George Polya Quotes About Mathematics

Quotes about: Mathematics

• 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.

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

  George Polya

  Education, Math, Different

• 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

• Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told the young man had gone off to become a poet. Hilbert is reported to have remarked: 'I never thought he had enough imagination to be a mathematician.'

  George Polya

  Creativity, Men, Imagination

• 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

• Beauty in mathematics is seeing the truth without effort.

  George Polya

  Education, Math, Effort

• Geometry is the science of correct reasoning on incorrect figures.

  George Polya

  Education, Math, Figures

• Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice. Trying to swim, you imitate what other people do with their hands and feet to keep their heads above water, and, finally, you learn to swim by practicing swimming. Trying to solve problems, you have to observe and to imitate what other people do when solving problems, and, finally, you learn to do problems by doing them.

  George Polya

  Education, Math, Swimming

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

  George Polya

  Class, Important, May

  George Polya (1981). “Mathematical Discovery”, John Wiley & Sons Incorporated

• In order to solve this differential equation you look at it until a solution occurs to you.

  George Polya

  Math, Order, Looks

• 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

• The principle is so perfectly general that no particular application of it is possible.

  George Polya

  Knowledge, Math, Principles

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

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

  George Polya

  Wise, Knowledge, Science

• 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 effort it takes to see them.

  George Polya

  Independent, Ideas, Numbers

• 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”

• I am too good for philosophy and not good enough for physics. Mathematics is in between.

  George Polya

  Philosophy, Math, Not Good Enough

• 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 has two faces: it is the rigorous science of Euclid, but it is also something else. Mathematics presented in the Euclidean way appears as a systematic, deductive science; but mathematics in the making appears as an experimental, inductive science. Both aspects are as old as the science of mathematics itself.

  George Polya

  Education, Math, Two

  George Pólya (1945). “How to Solve it: A New Aspect of Mathematical Method”

• 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 serve equally all his students, future users and nonusers of mathematics, should teach problem solving so that it is about one-third mathematics and two-thirds common sense.

  George Polya

  Education, Teacher, Teaching

• 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 who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.

  George Polya

  Real, Math, Tree

• 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

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

  George Polya

  Knowledge, Math, Obvious Things

  George Pólya (1968). “Mathematical discovery: on understanding, learning, and teaching problem solving”

• If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may give the youngsters the impression that mathematics consists in proving the most obvious things in the least obvious way.

  George Polya

  Book, Obvious Things, Giving

  George Pólya (1968). “Mathematical discovery: on understanding, learning, and teaching problem solving”

• Mathematics is not a spectator sport!

  George Polya

  Sports, Math, Mathematics

• 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 be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.

  George Polya

  Expression, Order, Two

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

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