Quotes of All Topics . Occasions . Authors
God does arithmetic.
Mathematics is the queen of the sciences.
The Infinite is only a manner of speaking.
Ask her to wait a moment - I am almost done.
Mathematicians stand on each other's shoulders.
In mathematics there are no true controversies.
Theory attracts practice as the magnet attracts iron.
Life stands before me like an eternal spring with new and brilliant clothes.
Mathematics is the queen of science, and arithmetic the queen of mathematics.
Mathematics is concerned only with the enumeration and comparison of relations.
His second motto: Thou, nature, art my goddess; to thy laws my services are bound.
You have no idea, how much poetry there is in the calculation of a table of logarithms!
I have had my results for a long time: but I do not yet know how I am to arrive at them.
There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.
I protest against the use of infinite magnitude ..., which is never permissible in mathematics.
I believe you are more believing in the Bible than I. I am not, and, you are much happier than I.
The total number of Dirichlet's publications is not large: jewels are not weighed on a grocery scale.
When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again.
The enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.
Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.
Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems.
If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries.
It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.
When a philosopher says something that is true then it is trivial. When he says something that is not trivial then it is false.
It is always noteworthy that all those who seriously study this science [the theory of numbers] conceive a sort of passion for it.
Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density.
My young friend, I wish that science would intoxicate you as much as our good Göttingen beer! Upon seeing a student staggering down a street.
I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect.
Further, the dignity of the science itself seems to require that every possible means be explored for the solution of a problem so elegant and so celebrated.
We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.
The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.
Sophie Germain proved to the world that even a woman can accomplish something in the most rigorous and abstract of sciences and for that reason would well have deserved an honorary degree.
You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length.
I have the vagary of taking a lively interest in mathematical subjects only where I may anticipate ingenious association of ideas and results recommending themselves by elegance or generality.
It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.
No contradictions will arise as long as Finite Man does not mistake the infinite for something fixed, as long as he is not led by an acquired habit of mind to regard the infinite as something bounded.
To praise it would amount to praising myself. For the entire content of the work... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years.
To such idle talk it might further be added: that whenever a certain exclusive occupation is coupled with specific shortcomings, it is likewise almost certainly divorced from certain other shortcomings.
I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of.
Mathematics is the queen of sciences and number theory is the queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but in all relations she is entitled to the first rank.
I mean the word proof not in the sense of the lawyers, who set two half proofs equal to a whole one, but in the sense of a mathematician, where half proof = 0, and it is demanded for proof that every doubt becomes impossible.
For three days now this angel, almost too heavenly for earth has been my fiancée ... Life stands before me like an eternal spring with new and brilliant colours. Upon his engagement to Johanne Osthof of Brunswick; they married 9 Oct 1805.
I am giving this winter two courses of lectures to three students, of which one is only moderately prepared, the other less than moderately, and the third lacks both preparation and ability. Such are the onera of a mathematical profession.
By explanation the scientist understands nothing except the reduction to the least and simplest basic laws possible, beyond which he cannot go, but must plainly demand them; from them however he deduces the phenomena absolutely completely as necessary.
I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.
Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible.
The higher arithmetic presents us with an inexhaustible store of interesting truths - of truths, too, which are not isolated, but stand in a close internal connection, and between which, as our knowledge increases, we are continually discovering new and sometimes wholly unexpected ties.
Sin2 φ is odious to me, even though Laplace made use of it; should it be feared that sin2 φ might become ambiguous, which would perhaps never occur, or at most very rarely when speaking of sin(φ2), well then, let us write (sin φ)2, but not sin2 φ, which by analogy should signify sin (sin φ)
...as our friend Zach has often noted, in our days those who do the best for astronomy are not the salaried university professors, but so-called dillettanti, physicians, jurists, and so forth.Lamenting the fragmentary time left to a professor has remaining after fulfilling his teaching duties.
There are problems to whose solution I would attach an infinitely greater importance than to those of mathematics, for example touching ethics, or our relation to God, or concerning our destiny and our future; but their solution lies wholly beyond us and completely outside the province of science.