Euler Quotes

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

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

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

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

I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain ... But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further - then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty. ~ Hermann Von Helmholtz

Now I will have less distraction. ~ 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

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

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

But that would mean it was originally a sideways number eight. That makes no sense at all. Unless..." She paused as understanding dawned. "You think it was the symbol for infinity?"
"Yes, but not the usual one. A special variant. Do you see how one line doesn't fully connect in the middle? That's Euler's infinity symbol. Absolutus infinitus."
"How is it different from the usual one?"
"Back in the eighteenth century, there were certain mathematical calculations no one could perform because they involved series of infinite numbers. The problem with infinity, of course, is that you can't come up with a final answer when the numbers keep increasing forever. But a mathematician named Leonhard Euler found a way to treat infinity as if it were a finite number- and that allowed him to do things in mathematical analysis that had never been done before." Tom inclined his head toward the date stone. "My guess is whoever chiseled that symbol was a mathematician or scientist."
"If it were my date stone," Cassandra said dryly, "I'd prefer the entwined hearts. At least I would understand what it means."
"No, this is much better than hearts," Tom exclaimed, his expression more earnest than any she'd seen from him before. "Linking their names with Euler's infinity symbol means..." He paused, considering how best to explain it. "The two of them formed a complete unit... a togetherness... that contained infinity. Their marriage had a beginning and end, but every day of ~ Lisa Kleypas

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

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

As Boy had once heard his father say: Your desire will tell you who you are, you can't reason with a boner – it's as simple as that! ~ Nemo 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

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

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

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

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

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

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

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

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

Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..."
Klapaucius thought, and thought some more. Finally he nodded and said:
"Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit."
"Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming:

Come, let us hasten to a higher plane,
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n,
Commingled in an endless Markov chain!

Come, every frustum longs to be a cone,
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.

In Reimann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.

I'll grant thee random access to my heart,
Thou'lt tell me all the constants of thy love;
And so we two shall all love's lemmas prove,
And in bound partition never part.

For what did Cauchy know, or Christoffel,
Or Fourier, or any Boole or Euler, ~ Stanisław Lem

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