Mathieu reacted consistently against greco-Latin classicism, Renaissance's legacy and all forms of later geometric abstraction. He considers lyrical abstraction as the latest revolution to happen in the history of arts : freed from realism by Impressionism, from shapes by Cubism, from representation of perceptible reality by geometric abstraction, art experiences the liberation of the all its past references from nature. From his reflexion he develops his own expression of a lyrical abstraction : "Henceforth in the history of shapes as in the history of the world, the sign precedes its meaning".