promise for business applications

For CIOs, the promise is attractive. If the machine can solve complex abstract equations, it will soon be able to optimize network architectures or financial algorithms with particularly formidable efficiency, offering potential benefits across various industries.

Scientific skepticism rises

However, the scientific community is reacting and raising a vital question. How can one trust a result generated by an unverifiable black box? This concern highlights the challenge of verifying AI-generated proofs without transparency into the model's reasoning process.

Criticism and legal controversy

The Association for Human Mathematics condemns this as a publicity stunt, published during a copyright infringement legal storm. In science as in business, a result has no value if it is not auditable, and the controversy underscores the need for rigorous validation.

Need for audit and transparency

So how can one validate a technical solution if even the model designers are unable to explain the reasoning of their artificial intelligence? This question points to the fundamental problem of explainability in AI, which is crucial for both scientific and business applications.

Independent oversight emerges

Faced with this opacity, nine leading global researchers have therefore founded a completely independent oversight body. In France, the École normale supérieure supports this new independent advisory group, aiming to impose publication and audit standards on tech giants.