Doubt everything or believe everything: these are two equally convenient strategies. With either we dispense with the need for reflection.

It is with logic that one proves; it is with intuition that one invents.

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 they would consider it ridiculous to ask for an eclipse by prayer.

Point set topology is a disease from which the human race will soon recover.

A reality completely independent of the spirit that conceives it, sees it, or feels it, is an impossibility. A world so external as that, even if it existed, would be forever inaccessible to us.

Every phenomenon, however trifling it be, has a cause, and a mind infinitely powerful, and infinitely well-informed concerning the laws of nature could have foreseen it from the beginning of the ages. If a being with such a mind existed, we could play no game of chance with him; we should always lose.

[T]he different branches of Arithmetic - Ambition [G]eometry is not true, it is advantageous.