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.

I have hardly known a mathematician who was capable of reasoning.

If in a discussion of many matters … we are not able to give perfectly exact and self-consistent accounts, do not be surprised: rather we would be content if we provide accounts that are second to none in probability.

The excessive increase of anything causes a reaction in the opposite direction.

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.
[Often seen condensed to: 'Geometry is knowledge of the eternally existent'.]

Trees and fields tell me nothing: men are my teachers.

Wisdom alone is a science of other sciences, and of itself.

The beauty of life is, therefore, geometrical beauty of a type that Plato would have much appreciated.

Every theory of love, from Plato down, teaches that each individual loves in the other sex what he lacks in himself.

[Plato] was the first to envisage the idea of timeless existence and to emphasize it—against reason—as a reality, more [real] than our actual experience…

Amicus Plato amicus Aristoteles magis amica verita.
Plato is my friend, Aristotle is my friend, but my greatest friend is truth.

The thoughts of Plato and Machiavelli... don't seem quite enough armor for a world beset with splitting the atoms, urban guerrillas, nineteen varieties of psychotherapists, amplified guitars, napalm, computers, astronauts, and an atmosphere polluted simultaneously with auto exhaust and TV commercials.

This missing science of heredity, this unworked mine of knowledge on the borderland of biology and anthropology, which for all practical purposes is as unworked now as it was in the days of Plato, is, in simple truth, ten times more important to humanity than all the chemistry and physics, all the technical and indsutrial science that ever has been or ever will be discovered.

But, indeed, the science of logic and the whole framework of philosophical thought men have kept since the days of Plato and Aristotle, has no more essential permanence as a final expression of the human mind, than the Scottish Longer Catechism.

For the philosopher, order is the entirety of repetitions manifested, in the form of types or of laws, by perceived objects. Order is an intelligible relation. For the biologist, order is a sequence in space and time. However, according to Plato, all things arise out of their opposites. Order was born of the original disorder, and the long evolution responsible for the present biological order necessarily had to engender disorder.
An organism is a molecular society, and biological order is a kind of social order. Social order is opposed to revolution, which is an abrupt change of order, and to anarchy, which is the absence of order.
I am presenting here today both revolution and anarchy, for which I am fortunately not the only one responsible. However, anarchy cannot survive and prosper except in an ordered society, and revolution becomes sooner or later the new order. Viruses have not failed to follow the general law. They are strict parasites which, born of disorder, have created a very remarkable new order to ensure their own perpetuation.