Stanislaw Ulam Quotes

When something is beautiful in math, everything is just perfectly lined up, and you see through sheer thought that something really beautiful can take place.

I have found a very great number of exceedingly beautiful theorems.

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics.

Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics.

Mathematics rightly viewed possesses not only truth but supreme beauty.

A elegantly executed proof is a poem in all but the form in which it is written.

Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

Math is the only place where truth and beauty mean the same thing.

Euclid Alone Has Looked on Beauty Bare.

Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone.

The mathematical sciences particularly exhibit order symmetry and limitations; and these are the greatest forms of the beautiful.

As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.

If numbers aren't beautiful, I don't know what is.

I am very seldom interested in applications. I am more interested in the elegance of a problem. Is it a good problem, an interesting problem?

The teleology of the Universe is directed to the production of Beauty... The type of Truth required for the final stretch of Beauty is a discovery and not a recapitulation... Apart from Beauty, Truth is neither good, nor bad... Truth matters because of beauty.

...which causes me to wonder, my own purpose on so many days as humble as the spider's, what is beautiful that I make? What is elegant? What feeds the world?

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

Beauty can afford to laugh at distinctions: it is itself the greatest distinction.

Let us be elegant or die! --Amy

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.

To speak freely of mathematics, I find it the highest exercise of the spirit; but at the same time I know that it is so useless that I make little distinction between a man who is only a mathematician and a common artisan. Also, I call it the most beautiful profession in the world; but it is only a profession.

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

Fractals, the theory of relativity, the genome: these are magnificently beautiful constructs.

Geometry is the archetype of the beauty of the world.

If you write beautifully, you write beautifully, that's all.