Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don't look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.

Sigmund Freud was a novelist with a scientific background. He just didn’t know he was a novelist. All those damn psychiatrists after him, they didn’t know he was a novelist either."

(Interview in Writers at Work: The Paris Review Interviews, Eighth Series, ed. George Plimpton, 1988)

The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians have never decided whether they should feel excited or upset by such events.

Analytically speaking, Sigmund Freud talked out of his arse

We will therefore turn to the less ambitious question of what men themselves show by their behavior to be the purpose and intention of their lives. What do they demand of life and wish to achieve in it? The answer to this can hardly be in doubt. They strive for happiness; they want to become happy and to remain so. This endeavor has two sides, a positive and a negative aim. It aims, on the one hand, at an absence of pain and unpleasure, and, on the other, at the experiencing of strong feelings of pleasure. In its narrower sense the word 'happiness' only relates to the last. In conformity with this dichotomy in his aims, man's activity develops in two directions, according as it seeks to realize — in the main, or even exclusively — the one or the other of these aims.