How to Solve It: A New Aspect of Mathematical Method
George Pólya
Top 10 Best Quotes
“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 first one, then the other, not both at the same time.”
“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.”
“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.”
“Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics. And what does it mean [to be] doing mathematics? In the first place, it means to be able to solve mathematical problems.”
“Nothing is more important than to see the sources of invention which are, in my opinion, more interesting than the inventions themselves.”
“It is generally useless to carry out details without having seen the main connection, or having made a sort of plan.”
“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, no more ideas than the inexperienced, but appreciates more what he has and uses it better.”
“Good problems and mushrooms of certain kinds have something in common; they grow in clusters.”
“If you cannot solve the proposed problem...try to solve first some related problem.”
“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.”
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Book Keywords:
humor, expert, stem, idea, communication, problem, math, luck, wait, brains, patience, inconspicuous, duty, style, appreciation, discovery, great, science, connection, rule, mathematics, teacher, solution, opportunity
