One does not ask whether a scientific theory is true, but only whether it is convenient.

Intuition is more important to discovery than logic.

If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.

How is error possible in mathematics?

All great progress takes place when two sciences come together, and when their resemblance proclaims itself, despite the apparent disparity of their substance.

Astronomy is useful because it raises us above ourselves; it is useful because it is grand; .... It shows us how small is man's body, how great his mind, since his intelligence can embrace the whole of this dazzling immensity, where his body is only an obscure point, and enjoy its silent harmony.

Geometry is not true, it is advantageous.