George Pólya: Quotes about understanding

George Pólya was Hungarian mathematician. Explore interesting quotes on understanding.
George Pólya: 70   quotes 2   likes

“We wish to see… the typical attitude of the scientist who uses mathematics to understand the world around us. …In the solution of a problem …there are typically three phases.”

George Pólya

Mathematical Methods in Science (1977)
Context: We wish to see... the typical attitude of the scientist who uses mathematics to understand the world around us.... In the solution of a problem... there are typically three phases. The first phase is entirely or almost entirely a matter of physics; the third, a matter of mathematics; and the intermediate phase, a transition from physics to mathematics. The first phase is the formulation of the physical hypothesis or conjecture; the second, its translation into equations; the third, the solution of the equations. Each phase calls for a different kind of work and demands a different attitude.<!--p.164

World , Mathematics , Understanding , Problem

“To write and speak correctly is certainly necessary; but it is not sufficient. A derivation correctly presented in the book or on the blackboard may be inaccessible and uninstructive, if the purpose of the successive steps is incomprehensible, if the reader or listener cannot understand how it was humanly possible to find such an argument….”

George Pólya book How to Solve It

Source: How to Solve It (1945), p. 207

Books , Understanding , Success

“Euclid's manner of exposition, progressing relentlessly from the data to the unknown and from the hypothesis to the conclusion, is perfect for checking the argument in detail but far from being perfect for making understandable the main line of the argument.”

George Pólya book How to Solve It

Source: How to Solve It (1945), p. 70

Understanding , Perfection

“If we deal with our problem not knowing, or pretending not to know the general theory encompassing the concrete case before us, if we tackle the problem "with bare hands", we have a better chance to understand the scientist's attitude in general, and especially the task of the applied mathematician.”

George Pólya

Mathematical Methods in Science (1977)

Understanding , Problem , Chance