George Pólya: Student

George Pólya was Hungarian mathematician. Explore interesting quotes on student.

George Pólya: 70 quotes2 likes

“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 Pólya book How to Solve It

2nd ed. (1957), p. xv
How to Solve It (1945)

“"Groping" and "muddling through" is usually described as a solution by trial and error…. a series of trials, each of which attempts to correct the error committed by the preceding and, on the whole, the errors diminished as we proceed and the successive trials come closer and closer to the desired final result…. we may wish a better characterization…"successive trials" or "successive corrections" or "successive approximations."… You use successive approximations when… looking for a word in the dictionary… A mathematician may apply the term… to a highly sophisticated procedure… to treat some very advanced problem… that he cannot treat otherwise. The term even applies to science as a whole; the scientific theories which succeed each other, each claiming a better explanation… may appear as successive approximations to the truth.
Therefore, the teacher should not discourage his students from using trial and error—on the contrary, he should encourage the intelligent use of the fundamental method of successive approximations. Yet he should convincingly show that for… many… situations, straightforward algebra is more efficient than successive approximations.”

George Pólya, Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (1962)

“For many of the stories told the final form resulted from a sort of informal psychological experiment. I discussed the subject with several different classes… Several passages… have been suggested by answers of my students, or… modified… by the reaction of my audience.”

Induction and Analogy in Mathematics (1954)

“The general or amateur student should also get a taste of demonstrative reasoning… he should acquire a standard with which he can compare alleged evidence of all sorts aimed at him in modern life.”

Induction and Analogy in Mathematics (1954)

“Why should the typical student be interested in those wretched triangles? …He is to be brought to see that without the knowledge of triangles there is not trigonometry; that without trigonometry we put back the clock millennia to Standard Darkness Time and antedate the Greeks.”

Mathematical Methods in Science (1977)