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George Pólya citáty
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George Pólya bol maďarský matematik. Zaoberal sa veľkým množstvom matematických disciplín, najmä kombinatorikou, teóriou pravdepodobnosti, komplexnou analýzou, parciálnymi diferenciálnymi rovnicami, teóriou potenciálu, teóriou čísel, matematickou fyzikou, či geometriou. Zaoberal sa tiež heuristickými metódami a teóriou vyučovania matematiky. Je autorom viacerých kníh, spomedzi ktorých je pravdepodobne najznámejšia kniha How to Solve It vydaná v roku 1945 a pojednávajúca o metódach riešenia matematických problémov. Wikipedia  

✵ 13. december 1887 – 7. september 1985
George Pólya fotka
George Pólya: 35   citátov 0   Páči sa

George Pólya: Citáty v angličtine

“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.”

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George Pólya

Mathematical Methods in Science (1977)

“\frac {dy}{dx} = \frac {\omega^2x}{g}…The first derivative, the result of the differentiation of y with respect to x, was written by Leibniz in the form
\frac {dy}{dx}…Leibniz's notation …is both extremely useful and dangerous. Today, as the concepts of limit and derivative are sufficiently clarified, the use of the notation… need not be dangerous. Yet, the situation was different in the 150 years between the discovery of calculus by Newton and Leibniz and the time of Cauchy. The derivative \frac {dy}{dx} was considered as the ratio of two "infinitely small quanitites", of the infinitesimals dy and dx. …it greatly facilitated the systematization of the rules of the calculus and gave intuitive meaning to its formulas. Yet this consideration was also obscure… it brought mathematics into disrepute… some of the best minds… such as… Berkeley, complained that calculus is incomprehensible. …\frac {dy}{dx} is the limit of a ratio of dy to dx… Once we have realized this sufficiently clearly, we may, under certain circumstances, treat \frac {dy}{dx} so as if it were a ratio… and multiply by dx to achieve the separation of variables. We get
{dy} = \frac {\omega^2x}{g}xdx”

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George Pólya

Mathematical Methods in Science (1977)

“The best of ideas is hurt by uncritical acceptance and thrives on critical examination.”

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George Pólya kniha How to Solve It

Zdroj: How to Solve It (1945), p. 100

“If we could be any mathematician in the history of the world (besides ourselves), who would we rather be? …we narrowed the choice down to Euler and Pólya, and finally settled on George Pólya because of the sheer enjoyment of mathematics that he has conveyed by so many examples.”

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George Pólya

Donald E. Knuth, comments at Pólya's 90th birthday celebration quoted by Gerald L. Alexanderson, The Random Walks of George Polya (2000)

“People tell you that wishful thinking is bad. Do not believe it, this is just one of those generally accepted errors.”

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George Pólya

Zdroj: Mathematical Discovery (Volume 1), p. 6