Euler Quotes

For 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.

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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Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.

Leonhard Euler

Believe, Math, Order

"Calculus Gems: Brief Lives and Memorable Mathematics". Book by 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

Masters

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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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.

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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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 a 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.

Leonhard Euler

Education, Math, Opportunity

Opera Omnia, Series 1, Volume 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

Education, Book, Reading

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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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There is a famous formula, perhaps the most compact and famous of all formulas - developed by Euler from a discovery of de Moivre: e^(i pi) + 1 = 0... It appeals equally to the mystic, the scientist, the philosopher, the mathematician.

Edward Kasner

Education, Discovery, Philosopher

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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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Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.

James Clerk Maxwell

Science, Intelligent, 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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