French researcher and teacher working at the Jussieu University in Paris. He works on mathematical theories in the Artificial Intelligence field.

His works include a formal proof of Gödel's Completeness Theorem, but the most significant is the proof that Lambda Calculus, a logical language that has been in use for over 50 years, is the model of every cognitive activity in the human brain, which means that every thought is a calculus. He presented Lambda Calculus as the Alphabet of human thinking.

This theory has led to heated discussions amongst french scientists when it was first published in the Science et Vie magazine in February 2002. According to it, it is possible to formalise a human brain in the form of a Lambda Calculus program.

By establishing a formal relation between mathematics and Lambda Calculus, J.L. Krivine also shows a method for translating mathematical theorems demonstrations into computer programs.