Henri Poincare Quotes

Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning.

Mathematical Reasoning is not only exact; it has its own criteria of reality.

... mathematics is the science of skillful operations with concepts and rules invented just for this purpose.

A dozen more questions occurred to me. Not to mention twenty-two possible solutions to each one, sixteen resulting hypotheses and counter-theorems, eight abstract speculations, a quadrilateral equation, two axioms, and a limerick. That's raw intelligence for you.

It is hard to know what you are talking about in mathematics, yet no one questions the validity of what you say. There is no other realm of discourse half so queer.

One cannot really argue with a mathematical theorem.

Being exposed to theory, stimulated by a basic love of concepts and mathematics, was a marvelous experience.

It is not of the essence of mathematics to be conversant with the ideas of number and quantity.

Metaphysical thinking will always no doubt be a strong element in her mentality, and it is to be hoped that she will never lose her great, her sovereign powers in that direction.

I think part of the appeal of mathematical logic is that the formulas look mysterious - You write backward Es!

Thinking - in particular abstract thinking, which most of us are introduced to through the study of mathematics and literature - helps us learn that we can become problem solvers.

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

We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.

if you do not appreciate the mathematics, you cannot see, among the great variety of facts, that logic permits you to go from one to the other

The essence of mathematics lies precisely in its freedom.

An ounce of algebra is worth of a ton of verbal argument.

… mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

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

The student of mathematics must get rid of all arbitrary thinking and follow purely the demands of thought. In thinking in this way, the laws of the spiritual world flow into him. This regulated thinking leads to the most spiritual truths.

Mathematics is the queen of the sciences.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then suchand such another proposition is true of that thing.... Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning.

Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.

The whole of mathematics consists in the organization of a series of aids to the imagination in the process of reasoning.