Mathematics has the inhuman quality of starlight, brilliant and sharp, but cold.

Before one can generalize, formalize, and axiomatize, there must be a mathematical substance.

Without the concepts, methods and results found and developed by previous generations right down to Greek antiquity one cannot understand either the aims or achievements of mathematics in the last 50 years. [Said in 1950]

No mathematician of equal stature has risen from our generation... Hilbert was singularly free from national and racial prejudices; in all public questions, be they political, social or spiritual, he stood forever on the side of freedom.

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

... numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.

Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind.