Geometry. Euclid : the beginnings of geometry --
Lobachevski : Non-Euclidean geometry --
Descartes : geometry and algebra joined --
Arithmetic. Archimedes : numbers and counting --
Dedekind : irrational numbers --
Russell : the definition of number --
Advanced topics. Euler : a new branch of mathematics : topology --
Laplace : the theory of probability --
Boole : algebra and logic joined.