“Everyone knows that mathematics offers an excellent opportunity to learn demonstrative reasoning, but I contend also that there is no other subject in the usual curricula of the schools that affords a comparable opportunity to learn plausible reasoning. …let us learn proving, but also let us learn guessing.”
Induction and Analogy in Mathematics (1954)
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George Pólya 35
Hungarian mathematician 1887–1985Related quotes
Induction and Analogy in Mathematics (1954)
Context: The efficient use of plausible reasoning is a practical skill and it is learned... by imitation and practice.... what I can offer are only examples for imitation and opportunity for practice.
“We learn to be grateful to life. Every day it gives us the opportunity to learn something new.”
Original: Impariamo ad essere grati alla vita. Ogni giorno ci offre l'opportunità di imparare qualcosa di nuovo.
Source: prevale.net
“As one learns the language of a subject, one is also learning what the subject is.”
Language Education in a Knowledge Context (1980)
Context: As one learns the language of a subject, one is also learning what the subject is.... what we call a subject consists mostly, if not entirely, of its language. If you eliminate all the words of a subject, you have eliminated the subject.
Ch. 6 http://www.resologist.net/talent06.htm
Wild Talents (1932)
“From the errors of other nations, let us learn wisdom”
Source: Common Sense
“Anything new that we learn about the world involves plausible reasoning”
Induction and Analogy in Mathematics (1954)
Context: Demonstrative reasoning penetrates the sciences just as far as mathematics does, but it is in itself (as mathematics is in itself) incapable of yielding essentially new knowledge about the world around us. Anything new that we learn about the world involves plausible reasoning, which is the only kind of reasoning for which we care in everyday affairs.
WHO Director-General's opening remarks at the media briefing on COVID-19 - 20 March 2020 https://www.who.int/dg/speeches/detail/who-director-general-s-opening-remarks-at-the-media-briefing-on-covid-19---20-march-2020, World Health Organization.
An Old Man's Thoughts on Many Things, Of Education I
Account of his famous dream of the benzene structure, as quoted in A Life of Magic Chemistry : Autobiographical Reflections of a Nobel Prize Winner (2001) by George A. Olah, p. 54<!-- also partially quoted in Serendipity, Accidental Discoveries in Science (1989) by Royston M. Roberts , pp. 75-81 -->
Context: I was sitting writing on my textbook, but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were gamboling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold conformation; long rows sometimes more closely fitted together all twining and twisting in snake-like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the consequences of the hypothesis. Let us learn to dream, gentlemen, and then perhaps we shall learn the truth... but let us beware of publishing our dreams before they have been put to the proof by the waking understanding.