Leonhard Euler cytaty

Leonhard Euler Fotografia
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Leonhard Euler

Data urodzenia: 15. Kwiecień 1707
Data zgonu: 18. Wrzesień 1783

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Leonhard Euler – szwajcarski matematyk i fizyk; był pionierem w wielu obszarach obu tych nauk. Większą część życia spędził w Rosji i Prusach. Jest uważany za jednego z najbardziej produktywnych matematyków w historii.

Dokonał licznych odkryć w tak różnych gałęziach matematyki jak rachunek różniczkowy i całkowy oraz teoria grafów. Wniósł duży wkład w rozwój terminologii i notacji matematycznej, szczególnie trwały w dziedzinie analizy matematycznej. Jako pierwszy w historii użył na przykład pojęcia i oznaczenia funkcji. Opublikował wiele ważnych prac z zakresu mechaniki, optyki i astronomii.

Euler jest uważany za czołowego matematyka XVIII wieku i jednego z najwybitniejszych w całej historii. Oto przypisywane Laplace’owi zdanie wyrażające wpływ Eulera na matematykę:

Uczony ten należy do grona najbardziej twórczych – jego dzieła zapełniłyby 60-80 tomów kwarto.

Podobizna Eulera widnieje na szwajcarskim banknocie 10-frankowym szóstej serii; uczonego uwieczniono też na wielu szwajcarskich, niemieckich i rosyjskich znaczkach pocztowych. Na jego cześć jedna z asteroid zyskała miano „ Euler”.

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Cytaty Leonhard Euler

„Teraz mniej mnie będzie rozpraszało.“

— Leonhard Euler
gdy stracił wzrok w prawym oku; później, w 1766 roku zaćma w lewym oku spowodowała, że utracił wzrok całkowicie.

„Pani, przybywam z kraju, w którym wiesza się ludzi, gdy mówią zbyt dużo.“

— Leonhard Euler
odpowiedź, jakiej Euler udzielił pruskiej królowej, gdy spytała go, dlaczego jest tak mało rozmowny.

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„The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error.“

— Leonhard Euler
Context: It will seem a little paradoxical to ascribe a great importance to observations even in that part of the mathematical sciences which is usually called Pure Mathematics, since the current opinion is that observations are restricted to physical objects that make impression on the senses. As we must refer the numbers to the pure intellect alone, we can hardly understand how observations and quasi-experiments can be of use in investigating the nature of numbers. Yet, in fact, as I shall show here with very good reasons, the properties of the numbers known today have been mostly discovered by observation, and discovered long before their truth has been confirmed by rigid demonstrations. There are many properties of the numbers with which we are well acquainted, but which we are not yet able to prove; only observations have led us to their knowledge. Hence we see that in the theory of numbers, which is still very imperfect, we can place our highest hopes in observations; they will lead us continually to new properties which we shall endeavor to prove afterwards. The kind of knowledge which is supported only by observations and is not yet proved must be carefully distinguished from the truth; it is gained by induction, as we usually say. Yet we have seen cases in which mere induction led to error. Therefore, we should take great care not to accept as true such properties of the numbers which we have discovered by observation and which are supported by induction alone. Indeed, we should use such discovery as an opportunity to investigate more exactly the properties discovered and to prove or disprove them; in both cases we may learn something useful. Opera Omnia, ser. 1, vol. 2, p. 459 Spcimen de usu observationum in mathesi pura, as quoted by George Pólya, Induction and Analogy in Mathematics Vol. 1, Mathematics and Plausible Reasoning (1954)

„For since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear.“

— Leonhard Euler
Context: All the greatest mathematicians have long since recognized that the method presented in this book is not only extremely useful in analysis, but that it also contributes greatly to the solution of physical problems. For since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear. Wherefore there is absolutely no doubt that every effect in the universe can be explained as satisfactorily from final causes, by the aid of the method of maxima and minima, as it can from the effective causes themselves. Now there exist on every hand such notable instances of this fact, that, in order to prove its truth, we have no need at all of a number of examples; nay rather one's task should be this, namely, in any field of Natural Science whatsoever to study that quantity which takes on a maximum or a minimum value, an occupation that seems to belong to philosophy rather than to mathematics. Since, therefore, two methods of studying effects in Nature lie open to us, one by means of effective causes, which is commonly called the direct method, the other by means of final causes, the mathematician uses each with equal success. Of course, when the effective causes are too obscure, but the final causes are more readily ascertained, the problem is commonly solved by the indirect method; on the contrary, however, the direct method is employed whenever it is possible to determine the effect from the effective causes. But one ought to make a special effort to see that both ways of approach to the solution of the problem be laid open; for thus not only is one solution greatly strengthened by the other, but, more than that, from the agreement between the two solutions we secure the very highest satisfaction. introduction to De Curvis Elasticis, Additamentum I to his Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes 1744; translated on pg10-11, [https://www.dropbox.com/s/o09w82abgtftpfr/1933-oldfather.pdf "Leonhard Euler's Elastic Curves"], Oldfather et al 1933

„Of course, when the effective causes are too obscure, but the final causes are more readily ascertained, the problem is commonly solved by the indirect method“

— Leonhard Euler
Context: All the greatest mathematicians have long since recognized that the method presented in this book is not only extremely useful in analysis, but that it also contributes greatly to the solution of physical problems. For since the fabric of the universe is most perfect, and is the work of a most wise Creator, nothing whatsoever takes place in the universe in which some relation of maximum and minimum does not appear. Wherefore there is absolutely no doubt that every effect in the universe can be explained as satisfactorily from final causes, by the aid of the method of maxima and minima, as it can from the effective causes themselves. Now there exist on every hand such notable instances of this fact, that, in order to prove its truth, we have no need at all of a number of examples; nay rather one's task should be this, namely, in any field of Natural Science whatsoever to study that quantity which takes on a maximum or a minimum value, an occupation that seems to belong to philosophy rather than to mathematics. Since, therefore, two methods of studying effects in Nature lie open to us, one by means of effective causes, which is commonly called the direct method, the other by means of final causes, the mathematician uses each with equal success. Of course, when the effective causes are too obscure, but the final causes are more readily ascertained, the problem is commonly solved by the indirect method; on the contrary, however, the direct method is employed whenever it is possible to determine the effect from the effective causes. But one ought to make a special effort to see that both ways of approach to the solution of the problem be laid open; for thus not only is one solution greatly strengthened by the other, but, more than that, from the agreement between the two solutions we secure the very highest satisfaction. introduction to De Curvis Elasticis, Additamentum I to his Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes 1744; translated on pg10-11, [https://www.dropbox.com/s/o09w82abgtftpfr/1933-oldfather.pdf "Leonhard Euler's Elastic Curves"], Oldfather et al 1933

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„Madam, I have come from a country where people are hanged if they talk.“

— Leonhard Euler
In Berlin, to the Queen Mother of Prussia, on his lack of conversation in his meeting with her, on his return from Russia; as quoted in Science in Russian Culture : A History to 1860 (1963) Alexander Vucinich Variant: Madame... I have come from a country where one can be hanged for what one says.

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„It would be a considerable invention indeed, that of a machine able to mimic speech, with its sounds and articulations. … I think it is not impossible.“

— Leonhard Euler
Letter to Friederike Charlotte of Brandenburg-Schwedt (16 June 1761) Lettres à une Princesse d'Allemagne sur différentes questions de physique et de philosophie, Royer, 1788, p. 265 As quoted in An Introduction to Text-to-Speech Synthesis (2001) by Thierry Dutoit, p. 27; also<!--slightly misquoted--> in Fabian Brackhane and Jürgen Trouvain "Zur heutigen Bedeutung der Sprechmaschine Wolfgang von Kempelens" (in: Bernd J. Kröger (ed.): Elektronische Sprachsignalverarbeitung 2009, Band 2 der Tagungsbände der 20.<!--20th--> Konferenz "Elektronische Sprachsignalverarbeitung" (ESSV), Dresden: TUDpress, 2009, pp. 97–107)

„Now I will have less distraction.“

— Leonhard Euler
Upon losing the use of his right eye; as quoted in In Mathematical Circles (1969) by H. Eves

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