Euler Quotes:

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

- Pierre-Simon Laplace

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

topic: Masters, Euler

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

source: "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.

topic: Education, Wise, Perfect, Most Wise, Euler

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

- Leonhard Euler

topic: Foundation, Logic, Certainty, Euler

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

source: "Calculus Gems: Brief Lives and Memorable Mathematics". Book by George F. Simmons, 1992.

topic: Believe, Math, Order, Mathematics By Mathematicians, Euler

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

- Leonhard Euler

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

topic: Country, People, Euler

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

- Leonhard Euler

topic: Numbers, Number 2, Letters, Euler

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

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

topic: May, Statistics, Causes, Mystery Of Nature, Euler

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

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

topic: Zero, Answers, Mystery, Euler

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

topic: Regret, Numbers, Effort, Euler

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

topic: Education, Giving Up, Taken, Divergent Series, Euler

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

source: Opera Omnia, Series 1, Volume 2, 1913.

topic: Education, Opportunity, Errors, Euler

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

- Leonhard Euler

topic: World, Places In The World, Minimum, Euler

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

topic: Arise, Should, Function, Euler

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

topic: Discipline, Ignorant, Noble, Euler

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

topic: Discovery, Bridges, Principles, Euler

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

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

topic: Expression, Numbers, Variables, Euler

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

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

topic: Independent, Careers, Long, Mathematical Logic, Surprising Things

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

topic: Zero, People, Doubt, Euler

... 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

topic: Education, Book, Reading, Sunday Afternoons, Euler

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

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

topic: Essence, Skins, Depth, Skin Deep, Euler

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

topic: Education, Discovery, Philosopher, Euler

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

topic: Intelligent, Ideas, Law, Euler

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

topic: Leadership, Independent, Fields, Euler, Geometric

Too much knowledge could be a bad thing. I was lead to the Szemerédi theorem by proving a result, about squares, that Euler had already proven, and I relied on an "obvious" fact, about arithmetical progressions, that was unproved at the time. But that lead me to try and prove that formerly unproved statement- about arithmetical progressions-and that ultimately lead to the Szemerédi Theorem.

- Endre Szemeredi

topic: Science, Squares, Trying, Euler

The person who did most to give to analysis the generality and symmetry which are now its pride, was also the person who made mechanics analytical; I mean Euler.

- William Whewell

topic: Mean, Pride, Giving, Euler

Euler - The unsurpassed master of analytic invention.

- Richard Courant

source: Richard Courant (1948). “Lectures on the theory of functions”

topic: Invention, Masters, Mathematician, Analytics, Euler

Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estate of 170,587 thalers in cash and securities. Nothing is known of Gauss's investment methods.

- William Poundstone

source: William Poundstone (2010). “Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street”, p.132, Macmillan

topic: Years, Cash, Salary, Euler

In the "commentatio" (note presented to the Russian Academy) in which his theorem on polyhedra (on the number of faces, edges and vertices) was first published Euler gives no proof. In place of a proof, he offers an inductive argument: he verifies the relation in a variety of special cases. There is little doubt that he also discovered the theorem, as many of his other results, inductively.

- George Polya

topic: Discovery, Numbers, Giving, Euler

Euler calculated the force of the wheels necessary to raise the water in a reservoir ... My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry!

- Frederick The Great

topic: Vanity, Water, Wheels, Euler

I am intentionally avoiding the standard term which, by the way, did not exist in Euler's time. One of the ugliest outgrowths of the "new math" was the premature introduction of technical terms.

- George Polya

topic: Math, Discovery, Way, Euler

Euler calculated without effort, just as men breathe, as eagles sustain themselves in the air.

- Francois Arago

topic: Men, Air, Eagles, Euler