Quotes about mathematics

I am trying to make the terminology functorial with respect to the ideas.
—Serge Lang, Number Theory III: Diophantine Geometry

The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?
—Jerry Bona

Mathematics is the art of giving the same name to different things.
—Henri Poincare, "L'avenir des mathematiques", quoted by Emily Riehl, Category Theory in Context, Section 1.5

God made the integers; all the rest is the work of man.
—Leopold Kronecker

Mathematics, rightly viewed, possesses not only truth but supreme beauty—a beauty cold and austere, like that of a sculpture, without appeal to any part of our weaker nature, without the gorgeous trapping of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.
—Bertrand Russell, Mysticism and Logic, "The Study of Mathematics"

You know, people think mathematics is complicated. Mathematics is the simple bit. It's the stuff we can understand. It's cats that are complicated. I mean, what is it in those little molecules and stuff that make one cat behave differently than another, or that make a cat? And how do you define a cat? I have no idea.
—John Conway, source

Textbooks in algebraic geometry should be written by Italians and corrected by Germans.
—Gian-Carlo Rota, Indiscrete Thoughts, "A Mathematician's Gossip"

When we ask for foundations of mathematics, we must first look for the unstated wishes that motivate our questions. When you search into the Western mind, you discover the craving that all things should be reduced to one, that the laws of nature should all be consequences of one law, that all principles should be reduced to one principle. It is a great Jewish idea. One God, one this, one that, one everything. We want foundations because we want oneness.
—Gian-Carlo Rota, Indiscrete Thoughts, "A Mathematician's Gossip"

Universal algebra has made it. Not, as the founders wanted, as the unified language for algebra, but rather, as the proper language for the unforeseen and fascinating algebraic systems that are being discovered in computer algebra, like the fauna of a new continent.
—Gian-Carlo Rota, Indiscrete Thoughts, "A Mathematician's Gossip"

The justification of probabilistic reasoning by measure theory has never been fully convincing… Probabilistic reasoning is syntactic, whereas its measure theoretic justification is highly semantic. Probability remains a rare instance of a syntax that has been justified only by the mercy of one known semantic model.
—Gian-Carlo Rota, Indiscrete Thoughts, "A Mathematician's Gossip"

Of some subjects we may say they exist, of others, that we wish they existed. Cluster analysis is one of the latter.
—Gian-Carlo Rota, Indiscrete Thoughts, "A Mathematician's Gossip"

Pattern recognition is big business today. Too bad that none of the self-styled specialists in the subject—let us charitably admit it is a subject—know mathematics, even those who know how to read and write.
—Gian-Carlo Rota, Indiscrete Thoughts, "A Mathematician's Gossip"

Mathematics is prestidigitation.
—Carl Linderholm, Mathematics Made Difficult