# Frasi di Carl Friedrich Gauss

## Carl Friedrich Gauss

**Data di nascita:** 30. Aprile 1777**Data di morte:** 23. Febbraio 1855

Johann Carl Friedrich Gauss - è stato un matematico, astronomo e fisico tedesco, che ha dato contributi determinanti in analisi matematica, teoria dei numeri, statistica, calcolo numerico, geometria differenziale, geodesia, geofisica, magnetismo, elettrostatica, astronomia e ottica.

Talvolta definito "il Principe dei matematici" come Eulero o "il più grande matematico della modernità" , è annoverato fra i più importanti matematici della storia avendo contribuito in modo decisivo all'evoluzione delle scienze matematiche, fisiche e naturali. Definì la matematica come "la regina delle scienze".

## Frasi Carl Friedrich Gauss

### „[In risposta ai tentativi di Olbers nel 1816 a convincerlo a lavorare sul teorema di Fermat] Vi confesso che il Teorema di Fermat come proposizione isolata mi interessa veramente poco, perché potrei facilmente buttar giù una moltitudine di proposizioni del genere, che uno non possa né dimostrare né trattare.“

— Carl Friedrich Gauss

citato in Simon Singh, L'ultimo teorema di Fermat, Bur Saggi

### „The centre and the radius of this auxiliary sphere are here quite arbitrary.“

— Carl Friedrich Gauss

Context: In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere, which are the end points of the radii drawn parallel to the lines. The centre and the radius of this auxiliary sphere are here quite arbitrary. The radius may be taken equal to unity. This procedure agrees fundamentally with that which is constantly employed in astronomy, where all directions are referred to a fictitious celestial sphere of infinite radius. Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.
"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in [http://books.google.com/books?id=SYJsAAAAMAAJ& General Investigations of Curved Surfaces of 1827 and 1825] (1902)

### „The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it.“

— Carl Friedrich Gauss

Context: The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it. But when a person of that sex, that, because of our mores and our prejudices, has to encounter infinitely more obstacles and difficulties than men in familiarizing herself with these thorny research problems, nevertheless succeeds in surmounting these obstacles and penetrating their most obscure parts, she must without doubt have the noblest courage, quite extraordinary talents and superior genius.
Letter to Sophie Germain (30 April 1807) ([...]; les charmes enchanteurs de cette sublime science ne se décèlent dans toute leur beauté qu'à ceux qui ont le courage de l'approfondir. Mais lorsqu'une personne de ce sexe, qui, par nos meurs [sic] et par nos préjugés, doit rencontrer infiniment plus d'obstacles et de difficultés, que les hommes, à se familiariser avec ces recherches épineuses, sait néanmoins franchir ces entraves et pénétrer ce qu'elles ont de plus caché, il faut sans doute, qu'elle ait le plus noble courage, des talents tout à fait extraordinaires, le génie superieur.)

### „The perturbations which the motions of planets suffer from the influence other planets, are so small and so slow that they only become sensible after a long interval of time; within a shorter time“

— Carl Friedrich Gauss

Context: The perturbations which the motions of planets suffer from the influence other planets, are so small and so slow that they only become sensible after a long interval of time; within a shorter time, or even within one or several revolutions, according to circumstances, the motion would differ so little from motion exactly described, according to the laws of Kepler, in a perfect ellipse, that observations cannot show the difference. As long as this is true, it not be worth while to undertake prematurely the computation of the perturbations, but it will be sufficient to adapt to the observations what we may call an osculating conic section: but, afterwards, when the planet has been observed for a longer time, the effect of the perturbations will show itself in such a manner, that it will no longer be possible to satisfy exactly all the observations by a purely elliptic motion; then, accordingly, a complete and permanent agreement cannot be obtained, unless the perturbations are properly connected with the elliptic motion.
Theoria motus corporum coelestium... (1809) Tr. Charles Henry Davis as Theory of the Motion of the Heavenly Bodies moving about the Sun in Conic Sections (1857)

### „It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.“

— Carl Friedrich Gauss

Context: It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. [Wahrlich es ist nicht das Wissen, sondern das Lernen, nicht das Besitzen sondern das Erwerben, nicht das Da-Seyn, sondern das Hinkommen, was den grössten Genuss gewährt. ] When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again. The never-satisfied man is so strange; if he has completed a structure, then it is not in order to dwell in it peacefully, but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others.
Letter to Farkas Bolyai (2 September 1808)

### „But of all these principles ours is the most simple; by the others we should be led into the most complicated calculations.“

— Carl Friedrich Gauss

Context: The principle that the sum of the squares of the differences between the observed and computed quantities must be a minimum may, in the following manner, be considered independently of the calculus of probabilities. When the number of unknown quantities is equal to the number of the observed quantities depending on them, the former may be so determined as exactly to satisfy the latter. But when the number of the former is less than that of the latter, an absolutely exact agreement cannot be obtained, unless the observations possess absolute accuracy. In this case care must be taken to establish the best possible agreement, or to diminish as far as practicable the differences. This idea, however, from its nature, involves something vague. For, although a system of values for the unknown quantities which makes all the differences respectively less than another system, is without doubt to be preferred to the latter, still the choice between two systems, one of which presents a better agreement in some observations, the other in others, is left in a measure to our judgment, and innumerable different principles can be proposed by which the former condition is satisfied. Denoting the differences between observation and calculation by A, A’, A’’, etc., the first condition will be satisfied not only if AA + A’ A’ + A’’ A’’ + etc., is a minimum (which is our principle) but also if A4 + A’4 + A’’4 + etc., or A6 + A’6 + A’’6 + etc., or in general, if the sum of any of the powers with an even exponent becomes a minimum. But of all these principles ours is the most simple; by the others we should be led into the most complicated calculations.
Theoria motus corporum coelestium in sectionibus conicis solem ambientum (1809) Tr. Charles Henry Davis as [http://books.google.com/books?id=cspWAAAAMAAJ& Theory of the Motion of the Heavenly Bodies moving about the Sun in Conic Sections] (1857)

### „Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.“

— Carl Friedrich Gauss

Context: In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere, which are the end points of the radii drawn parallel to the lines. The centre and the radius of this auxiliary sphere are here quite arbitrary. The radius may be taken equal to unity. This procedure agrees fundamentally with that which is constantly employed in astronomy, where all directions are referred to a fictitious celestial sphere of infinite radius. Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.
"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in [http://books.google.com/books?id=SYJsAAAAMAAJ& General Investigations of Curved Surfaces of 1827 and 1825] (1902)

### „The principle that the sum of the squares of the differences between the observed and computed quantities must be a minimum may, in the following manner, be considered independently of the calculus of probabilities.“

— Carl Friedrich Gauss

Context: The principle that the sum of the squares of the differences between the observed and computed quantities must be a minimum may, in the following manner, be considered independently of the calculus of probabilities. When the number of unknown quantities is equal to the number of the observed quantities depending on them, the former may be so determined as exactly to satisfy the latter. But when the number of the former is less than that of the latter, an absolutely exact agreement cannot be obtained, unless the observations possess absolute accuracy. In this case care must be taken to establish the best possible agreement, or to diminish as far as practicable the differences. This idea, however, from its nature, involves something vague. For, although a system of values for the unknown quantities which makes all the differences respectively less than another system, is without doubt to be preferred to the latter, still the choice between two systems, one of which presents a better agreement in some observations, the other in others, is left in a measure to our judgment, and innumerable different principles can be proposed by which the former condition is satisfied. Denoting the differences between observation and calculation by A, A’, A’’, etc., the first condition will be satisfied not only if AA + A’ A’ + A’’ A’’ + etc., is a minimum (which is our principle) but also if A4 + A’4 + A’’4 + etc., or A6 + A’6 + A’’6 + etc., or in general, if the sum of any of the powers with an even exponent becomes a minimum. But of all these principles ours is the most simple; by the others we should be led into the most complicated calculations.
Theoria motus corporum coelestium in sectionibus conicis solem ambientum (1809) Tr. Charles Henry Davis as [http://books.google.com/books?id=cspWAAAAMAAJ& Theory of the Motion of the Heavenly Bodies moving about the Sun in Conic Sections] (1857)

### „In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere“

— Carl Friedrich Gauss

Context: In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere, which are the end points of the radii drawn parallel to the lines. The centre and the radius of this auxiliary sphere are here quite arbitrary. The radius may be taken equal to unity. This procedure agrees fundamentally with that which is constantly employed in astronomy, where all directions are referred to a fictitious celestial sphere of infinite radius. Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.
"Gauss's Abstract of the Disquisitiones Generales circa Superficies Curvas presented to the Royal Society of Gottingen" (1827) Tr. James Caddall Morehead & Adam Miller Hiltebeitel in [http://books.google.com/books?id=SYJsAAAAMAAJ& General Investigations of Curved Surfaces of 1827 and 1825] (1902)

### „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.“

— Carl Friedrich Gauss

Context: 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. So there are mere philologists, mere jurists, mere soldiers, mere merchants, etc. 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.
Gauss-Schumacher Briefwechsel (1862)

### „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 ½ proof = 0, and it is demanded for proof that every doubt becomes impossible.“

— Carl Friedrich Gauss

In a letter to Heinrich Wilhelm Matthias Olbers (14 May 1826), defending Chevalier d'Angos against presumption of guilt (by Johann Franz Encke and others), of having falsely claimed to have discovered a comet in 1784; as quoted in Calculus Gems (1992) by George F. Simmons

### „Believe me,... the bitterness of life, or at least of mine, which runs through it like a strand of red, and becomes less and less endurable as I grow older, is not compensated in the hundredth part by the joy of life. I will freely admit that these burdens, which to me have been so grievous, would have been lighter to many another; but our temperament is part of ourselves, given to us by the Creator with our very existence, and we have very little power to change it. I find, on the other hand, in this very consciousness of the vanity of life, which nearly all men must confess to as they draw near the end, my strongest assurance of the approach of a more beautiful metamorphosis. In this, my dear friend, let us find comfort, and endeavour to call up calmness to bear life out to the end.“

— Carl Friedrich Gauss

As quoted in Kneller, Karl Alois, Kettle, Thomas Michael, 1911.[https://archive.org/stream/christianitylead00kneluoft#page/44/mode/2up "Christianity and the leaders of modern science; a contribution to the history of culture in the nineteenth century"], Freiburg im Breisgau, p. 44-45

### „But in our opinion truths of this kind should be drawn from notions rather than from notations.“

— Carl Friedrich Gauss

About the proof of Wilson's theorem. Disquisitiones Arithmeticae (1801) Article 76