Euler Quotes

• Puesto que la trama del universo es perfectísima y obra de un Creador sapientísimo, nada ocurre en el universo en que no aparezca alguna regla de máximo o mínimo.

  Leonhard Euler

  Education, Wise, Perfect

  Leonhard Euler, C. Truesdell (1980). “The Rational Mechanics of Flexible Or Elastic Bodies 1638 - 1788: Introduction to Vol. X and XI”, p.200, Springer Science & Business Media

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• Logic is the foundation of the certainty of all the knowledge we acquire.

  Leonhard Euler

  Foundation, Logic, Certainty

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• Los matemáticos han intentado en vano hasta hoy descubrir algún orden en la secuencia de los números primos, y tenemos razones para creer que se trata de un misterio en el que la mente humana nunca penetrará.

  Leonhard Euler

  Creer, Matemáticas, Orden

  "Joyas del cálculo: Vidas breves y matemáticas memorables". Libro de George F. Simmons, 1992.

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

  Leonhard Euler

  Country, People, Ifs

  "Science in Russian Culture: A History to 1860". Book by Alexander Vucinich, June 1963.

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• For the sake of brevity, we will always represent this number 2.718281828459... by the letter e.

  Leonhard Euler

  Numbers, Number 2, Letters

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• Read Euler, read Euler. He is the master of us all.

  Pierre-Simon Laplace

  Másters

  Article by Gugliemo Libri in the Journal des Savants, p. 51, January 1846.

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• Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.

  Leonhard Euler

  Science, May, Statistics

  Leonhard Euler (1955). “Commentationes mechanicae ad theoriam corporum fluidorum pertinentes 2nd part”, p.80, Springer Science & Business Media

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• A quienes preguntan cuál es la cantidad infinitamente pequeña en matemáticas, les respondemos que en realidad es cero. De ahí que no haya tantos misterios ocultos en este concepto como se suele creer.

  Leonhard Euler

  Zero, Answers, Mystery

  "Fundamentals of Teaching Mathematics at University Level". Book by Benjamin Baumslag, 2000.

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• It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts.

  Adrien-Marie Legendre

  Regret, Numbers, Effort

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• Notable enough, however, are the controversies over the series 1 - 1 + 1 - 1 + 1 - ... whose sum was given by Leibniz as 1/2, although others disagree. ... Understanding of this question is to be sought in the word "sum"; this idea, if thus conceived - namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken - has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.

  Leonhard Euler

  Education, Giving Up, Taken

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• El tipo de conocimiento que sólo se apoya en observaciones y que aún no se ha demostrado debe distinguirse cuidadosamente de la verdad; se obtiene por inducción, como solemos decir. Sin embargo, hemos visto casos en los que la mera inducción conducía al error. Por lo tanto, debemos tener mucho cuidado de no aceptar como verdaderas tales propiedades de los números que hemos descubierto por observación y que se apoyan únicamente en la inducción. De hecho, deberíamos aprovechar tal descubrimiento como una oportunidad para investigar más exactamente las propiedades descubiertas y probarlas o refutarlas; en ambos casos podemos aprender algo útil.

  Leonhard Euler

  Educación, Matemáticas, Oportunidad

  Opera Omnia, Serie 1, Volumen 2, 1913.

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• Since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear ... there is absolutely no doubt that every affect in the universe can be explained satisfactorily from final causes, by the aid of the method of maxima and minima, as it can be from the effective causes themselves ... Of course, when the effective causes are too obscure, but the final causes are readily ascertained, the problem is commonly solved by the indirect method.

  Leonhard Euler

  Wise, Perfect, Doubt

  "A method for finding curved lines enjoying properties of maximum or minimum, or solution of isoperimetric problems in the broadest accepted sense". Book by Leonhard Euler, 1744.

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• Nothing takes place in the world whose meaning is not that of some maximum or minimum.

  Leonhard Euler

  World, Minimum, Maximum

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• After exponential quantities the circular functions, sine and cosine, should be considered because they arise when imaginary quantities are involved in the exponential.

  Leonhard Euler

  Education, Math, Arise

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• In the meantime, most noble Sir, you have assigned this question to the geometry of position, but I am ignorant as to what this new discipline involves, and as to which types of problem Leibniz and Wolff expected to see expressed in this way.

  Leonhard Euler

  Discipline, Ignorant, Noble

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• Thus you see, most noble Sir, how this type of solution to the Königsberg bridge problem bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.

  Leonhard Euler

  Discovery, Bridges, Principles

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• A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities.

  Leonhard Euler

  Expression, Numbers, Variables

  Leonhard Euler (2012). “Introduction to Analysis of the Infinite”, p.3, Springer Science & Business Media

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• Perhaps the most surprising thing about mathematics is that it is so surprising.

  Edward Charles Titchmarsh

  Math, Logic, Surprising

  "Mathematical Maxims and Minims". Book by Nicholas J. Rose, 1986.

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• If a nonnegative quantity was so small that it is smaller than any given one, then it certainly could not be anything but zero. To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. These supposed mysteries have rendered the calculus of the infinitely small quite suspect to many people. Those doubts that remain we shall thoroughly remove in the following pages, where we shall explain this calculus.

  Leonhard Euler

  Zero, Math, People

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• I soon found an opportunity to be introduced to a famous professor Johann Bernoulli. ... True, he was very busy and so refused flatly to give me private lessons; but he gave me much more valuable advice to start reading more difficult mathematical books on my own and to study them as diligently as I could; if I came across some obstacle or difficulty, I was given permission to visit him freely every Sunday afternoon and he kindly explained to me everything I could not understand.

  Leonhard Euler

  Educación, Libro, Lectura

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• Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence.

  Keith Devlin

  Essence, Skins, Depth

  "Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills". Book by Paul J. Nahin, 2006.

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• Hay una fórmula famosa, quizá la más compacta y famosa de todas las fórmulas, desarrollada por Euler a partir de un descubrimiento de De Moivre: e^(i pi) + 1 = 0... Atrae por igual al místico, al científico, al filósofo y al matemático.

  Edward Kasner

  Educación, Descubrimiento, Filósofo

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• Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.

  Edward Charles Titchmarsh

  Independent, Careers, Long

  "Mathematical Maxims and Minims". Book by Nicholas J. Rose, 1986.

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• Así, encontramos a Euler y a D'Alembert dedicando su talento y su paciencia al establecimiento de las leyes de rotación de los cuerpos sólidos. Lagrange ha incorporado su propio análisis del problema a su tratamiento general de la mecánica, y desde su época M. Poinsôt ha puesto el tema bajo el poder de un análisis más profundo que el del cálculo, en el que las ideas ocupan el lugar de los símbolos, y las proposiciones inteligentes sustituyen a las ecuaciones.

  James Clerk Maxwell

  Ciencia, Inteligencia, Ideas

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• It is the invaluable merit of the great Basle mathematician Leonard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics.

  Thomas Reid

  Leadership, Independent, Math

  "Mathematical Maxims and Minims". Book by Nicholas J. Rose, 1988.

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