Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Mathematics is the art of giving the same name to different things.

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe —because, like Spinoza's God, it won't love us in return.

A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying in the figure are equal to one another.

A line is breadthless length.

A point is that which has no part.

The old woman was not only ugly with the ugliness age brings us all but showed signs of formidable ugliness by birth —pickle-jar chin, mainsail ears and a nose like a trigonometry problem. What's more, she had the deep frown and snit wrinkles that come from a lifetime of bad character.

Prime numbers are what is left when you have taken all the patterns away. I think prime numbers are like life. They are very logical but you could never work out the rules, even if you spent all your time thinking about them.

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherealisation of common sense.

Clutching the shredded tatters of my pride and dignity, I trudged to the office hours of my math instructor every week, seeking an explanation for the increasingly mysterious problems in the textbook. My instructor welcomed my presence as she would welcome the Angel of Death. Irritated? She was terrified. Explain… the problems? Articulate… the steps? Relate… the concepts? I would ask questions, and she would respond by completing yet another sample problem as fast as she possibly could, blushing nervously. I felt like I was on a Star Trek episode. “Captain, I think I understand… the creature communicates through multivariable calculus problems!”

The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not being, which we call the imaginary root of negative unity.

Reyes, the indecipherable providence
That doles out the prodigal and the scant,
Gave to some the sector or the arc,
But to you the total circumference.

Looking into a college textbook as an adult is a shock (and a vivid reminder of why we were so glad to get out of school). The prose style is at once puerile and impenetrable, Goodnight Moon rewritten by Henry James. The tone varies from condescension worthy of a presidential press conference to sly chumminess worthy of the current president. The professorial wit is duller than the professorial dicta, and these are dulled to unbearable numbness by the need to exhibit professorial self-importance. No idea, however simple—“When there's more of something, it costs less”—can be expressed without rendering it onto a madras sport coat of a graph and translating it into a rebus puzzle full of peculiar signs and notations. Otherwise the science of economics wouldn't seem as profound to outsiders as organic chemistry does.