"In the "commentatio" (note presented to the Russian……" — George Polya
"In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively."
—
George Polya
★
★
★
★
★
0.0 avg (0 ratings)
47 Quotes by George Polya
George Polya has 47 quotes on this site.
A few more worth reading:
-
Quite often, when an idea that could be helpful presents itself, we do not appreciate it, for it is so…
-
The world is anxious to admire that apex and culmination of modern mathematics: a theorem so perfectly general that no…
-
The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the…
-
The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit…
-
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for…
-
When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.
-
Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as…
-
If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try…
-
A great discovery solves a great problem, but there is a grain of discovery in the solution of any problem.…
-
Look around when you have got your first mushroom or made your first discovery: they grow in clusters.
-
The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and…
-
If the proof starts from axioms, distinguishes several cases, and takes thirteen lines in the text book ... it may…
See all 47 quotes by George Polya »
More Academy Quotes
This quote is filed under Academy Quotes,
one of 252 quotes in that category. Here are a few more:
-
There is, however, another purpose to which academies contribute. When they consist of a limited number of persons, eminent for…
— Charles Babbage
-
Soviet regime in a way deprived me from my childhood in my homeland, because my father was in military, and…
— Mikhail Baryshnikov
-
We lived, until I was 12 or so, in communal apartment with five different families and the same kitchen, in…
— Mikhail Baryshnikov
-
Academe, n.: An ancient school where morality and philosophy were taught. Academy, n.: A modern school where football is taught.
— Ambrose Bierce
-
I'm a member of the Academy, but I don't know who all the other Academy members are. It's not like…
— Albert Brooks
-
High school was interesting, because I went from a public school middle school to an academy where the first year…
— Kyle Chandler
-
Music is my life, professionally, for nearly 60 years. To be recognized by the academy is still the highest honor.
— Ray Charles
-
You've probably noticed already that I'm dressed like a grown-up... I apologize to the Academy, and I promise that I…
— Cher
-
That best academy, a mother's knee.
— James Russell Lowell
-
The manager sits down with me; I sit down with the board. We assess the success of the year. The…
— David Gill
-
Academies that are founded at public expense are instituted not so much to cultivate men's natural abilities as to restrain…
— Baruch Spinoza
-
When I am dead, let it be said of me: he belonged to no school, to no church, to no…
— Gustave Courbet
See all 252 Academy Quotes »