“The biggest progress of mathematics have been to subject it to formal logics. There are sets, functions, and other abstract (i.e. invented or imaginary) relations, then everything else is discovering interesting particular cases. A group (or other structure) is nothing else than a particular case of a function from the Cartesian product of a set with itself, and into itself. Sets and functions are themselves interesting particular cases of abstract relations, the other important one being the equivalence relation. The groups in geometry are nothing else than an interesting equivalence relation called congruence or symmetry. Fields in algebra are functions etc. etc.

“The biggest progress of mathematics have been to subject it to formal logics. There are sets, functions, and other abstract (i.e. invented or imaginary) relations, then everything else is discovering interesting particular cases. A group (or other structure) is nothing else than a particular case of a function from the Cartesian product of a set with itself, and into itself. Sets and functions are themselves interesting particular cases of abstract relations, the other important one being the equivalence relation. The groups in geometry are nothing else than an interesting equivalence relation called congruence or symmetry. Fields in algebra are functions etc. etc. “