George Polya Quotes About Science

Quotes about: Science

• 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 paper.

  George Polya

  Science, Doe, Needs

  "Speaking of Science: Notable Quotes on Science, Engineering, and the Environment" by Jon Fripp, Michael Fripp, Deborah Fripp, Newnes (p. 45), 2000.

• 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 challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

  George Polya

  Mean, Science, Discovery

• If there is a problem you can't solve, then there is an easier problem you can't solve: find it.

  George Polya

  Education, Knowledge, Math

• 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 something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.

  George Polya

  Teacher, Book, Hard Work

• 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 feasible.

  George Polya

  Science, Anxiety, World

• There are many questions which fools can ask that wise men cannot answer.

  George Polya

  Wise, Knowledge, Science

• 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 get a bright idea.

  George Polya

  Good Luck, Math, Science

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

• One of the first and foremost duties of the teacher is not to give his students the impression that mathematical problems have little connection with each other, and no connection at all with anything else. We have a natural opportunity to investigate the connections of a problem when looking back at its solution.

  George Polya

  Teacher, Science, Opportunity

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

• The teacher can seldom afford to miss the questions: What is the unknown? What are the data? What is the condition? The student should consider the principal parts of the problem attentively, repeatedly, and from from various sides.

  George Polya

  Teacher, Science, Data

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

• 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 theorem, and I said it is not proved and it may be difficult. Von Neumann didn't say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

  George Polya

  Teaching, Writing, Science

  "How to Solve It" by George Polya, 2nd edition, (p. xv), 1957.

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

  George Polya

  Science, Creative, Guessing

  "Induction and Analogy in Mathematics". Book by George Polya, 1954.

• 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

  George Polya

  Hard Work, Science, Lazy

• When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.

  George Polya

  Teaching, Math, Science

• 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 can. ... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind.

  George Polya

  Science, Understanding, Mind

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

• Look around when you have got your first mushroom or made your first discovery: they grow in clusters.

  George Polya

  Science, Discovery, Mushrooms

  George Pólya (1948). “How to solve it: a new aspect of mathematical method”

• The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line.

  George Polya

  Mean, Science, Discovery

• The open secret of real success is to throw your whole personality into your problem.

  George Polya

  Success, Real, Science

  George Pólya (1957). “How to solve it: a new aspect of mathematical method”

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