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

A first fact should surprise us, or rather would surprise us if we were not used to it. How does it happen there are people who do not understand mathematics? If mathematics invokes only the rules of logic, such as are accepted by all normal minds...how does it come about that so many persons are here refractory?

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

In the old days when people invented a new function they had something useful in mind.

It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.

How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.

Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.