Gérard Toulouse has been a very successful and innovative scientist at a time of transition in theoretical physics from fundamental issues of microphysics to statistical problems posed by the behavior of condensed matter and other fields. Gérard Toulouse brought a somewhat unexpected and deep idea borrowed from abstract mathematics to classify defects in condensed matter. Relying on bold extensions of concepts of condensed matter physics, he solved very hard problems in the field of complexity like spin glasses and even the behavior of neural networks, opening so completely new paths.