Quotes on Mathematical

One can't believe impossible things.

Can you do Division? Divide a loaf by a knife - what's the answer to that?

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza's God, it won't love us in return.

Theory attracts practice as the magnet attracts iron.

I have had my results for a long time: but I do not yet know how I am to arrive at them.

A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.

If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.

...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.

For the historian everything begins and ends with time, a mathematical, godlike_x000D_ _x000D_ time, a notion easily mocked, time external to men, 'exogenous,' as economists_x000D_ _x000D_ would say, pushing men, forcing them, and painting their own individual times_x000D_ _x000D_ the same color: it is, indeed, the imperious time of the world.

He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.

Six is a number perfect in itself, and not because God created the world in six days; rather the contrary is true. God created the world in six days because this number is perfect, and it would remain perfect, even if the work of the six days did not exist.

. . . by natural selection our mind has adapted itself to the conditions of the external world. It has adopted the geometry most advantageous to the species or, in other words, the most convenient. Geometry is not true, it is advantageous.

All things began in Order, so shall they end, and so shall they begin again, according to the Ordainer of Order, and the mystical mathematicks of the City of Heaven.

The mathematical facts worthy of being studied are those which, by their analogy with other facts, are capable of leading us to the knowledge of a physical law. They reveal the kinship between other facts, long known, but wrongly believed to be strangers to one another.

You almost can't avoid having some version of the multiverse in your studies if you push deeply enough in the mathematical descriptions of the physical universe.

The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction.

Everything that is really great and inspiring is created by the individual who can labor in freedom.

Eternity is said not to be an extension of time but an absence of time, and sometimes it seemed to me that her abandonment touched that strange mathematical point of endlessness, a point with no width, occupying no space.

In mathematical quarters, the regular division of the plane has been considered theoretically. ... [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it.

Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.