Euler's Quotes & Sayings

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

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

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

You look like Euler's equation, he murmured as he looked me up and down.
Nerd translation: Euler's equation is said to be the most perfect formula ever written. Simple but elegant. Beautiful. — Cynthia Hand

In his life of seventy-six years, Euler created enough mathematics to fill seventy-four substantial volumes, the most total pages of any mathematician. By the time all of his work had been published (and new material continued to appear for seventy-nine years after his death) it amounted to a staggering 866 items, including articles and books on the most cutting-edge topics, elementary textbooks, books for the nonscientist, and technical manuals. These figures do not account for the projected fifteen volumes of correspondence and notebooks that are still being compiled. — David S. Richeson

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

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. Poinsot 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

According to my almond-eyed little spy, the great surgeon, may his own liver rot, lied to me when he declared yesterday with a deathhead's grin that the operazione had been perfetta. Well, it had been so in the sense Euler called zero the perfect number. Actually, they ripped me open, cast one horrified look at my decayed fegato, and without touching it sewed me up again. — Vladimir Nabokov

Read Euler, read Euler, he is the master of us all. — Pierre-Simon Laplace

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

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

Euler's proof that in Konigsberg there is no path crossing all seven bridges only once was based on a simple observation. Nodes with an odd number of links must be either the starting or the end point of the journey. A continuous path that goes through all the bridges can have only one starting and one end point. Thus, such a path cannot exist on a graph that has more than two nodes with an odd number of links. As the Konigsberg graph had four such nodes, one could not find the desired path. — Albert-Laszlo Barabasi

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

"Read Euler: he is our master in everything." — Pierre-Simon Laplace

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

A thought had come to Thozan more than once: the ultimate reason we are set in this world is to break each other's hearts... — Nemo Euler

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

Euler - The unsurpassed master of analytic invention. — Richard Courant

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

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

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

Shut up about Leibniz for a moment, Rudy, because look here: You - Rudy - and I are on a train, as it were, sitting in the dining car, having a nice conversation, and that train is being pulled along at a terrific clip by certain locomotives named The Bertrand Russell and Riemann and Euler and others. And our friend Lawrence is running alongside the train, trying to keep up with us - it's not that we're smarter than he is, necessarily, but that he's a farmer who didn't get a ticket. And I, Rudy, am simply reaching out through the open window here, trying to pull him onto the fucking train with us so that the three of us can have a nice little chat about mathematics without having to listen to him panting and gasping for breath the whole way. — Neal Stephenson

In retrospect, Euler's unintended message is very simple: Graphs or networks have properties, hidden in their construction, that limit or enhance our ability to do things with them. For more than two centuries the layout of Konigsberg's graph limited its citizens' ability to solve their coffeehouse problem. But a change in the layout, the addition of only one extra link, suddenly removed this constraint. — Albert-Laszlo Barabasi

Transcendental [numbers], They transcend the power of algebraic methods. — Leonhard 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

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

Now I will have less distraction. — Leonhard Euler

When Euler died, he simply said I am finished and collapsed, to which someone in the audience muttered darkly" Another conjecture of Euler is proved — Paul Erdos

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

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

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

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

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

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

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

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