Philosophical and mathematical duality in Albert Lautman’s work

The terms “duality” and “dual” appear repeatedly in the writings of the mathematical philosopher and World War II French Resistance fighter Albert Lautman (1908-1944); however, a first comparative analysis attests to the variety of meanings, uses and functions that he ascribes to the very notion of duality. Let us give a first example: Lautman speaks of duality when two points of view, sometimes distinct, sometimes opposed, sometimes complementary, can be adopted to study the same mathematical entity.