Mathematical Imagination Quotes

There is an astonishing imagination, even in the science of mathematics.

Pure mathematics is, in its way, the poetry of logical ideas.

I am interested in mathematics only as a creative art.

One factor that has remained constant through all the twists and turns of the history of physical science is the decisive importance of the mathematical imagination.

My dad, a mathematician, raised me to believe that mathematics is beautiful, so math is a part of my imaginative terrain. In my late 20s I wrote several 11-line poems because I wanted to create poems that couldn't be uniformly divided into couplets, tercets, or quatrains, 11 being a prime number.

But think of Adam and Eve like an imaginary number, like the square root of minus one: you can never see any concrete proof that it exists, but if you include it in your equations, you can calculate all manner of things that couldn't be imagined without it.

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

It is here [in mathematics] that the artist has the fullest scope of his imagination.

There is an astonishing imagination, even in the science of mathematics. ... We repeat, there was far more imagination in the head of Archimedes than in that of Homer.

Mathematics is not a contemplative but a creative subject; no one can draw much consolation from it when he has lost the power or the desire to create; and that is apt to happen to a mathematician rather soon. It is a pity, but in that case he does not matter a great deal anyhow, and it would be silly to bother about him.

A mathematician, like a painter or a poet, is a maker of patterns.

Still more astonishing is that world of rigorous fantasy which we call mathematics.

The pure mathematician, like the musician, is a free creator of his world of ordered beauty.

The constructs of the mathematical mind are at the same time free and necessary. The individual mathematician feels free to define his notions and set up his axioms as he pleases. But the question is will he get his fellow mathematician interested in the constructs of his imagination. We cannot help the feeling that certain mathematical structures which have evolved through the combined efforts of the mathematical community bear the stamp of a necessity not affected by the accidents of their historical birth.

As for everything else, so for a mathematical theory: beauty can be perceived but not explained.

Mathematicians are stiff abstract guys. They'll tell you they don't need the physical world. But then when I show them my bubbles they're like little children.

The Geometer has the special privilege to carry out, by abstraction, all constructions by means of the intellect. Who, then, would wish to prevent me from freely considering figures hanging on a balance imagined to be at an infinite distance beyond the confines of the world?

They [formulae 1.10 - 1.12 of Ramanujan] must be true because, if they were not true, no one would have had the imagination to invent them.

I've dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own. A twelve is very different from a thirteen, for example. Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won't think twice about breaking the law to get what he wants. Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he's told; nine is deep and mystical, a Buddha of contemplation.