Appears in collection : Synthetic mathematics, logic-affine computation and efficient proof systems / Mathématiques synthétiques, calcul logique affine et systèmes de preuve efficients

In a longstanding and still ongoing research project, I have been developing a synthetic approach to probability theory based on axiomatising a primitive notion of random variable. In this talk, I shall discuss the process of developing of the axiomatisation, touching on various considerations that influenced the choice of axioms, the current state of the theory, and lessons learned from the process so far.