George Polya Quotes

47 quotes in 789 categories

• Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so inconspicuous. The expert has, perhaps,…
• The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no particular application of it is…
• The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to…
• The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you…
• Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and…
• When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.
• Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and…
• If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it…
• 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,…
• Look around when you have got your first mushroom or made your first discovery: they grow in clusters.
• The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this…
• If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression…
• In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must…
• There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain…
• The open secret of real success is to throw your whole personality into your problem.
• Geometry is the science of correct reasoning on incorrect figures.
• My method to overcome a difficulty is to go round it.
• 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…
• Beauty in mathematics is seeing the truth without effort.
• If there is a problem you can't solve, then there is an easier problem you can't solve: find it.

Browse George Polya Quotes by Category