Henri Poincare Quotes

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect.

Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.

There is no royal road to geometry.

I enjoyed mathematics from a very young age. At the beginning of college, I had this illusion, which was kind of silly in retrospect, that if I just understood math and physics and philosophy, I could figure out everything else from first principles.

One geometry cannot be more true than another; it can only be more convenient. Geometry is not true, it is advantageous.

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world

A mathematical theorem can be true whether or not it is realized in the world.

The science [geometry] is pursued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes.

On Pragmatism: It's all very well in theory but it doesn't work in practice

I am never satisfied until I can make a mathematical model of what I am studying. If I succeed in making one, I understand. If I cannot, I do not understand.

In practical life we are compelled to follow what is most probable ; in speculative thought we are compelled to follow truth. A man would perish of hunger and thirst, if he refused to eat or drink, till he had obtained positive proof that food and drink would be good for him. But in philosophic reflection this is not so. On the contrary, we must take care not to admit as true anything, which is only probable. For when one falsity has been let in, infinite others follow.

God Bless Theoretical Mathematics And May It Never Be Of Use To Anyone

The science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value.

What is mathematics? It is only a systematic effort of solving puzzles posed by nature.

To me, mathematics, computer science, and the arts are insanely related. They're all creative expressions.

Formal logic is mathematics, and there are philosophers like Wittgenstein that are very mathematical, but what they're really doing is mathematics - it's not talking about things that have affected computer science; it's mathematical logic.

My dad is a mathematician; I think we both have that problem-solving, looking-for-patterns way of thinking.

Philip Kitcher thinks that mathematics is surprisingly like empirical science. Few mathematicians would agree; philosophers too, from Socrates on, have held the opposite opinion.

I remember having this vague idea that what mathematicians did was that some authority, someone, gave them problems to solve, and they just sort of solved them.

I still think in a parallel universe, I became a mathematician.

I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.

When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed.

Most students who take math classes aren't going to be mathematicians. They're going to be engineers, statisticians - in many ways, that's the more important mission of math education.

Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs.

I thought I wanted to be a physicist in high school until I learned that there was much more math than philosophy in it. I assumed I would just sit around all day and think.