Carl Friedrich Gauss Quotes - Page 2

• In my opinion instruction is very purposeless for such individuals who do no want merely to collect a mass of knowledge, but are mainly interested in exercising (training) their own powers. One doesn't need to grasp such a one by the hand and lead him to the goal, but only from time to time give him suggestions, in order that he may reach it himself in the shortest way.

  Carl Friedrich Gauss

  Education, Exercise, Science

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• 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.

  Carl Friedrich Gauss

  Math, Ties, Interesting

  "Preface to Eisenstein's Mathematische Abhandlungen", Berlin, 1847.

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• I believe you are more believing in the Bible than I. I am not, and, you are much happier than I.

  Carl Friedrich Gauss

  Creer, creo

  "Carl Friedrich Gauss: Titan of Science". Book by Guy Waldo Dunnington, 1955.

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• Por fin, hace dos días, lo conseguí, no por mi esfuerzo, sino por la gracia del Señor. Como un relámpago, el enigma quedó resuelto. Soy incapaz de decir cuál fue el hilo conductor que conectó lo que sabía previamente con lo que hizo posible mi éxito.

  Carl Friedrich Gauss

  Éxito, Matemáticas, Dos

  "Círculos matemáticos al cuadrado". Libro de Howard W. Eves, 1972.

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• Pídele que espere un momento, ya casi he terminado.

  Carl Friedrich Gauss

  Divertido, ingenioso, potente

  Atribuido en "Men of Mathematics" de E. T. Bell, 1937.

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• I protest against the use of infinite magnitude ..., which is never permissible in mathematics.

  Carl Friedrich Gauss

  Use, Infinite, Mathematics

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• 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)

  Carl Friedrich Gauss

  Writing, Use, Analogies

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• 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.

  Carl Friedrich Gauss

  Education, Winter, Science

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• Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density.

  Carl Friedrich Gauss

  Density, Velocity, Mass

  Carl Friedrich Gauss (1965). “General investigations of curved surfaces”

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• [On Sophie Germain] When a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men... succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of [number theory], then without doubt she must have the noblest courage, quite extraordinary talents and superior genius.

  Carl Friedrich Gauss

  Sex, Freedom, Men

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• It is always noteworthy that all those who seriously study this science [the theory of numbers] conceive a sort of passion for it.

  Carl Friedrich Gauss

  Passion, Numbers, Study

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• Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers.

  Carl Friedrich Gauss

  Appreciation, Determination, Real

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• It may be true that people who are merely mathematicians have certain specific shortcomings; however that is not the fault of mathematics, but is true of every exclusive occupation. Likewise a mere linguist, a mere jurist, a mere soldier, a mere merchant, and so forth. One could add such idle chatter that when a certain exclusive occupation is often connected with certain specific shortcomings, it is on the other hand always free of certain other shortcomings.

  Carl Friedrich Gauss

  Science, Hands, People

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• 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.

  Carl Friedrich Gauss

  Numbers, Important, Problem

  "Disquisitiones Arithmeticae". Textbook by Carl Friedrich Gauss, Article 329, 1801.

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• That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral units, instead of positive, negative and imaginary (or even impossible), such an obscurity would have been out of the question.

  Carl Friedrich Gauss

  Squares, Views, Roots

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• 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.

  Carl Friedrich Gauss

  Spring, Angel, Science

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• Less depends upon the choice of words than upon this, that their introduction shall be justified by pregnant theorems.

  Carl Friedrich Gauss

  Choices, Justified, Introduction

  Carl Friedrich Gauss (1965). “General investigations of curved surfaces”

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• Mathematics is the queen of the sciences.

  Carl Friedrich Gauss

  Queens, Matemáticas, Aritmética

  "Gauss zum Gedächtniss". Libro de Wolfgang Sartorius von Waltershausen, 1856.

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• 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.

  Carl Friedrich Gauss

  Math, Science, Mechanic

  "Solid Shape". Book by Jan J. Koenderink, 1990.

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• His second motto: Thou, nature, art my goddess; to thy laws my services are bound.

  Carl Friedrich Gauss

  Art, Nature, Law

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• With a thousand joys I would accept a nonacademic job for which industriousness, accuracy, loyalty, and such are sufficient without specialized knowledge, and which would give a comfortable living and sufficient leisure, in order to sacrifice to my gods [mathematical research]. For example, I hope to get the editting of the census, the birth and death lists in local districts, not as a job, but for my pleasure and satisfaction.

  Carl Friedrich Gauss

  Loyalty, Jobs, Science

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• In mathematics there are no true controversies.

  Carl Friedrich Gauss

  Mathematics, Controversy

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• 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.

  Carl Friedrich Gauss

  Science, Law, Demand

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• A great part of its theories derives an additional charm from the peculiarity that important propositions, with the impress of simplicity on them, are often easily discovered by induction, and yet are of so profound a character that we cannot find the demonstrations till after many vain attempts; and even then, when we do succeed, it is often by some tedious and artificial process, while the simple methods may long remain concealed.

  Carl Friedrich Gauss

  Success, Character, Simple

  "Mathematical Circles Adieu". Book by Howard W. Eves, 1977.

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• In the last two months I have been very busy with my own mathematical speculations, which have cost me much time, without my having reached my original goal. Again and again I was enticed by the frequently interesting prospects from one direction to the other, sometimes even by will-o'-the-wisps, as is not rare in mathematic speculations.

  Carl Friedrich Gauss

  Two, One Direction, Interesting

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