Henri Poincare Quotes

Mathematics is not a contemplative but a creative subject.

Even the greatest mathematicians, the ones that we would put into our mythology of great mathematicians, had to do a great deal of leg work in order to get to the solution in the end.

Math research is more like a marathon.

You have to spend some energy and effort to see the beauty of math.

Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?

I am interested in mathematics only as a creative art.

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.

I love that once you know the basic rules of maths, you can do whatever you want with it.

As the prerogative of Natural Science is to cultivate a taste for observation, so that of Mathematics is, almost from the starting point, to stimulate the faculty of invention.

The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.

Pure mathematicians just love to try unsolved problems - they love a challenge.

We've lost something that's been with us for so long, and something that drew a lot of us into mathematics. But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention.

Maths should be more practical and more conceptual, but less mechanical.

Mathematicians aren't motivated by money and material gain, or even by practical applications of their work. For us it's the glory of solving one of the great unsolved problems that have outwitted previous generations of mathematicians. …. Despite all the things we've discovered over the last 7 millennia, there are still many things we don't understand.

The essence of mathematics lies precisely in its freedom.

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?

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.

And Archimedes, as he was washing, thought of a manner of computing the proportion of gold in King Hiero's crown by seeing the water flowing over the bathing-stool. He leaped up as one possessed or inspired, crying, "I have found it! Eureka!".

The true spirit of delight...is to be found in mathematics as surely as in poetry.

If you are receptive and humble, mathematics will lead you by the hand. Again and again, when I have been at a loss how to proceed, I have just had to wait until I have felt the mathematics led me by the hand. It has led me along an unexpected path, a path where new vistas open up, a path leading to new territory, where one can set up a base of operations, from which one can survey the surroundings and plan future progress.

He that gives a portion of his time and talent to the investigation of mathematical truth, will come to all other questions with a decided advantage over his opponents.

[Mathematics] unceasingly calls forth the faculties of observation and comparison; one of its principal weapons is induction: it has frequent recourse to trial and verification; and it affords a boundless scope for the exercise of the highest efforts of imagination and invention.