A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it cha….

The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing..

If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems..

A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey w….

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pen….

Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you c….

Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. Trying to swim, you imita….

The first rule of style is to have something to say. The second rule of style is to control yourself when, by chance, you have two things to say; say….

Solving problems is a practical art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice..

It may be more important in the mathematics class how you teach than what you teach..

Mathematics is being lazy. Mathematics is letting the principles do the work for you so that you do not have to do the work for yourself.

Mathematics is not a spectator sport!.

It is better to solve one problem five different ways, than to solve five problems one way..

The first and foremost duty of the high school in teaching mathematics is to emphasize methodical work in problem solving...The teacher who wishes to….

Mathematics consists in proving the most obvious thing in the least obvious way..

Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for so….

To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself….

In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second….

Pedantry and mastery are opposite attitudes toward rules. To apply a rule to the letter, rigidly, unquestioningly, in cases where it fits and in case….

The best of ideas is hurt by uncritical acceptance and thrives on critical examination..

An idea which can be used only once is a trick. If one can use it more than once it becomes a method..