Henri Poincare Quotes

If I were asked to name, in one word, the pole star round which the mathematical firmament revolves, the central idea which pervades the whole corpus of mathematical doctrine, I should point to Continuity as contained in our notions of space, and say, it is this, it is this!

The satirical direction I have chosen is an indication of my disappointment in man, which is the opposite way of saying that I have high expectations for the human race.

I thought of computers as very low class. I thought of myself as a pure mathematician and was interested in partial differential equations and topology and things like that.

I've always enjoyed mathematics. It is the most precise and concise way of expressing any idea.

Fractions, decimals, algebra, geometry, trigonometry, calculus, mechanics - these are the steps up the mountain side. How high is one going to get? For me, the pinnacle was Projective Geometry. Who today has even heard of this branch of mathematics?

I think I still like science and art better, but geometry is a big improvement over algebra.

My own view on religion is that of Lucretius. I regard it as a disease born of fear and as a source of untold misery to the human race.

The science of pure mathematics, in its modern developments, may claim to be the most original creation of the human spirit.

Newton's health, and confusion to mathematics.

Leibniz is at the disadvantage of not having seen it. Or perhaps we should count this as an advantage, for anyone who sees it is dumbfounded by the brilliance of the geometry, and it is difficult to criticize a man’s work when you are down on your knees shielding your eyes.

There isn't any way to libel the human race.

The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is no exaggeration to call Lobachevsky the Copernicus of Geometry [as did Clifford], for geometry is only a part of the vaster domain which he renovated; it might even be just to designate him as a Copernicus of all thought.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method

In the meantime, most noble Sir, you have assigned this question to the geometry of position, but I am ignorant as to what this new discipline involves, and as to which types of problem Leibniz and Wolff expected to see expressed in this way.

When people ask me what's my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.

Now, as Mandelbrot points out, ... Nature has played a joke on the mathematicians. The 19th-century mathematicians may not have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us.

At the age of eleven, I began Euclid, with my brother as my tutor. ... I had not imagined that there was anything so delicious in the world. After I had learned the fifth proposition, my brother told me that it was generally considered difficult, but I had found no difficulty whatsoever. This was the first time it had dawned on me that I might have some intelligence.

I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.

Mathematics is the bold luxury of pure reason, one of the few that remain today.

We cannot ... prove geometrical truths by arithmetic.

Pointing out that countless great mathematicians had tried to solve the problem and failed before you came along is in particularly bad taste and should be avoided completely.

Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation and criticism, by the logic of proofs and refutations.

To understand this for sense it is not required that a man should be a geometrician or a logician, but that he should be mad.

Euclid for children is barbarous.