One cannot reduce to concepts the distinction between two systems of three straight lines each (directed lines, of which the one system points forwar… - Carl Friedrich Gauss

We must admit with humility that, while number is purely a product of our mind, space has a reality outside of our mind, so that we cannot prescribe its laws a priori.

I protest against the use of infinite magnitude as something completed, which is never permissible in mathematics. Infinity is merely a way of speaking

The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it. But when a person of that sex, that, because of our mores and our prejudices, has to encounter infinitely more obstacles and difficulties than men in familiarizing herself with these thorny research problems, nevertheless succeeds in surmounting these obstacles and penetrating their most obscure parts, she must without doubt have the noblest courage, quite extraordinary talents and superior genius.