Pickover's lively, provocative travel guide takes readers into the fascinating realm of mystic math, from perfectly strange numbers to fractured geometries and other curious nooks and crannies of ancient worlds and modern times.

Human life is proverbially uncertain; few things are more certain than the solvency of a life-insurance company.

To the pure geometer the radius of curvature is an incidental characteristic - like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.

It is true that I should have been surprised in the past to learn that Professor Hardy had joined the Oxford Group. But one could not say the adverse chance was 1:10. Mathematics is a dangerous profession; an appreciable proportion of us go mad, and then this particular event would be quite likely.

The moving power of mathematical invention is not reasoning but imagination.

The joy of suddenly learning a former secret and the joy of suddenly discovering a hitherto unknown truth are the same to me - both have the flash of enlightenment, the almost incredibly enhanced vision, and the ecstasy and euphoria of released tension.

I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.

Next you'd see a raft sliding by, away off yonder, and maybe a galoot on it chopping. . . you'd see the ax flash and come down-you don't hear nothing; you see the ax go up again, and by the time it's above the man's head then you hear the k'chunk!-it had took all that time to come over the water.

It is not only the prisoners who grow coarse and hardened from corporal punishment, but those as well who perpetrate the act or are present to witness it.

Algebra reverses the relative importance of the factors in ordinary language.

We live today in a world where most of the really important developments in everything from math and physics and astronomy to public policy and psychology and classical music are so extremely abstract and technically complex and context-dependent that it's next to impossible for the ordinary citizen to feel that they (the developments) have much relevance to her actual life.

It will be another million years, at least, before we understand the primes.

To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess.

What the mortgage bubble was all about was big banks like Goldman Sachs taking big bundles of subprime mortgages that were lent out largely to low-income, highly risky borrowers, and applying this kind of magic-pixie-dust math to these bundles of securities and slapping AAA ratings on them.

[Math] curriculum is obsessed with jargon and nomenclature seemingly for no other purpose than to provide teachers with something to test the students on.

"The most powerful single idea in mathematics is the notion of a variable. "

It is impossible to be a mathematician without being a poet in soul.

Science is what we understand well enough to explain to a computer. Art is everything else we do.

Brian and I were both science students. You know science sort of math and physics side, you know.

Some people focus more on sonics. Some people focus more on story. I focus on both sonics and story, but music sometimes, just music itself, can turn into more of a maths problem. I guess everything in life is a math problem, but it can be more about an empirical route to getting the symmetry that you want, and this vibe, sonically.