Since Antiquity, the validity of a theorem has rested on the consensus of an elite capable of rereading it. Today, this model is collapsing. The complexity of certain modern demonstrations, sometimes reaching thousands of pages, exceeds the verification capabilities of a human brain. New technological tools are essential today.
An article from the New Scientist site discusses, for example, the programming language Lean. By transforming reasoning into computer code, it allows a machine to guarantee with absolute certainty the correctness of a theorem. The growing use of artificial intelligence in the discipline could lead to a revolution unlike anything mathematics has ever known.
The stakes are enormous. The mastery of these tools is no longer just an academic question, but also becomes geopolitical. Nations that master these tools will have a huge advantage in developing algorithms, whatever the field of research: cryptography, defense systems or even nuclear physics. The ability to produce perfect knowledge, free from any defect – and therefore without failure factors – is the new Holy Grail of digital sovereignty.
The algorithm as a new frontier of knowledge
The integration of artificial intelligence into this process is a complete game changer. If language models are known for their errors, approximations or lack of judgment, they can be coupled with “checking” tools like Lean. The AI then proposes theories that the machine validates or not. Enough to drastically accelerate research protocols.
Researchers like Kevin Buzzard or Fields Terence Tao have made it their mission to digitize the entire world’s mathematical corpus. This global library project would create an “indisputable” knowledge base accessible to machines. The stated goal is to organize and offer knowledge, not with a view to sharing with humanity, but with the machine.
By becoming a branch of theoretical computer science, mathematics loses its status as “last purely human science». This change will raise new ethical questions and will undoubtedly require some safeguards. What will become of the beauty of a demonstration if it is no longer understandable by humans? Does the mathematician risk becoming nothing more than a simple coder, an assistant to the machine?
Despite these legitimate fears, the future looks exciting and rich for the discipline. The rigor of the machine could lay unbreakable foundations for complex new theorems whose full extent we are only beginning to grasp.
