Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though th… - Henri Poincaré

Let us try to represent the figure formed by these two curves and their intersections in infinite number, each corresponding to a doubly asymptotic solution, these intersections form a kind of mesh, of fabric, of infinitely tight network; each of the two curves must never intersect itself, but it must fold back on itself in a very complex way in order to cross an infinite number of times all the meshes of the network. On will be struck by the complexity of this figure, which I do not even try to draw. Nothing is more likely to give us an idea of the complexity of the three-body problem and in general of all the problems of dynamics where there is no uniform integral and where the Bohlin series are divergent.

The very possibility of mathematical science seems an insoluble contradiction. If this science is deductive in appearance only, from where does it get its perfect rigor that no one dares to doubt? If, on the contrary, all the propositions it sets forth can be derived from one another by the rules of formal logic, why is mathematics not reducible to an immense tautology? Syllogism can teach us nothing that is essentially new and, if everything originated in the principle of identity, it should also be possible to reduce everything to it. Are we then to concede that the statements of all those theorems filling so many volumes are merely roundabout ways of saying that A is A?

All that is not thought is pure nothingness; since we can think only thought and all the words we use to speak of things can express only thoughts, to say there is something other than thought, is therefore an affirmation which can have no meaning.
And yet—strange contradiction for those who believe in time—geologic history shows us that life is only a short episode between two eternities of death, and that, even in this episode, conscious thought has lasted and will last only a moment. Thought is only a gleam in the midst of a long night. But it is this gleam which is everything.