Gauss Quotes

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

Mathematics is the queen of the sciences

He is like the fox, who effaces his tracks in the sand with his tail. {Describing the writing style of famous mathematician Carl Friedrich Gauss}

The moral high ground is a lovely place. It won’t stop a missile, though. It won’t alter the trajectory of a gauss round.

Life stands before me like an eternal spring with new and brilliant clothes.

I have had my results for a long time: but I do not yet know how I am to arrive at them.

Thou, nature, art my goddess; to thy laws my services are bound... {His second motto, from King Lear by Shakespeare}

Unless you are as smart as Johann Karl Friedrich Gauss, savvy as a half-blind Calcutta bootblack, tough as General William Tecumseh Sherman, rich as the Queen of England, emotionally resilient as a Red Sox fan, and as generally able to take care of yourself as the average nuclear missile submarine commander, you should never have been allowed near this document.

Few, But Pure.

The importance of C.F. Gauss for the development of modern physical theory and especially for the mathematical fundament of the theory of relativity is overwhelming indeed; also his achievement of the system of absolute measurement in the field of electromagnetism. In my opinion it is impossible to achieve a coherent objective picture of the world on the basis of concepts which are taken more or less from inner psychological experience.

There have been only three epoch-making mathematicians, Archimedes, Newton, and Eisenstein.

communication engineering began with Gauss, Wheatstone, and the first telegraphers.

It’s your life story if you’re a mathematician: every time you discover something neat, you discover that Gauss or Newton knew it in his crib.

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method—more daring than anything that the history of philosophy records—of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

Nobody ever looks in the mirror and says, “Let’s face it, I’m smarter than Gauss.” And yet, in the last hundred years, the joined effort of all these dummies-compared-to-Gauss has produced the greatest flowering of mathematical knowledge the world has ever seen.

The best that Gauss has given us was likewise an exclusive production. If he had not created his geometry of surfaces, which served Riemann as a basis, it is scarcely conceivable that anyone else would have discovered it. I do not hesitate to confess that to a certain extent a similar pleasure may be found by absorbing ourselves in questions of pure geometry.

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.

Mathematics is the queen of the sciences.

Pauca sed matura. (Few, but ripe.)

The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the abysses …

In describing the honourable mission I charged him with, M. Pernety informed me that he made my name known to you. This leads me to confess that I am not as completely unknown to you as you might believe, but that fearing the ridicule attached to a female scientist, I have previously taken the name of M. LeBlanc in communicating to you those notes that, no doubt, do not deserve the indulgence with which you have responded. {Explaining her use of a male pseudonym in a letter to Carl Friedrich Gauss, 1807}

I know this may sound like an excuse," he said. "But tensor functions in higher differential topology, as exemplified by application of the Gauss-Bonnett Theorem to Todd Polynomials, indicate that cohometric axial rotation in nonadiabatic thermal upwelling can, by random inference derived from translational equilibrium aggregates, array in obverse transitional order the thermodynamic characteristics of a transactional plasma undergoing negative entropy conversions." "Why don't you just shut up," said Hardesty.

As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics.

A mile from the sea, where pines give way to dusty poplars, is an isolated railroad stop, whence one June morning in 1925 a victoria brought a woman and her daughter down to Gausse's Hotel. The mother's face was of a fading prettiness that

{In a letter to his friend Rudolf Wagner} I believe you are more believing in the Bible than I. I am not.

For other great mathematicians or philosophers, he used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus.

The ‘real’ mathematics of the ‘real’ mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Riemann, is almost wholely ‘useless’ (and this is true of ‘applied’ as of ‘pure’ mathematics). It is not possible to justify the life of any genuine professional mathematician on the ground of the ‘utility’ of his work.… The great modern achievements of applied mathematics have been in relativity and quantum mechanics, and these subjects are, at present at any rate, almost as ‘useless’ as the theory of numbers. It

È bizzarro e ingiusto, disse Gauss, il fatto che si nasce in una determinata epoca e, volenti o nolenti, vi si resta imprigionati: un esempio calzante della penosa accidentalità dell'esistenza. Così uno ha un vantaggio spropositato rispetto al passato e diventa lo zimbello del futuro.

Insa, cand au trecut de primele suburbii ale Berlinului si Humboldt si-a inchipuit cum Gauss a cercetat corpurile ceresti prin telescopul sau in tot acest timp - corpuri ceresti ale caror orbite pot fi descrise in formule simple -, n-a mai fost in stare sa spuna care dintre ei doi a ramas acasa si care a colindat lumea.

...and his analysis proved him to be the first of theoretical astronomers no less than the greatest of 'arithmeticians.

And the moral high ground is a lovely place,” Marwick said, as if he were agreeing. “It won’t stop a missile, though. It won’t alter the trajectory of a gauss round. What

Základní věta algebry se tak nejmenuje náhodou, opravdu základní je. Ve svých pamětech Gauss poznamenal, že při jejím objevu (ako končíci student ve 22 letech) "pocítil mírnou radost".

In other words, our conscious representations are sometimes ordered (or arranged in a pattern) before they have become conscious to us. The 18th-century German mathematician Karl Friedrich Gauss gives an example of an experience of such an unconscious order of ideas: He says that he found a certain rule in the theory of numbers "not by painstaking research, but by the Grace of God, so to speak. The riddle solved itself as lightning strikes, and I myself could not tell or show the connection between what I knew before, what I last used to experiment with, and what produced the final success." The French scientist Henri Poincare is even more explicit about this phenomenon; he describes how during a sleepless night he actually watched his mathematical representations colliding in him until some of them "found a more stable connection. One feels as if one could watch one's own unconscious at work, the unconscious activity partially becoming manifest to consciousness without losing its own character. At such moments one has an intuition of the difference between the mechanisms of the two egos.

I confess that Fermat's Theorem as an isolated proposition has very little interest for me, for a multitude of such theorems can easily be set up, which one could neither prove nor disprove. But I have been stimulated by it to bring our again several old ideas for a great extension of the theory of numbers. Of course, this theory belongs to the things where one cannot predict to what extent one will succeed in reaching obscurely hovering distant goals. A happy star must also rule, and my situation and so manifold distracting affairs of course do not permit me to pursue such meditations as in the happy years 1796-1798 when I created the principal topics of my Disquisitiones arithmeticae. But I am convinced that if good fortune should do more than I expect, and make me successful in some advances in that theory, even the Fermat theorem will appear in it only as one of the least interesting corollaries. {In reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. The hope Gauss expressed for his success was never realised.}

I had better say something here about this question of age, since it is particularly important for mathematicians. No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game. To take a simple illustration at a comparatively humble level, the average age of election to the Royal Society is lowest in mathematics. We can naturally find much more striking illustrations. We may consider, for example, the career of a man who was certainly one of the world's three greatest mathematicians. Newton gave up mathematics at fifty, and had lost his enthusiasm long before; he had recognized no doubt by the time he was forty that his greatest creative days were over. His greatest idea of all, fluxions and the law of gravitation, came to him about 1666 , when he was twentyfour—'in those days I was in the prime of my age for invention, and minded mathematics and philosophy more than at any time since'. He made big discoveries until he was nearly forty (the 'elliptic orbit' at thirty-seven), but after that he did little but polish and perfect. Galois died at twenty-one, Abel at twenty-seven, Ramanujan at thirty-three, Riemann at forty. There have been men who have done great work a good deal later; Gauss's great memoir on differential geometry was published when he was fifty (though he had had the fundamental ideas ten years before). I do not know an instance of a major mathematical advance initiated by a man past fifty. If a man of mature age loses interest in and abandons mathematics, the loss is not likely to be very serious either for mathematics or for himself.

Debido a la clásica perfección de su estilo, las Disquisitiones eran de asimilación algo lenta, y cuando, al fin, algunos jóvenes de talento comenzaron a estudiar la obra profundamente, no pudieron adquirir ejemplares a consecuencia de la quiebra del editor. El mismo Eisenstein, discípulo favorito de Gauss, jamás tuvo un ejemplar.

Anlamını kavrayamadığın bir söz olmaz mı? -Olmaz! Pascal, Newton, Leibniz, Gauss, August Comte… Daha sayayım mı? Kısacası dünyada ne kadar gerçeğe benzer pozitif bir şey meydana koymuş bilgin, filozof varsa niçin hepsi matematikçidir? Çünkü fikirler soyuttur. Dünyada hiçbir fikir yoktur ki matematiğin soyutlama çerçevesinin dışında kalsın.

the queen of science is mathematics and the queen of mathematics is arithmetic

Ze všeho nejvíce Gausse rozčilovaly stále nové a nové pokusy různých geometrů dokázat pátý postulát. Nyní, když znal nový geometrický svět, když do něj bezpečně nahlížel, odhaloval v těchto domnělých důkazech chybu vždy hned při prvním pohledu. Jasně viděl, jak geometři tápají v tmách, jak plýtvají silami na těchto beznadějných pokusech - a pomoci jim nemohl; nesměl.

The great masters of modern analysis are Lagrange, Laplace, and Gauss, who were contemporaries. It is interesting to note the marked contrast in their styles. Lagrange is perfect both in form and matter, he is careful to explain his procedure, and though his arguments are general they are easy to follow. Laplace on the other hand explains nothing, is indifferent to style, and, if satisfied that his results are correct, is content to leave them either with no proof or with a faulty one. Gauss is as exact and elegant as Lagrange, but even more difficult to follow than Laplace, for he removes every trace of the analysis by which he reached his results, and studies to give a proof which while rigorous shall be as concise and synthetical as possible.

[On scientist Carl Friedrich Gauss] [Carl Friedrich] Gauss told his friend Rudolf Wagner, a professor of biology at Gottingen University, that he did not believe in the Bible but that he had meditated a great deal on the future of the human soul and speculated on the possibility of the soul being reincarnated on another planet. Evidently, Gauss was a Deist with a good deal of skepticism concerning religion.

As we have seen with reference to the experiences of Gauss and Poincare, the mathematicians also discovered the fact that our representations are "ordered" before we become aware of them. B.L. van der Waerden, who cites many examples of essential mathematical insights arising from the unconscious, concludes: "...the unconscious is not only able to associate and combine, but even to judge. The judgment of the unconscious is an intuitive one, but it is under favorable circumstances completely sure.

Certain opponents of Marxism dismiss it as an outworn economic dogma based upon 19th century prejudices. Marxism never was a dogma. There is no reason why its formulation in the 19th century should make it obsolete and wrong, any more than the discoveries of Gauss, Faraday and Darwin, which have passed into the body of science... The defense generally given is that the Gita and the Upanishads are Indian; that foreign ideas like Marxism are objectionable. This is generally argued in English the foreign language common to educated Indians; and by persons who live under a mode of production (the bourgeois system forcibly introduced by the foreigner into India.) The objection, therefore seems less to the foreign origin than to the ideas themselves which might endanger class privilege. Marxism is said to be based upon violence, upon the class-war in which the very best people do not believe nowadays. They might as well proclaim that meteorology encourages storms by predicting them. No Marxist work contains incitement to war and specious arguments for senseless killing remotely comparable to those in the divine Gita.

Grossmann went home to think about the question. After consulting the literature, he came back to Einstein and recommended the non-Euclidean geometry that had been devised by Bernhard Riemann.11 Riemann (1826–1866) was a child prodigy who invented a perpetual calendar at age 14 as a gift for his parents and went on to study in the great math center of Göttingen, Germany, under Carl Friedrich Gauss, who had been pioneering the geometry of curved surfaces. This was the topic Gauss assigned to Riemann for a thesis, and the result would transform not only geometry but physics.

Maiha “Allow me to introduce you to the Children of Mars. On lead guitar and eight barreled Calliope Gatlin, Colonel Fujiyama. On bass and manning the double-barreled thirty millimeter PPC's we have Major Howard. Singing backup and key boards we have Fight Captain Benz with a lovely ten millimeter rapid fire gauss rifle. Her lovely partner Captain Martin on drums with her ten millimeter Hell-bore pulse laser rifle. And singing lead and front man, a true artist with a bang from the Castile sniper rifle, our Big Daddy, Papa of Death and Destruction, the one, the only, the man, the myth, the legend, Lord James Nakatoma- Bailey.” When I finished Alice was giggling out loud.

What you learn after a long time in math-and I think the lesson applies much more broadly-is that there's always somebody ahead of you, whether they're right there in class with you or not. People just starting out look to people with good theorems, people with some good theorems look to people with lots of good theorems, people with lots of good theorems look to people with Fields Medals, people with Fields Medals look to the "inner circle" Medalists, and those people can always look toward the dead. Nobody ever looks in the mirror and says, "Let's face it, I'm smarter than Gauss." And yet, in the last hundred years, the joined effort of all these dummies-compared-to-Gauss has produced the greatest flowering of mathematical knowledge the world has ever seen.

Unless you are as smart as Johann Karl Friedrich Gauss, savvy as a half-blind Calcutta bootblack, tough as General William Tecumseh Sherman, rich as the Queen of England, emotionally resilient as a Red Sox fan, and as generally able to take care of yourself as the average nuclear missile submarine commander, you should never have been allowed near this document. Please dispose of it as you would any piece of high-level radioactive waste and then arrange with a qualified surgeon to amputate your arms at the elbows and gouge your eyes from their sockets. This warning is necessary because once, a hundred years ago, a little old lady in Kentucky put a hundred dollars into a dry goods company which went belly-up and only returned her ninety-nine dollars. Ever since then the government has been on our asses. If you ignore this warning, read on at your peril--you are dead certain to lose everything you've got and live out your final decades beating back waves of termites in a Mississippi Delta leper colony

One method that Einstein employed to help people visualize this notion was to begin by imagining two-dimensional explorers on a two-dimensional universe, like a flat surface. These “flatlanders” can wander in any direction on this flat surface, but the concept of going up or down has no meaning to them. Now, imagine this variation: What if these flatlanders’ two dimensions were still on a surface, but this surface was (in a way very subtle to them) gently curved? What if they and their world were still confined to two dimensions, but their flat surface was like the surface of a globe? As Einstein put it, “Let us consider now a two-dimensional existence, but this time on a spherical surface instead of on a plane.” An arrow shot by these flatlanders would still seem to travel in a straight line, but eventually it would curve around and come back—just as a sailor on the surface of our planet heading straight off over the seas would eventually return from the other horizon. The curvature of the flatlanders’ two-dimensional space makes their surface finite, and yet they can find no boundaries. No matter what direction they travel, they reach no end or edge of their universe, but they eventually get back to the same place. As Einstein put it, “The great charm resulting from this consideration lies in the recognition that the universe of these beings is finite and yet has no limits.” And if the flatlanders’ surface was like that of an inflating balloon, their whole universe could be expanding, yet there would still be no boundaries to it.10 By extension, we can try to imagine, as Einstein has us do, how three-dimensional space can be similarly curved to create a closed and finite system that has no edge. It’s not easy for us three-dimensional creatures to visualize, but it is easily described mathematically by the non-Euclidean geometries pioneered by Gauss and Riemann. It can work for four dimensions of spacetime as well. In such a curved universe, a beam of light starting out in any direction could travel what seems to be a straight line and yet still curve back on itself. “This suggestion of a finite but unbounded space is one of the greatest ideas about the nature of the world which has ever been conceived,” the physicist Max Born has declared.

It is a common misconception, in the spirit of the sentiments expressed in Q16, that Godel's theorem shows that there are many different kinds of arithmetic, each of which is equally valid. The particular arithmetic that we may happen to choose to work with would, accordingly, be defined merely by some arbitrarily chosen formal system. Godel's theorem shows that none of these formal systems, if consistent, can be complete; so-it is argued-we can keep adjoining new axioms, according to our whim, and obtain all kinds of alternative consistent systems within which we may choose to work. The comparison is sometimes made with the situation that occurred with Euclidean geometry. For some 21 centuries it was believed that Euclidean geometry was the only geometry possible. But when, in the eighteenth century, mathematicians such as Gauss, Lobachevsky, and Bolyai showed that indeed there are alternatives that are equally possible, the matter of geometry was seemingly removed from the absolute to the arbitrary. Likewise, it is often argued, Godel showed that arithmetic, also, is a matter of arbitrary choice, any one set of consistent axioms being as good as any other.

Before I walked into the door, the room got shades darker as a cloud did a summersault in front of the sun. I turned my head up to the sky and saw Gauss in the glass smirking down at me. In that moment I was reminded of a story about Gauss. 
 When he was in the fifth grade, his teacher wanted some quiet, so he asked his class to add up all the numbers from 1-100. Thinking he had plenty of time to relax, he was shocked that within minutes Gauss had an answer. Gauss had cleverly noticed that the numbers 1 and 100 added up to 101, and 2 and 99 also added up to 101 and on down until you hit 50 and 51. So there are 50 pairs of 101, and a simple multiplication problem by Gauss left his teacher perplexed.
 The recollection of this story reminded me about my own fifth grade experience. Thor was the volunteer at my school for the “Math Superstar” program. After each assignment, stars of various colors signifying degrees of excellence were stuck on all the papers handed in. Like the Olympics, gold was the highest honor. 
 Wendy, the girl who sat next to me, was baffled that no matter how many wrong answers I got (usually all of them), I consistently had gold stars on my papers. She thought Thor was showing a personal bias towards me, but the truth is that I knew where he kept his boxes of stars, so I simply awarded myself what I thought I deserved. Hey, Gauss, how’s that for clever?

The house is a normal-sized house, but once you step foot in the door, you are confronted with “The Dome.” Perfectly round, this room is one continuous curved wall of books. A copper dome sits on top with four stained glass windows fitted tight to allow for natural light to stream in. The four stained glass windows offer portraits of the four greatest mathematicians in history: Newton, Euler, Gauss, and Archimedes, though they are ordered alphabetically from left to right on the dome.

Progress in the apparently most rational of human pursuits was achieved in a highly irrational manner, epitomized by Gauss' 'I have had my solutions for a long time, but I do not yet know how I am to arrive at them'. The mind, owing to its hierarchic organization, functions on several levels at once, and often one level does not know what the other is doing; the essence of the creative act is bringing them together.

If the theory of numbers could be employed for any practical and obviously honourable purpose, if it could be turned directly to the furtherance of human happiness or the relief of human suffering, as physiology and even chemistry can, then surely neither Gauss nor any other mathematician would have been so foolish as to decry or regret such applications. But science works for evil as well as for good; and both Gauss and lesser mathematicians may be justified in rejoicing that there is one science at any rate, and that their own, whose very remoteness from ordinary human activities should keep it gentle and clean.

In my view, Euler's tranquil temperament, fairness, and generosity were integral to his greatness as a mathematician and scientist- he was never inclined to waste time and energy engaging in petty one-upmanship (like his mentor, Johann Bernoulli, who was known for getting into the eighteenth-century version of flame wars with his older brother, mathematician Jakob Bernoulli, and even with his own son, Daniel, over technical disputes), brooding about challenges to his authority (like Newton), or refusing to publish important findings because of the fear that they might be disputed (like Gauss).

Econometrics is the application of classical statistical methods to economic and financial series. The essential tool of econometrics is multivariate linear regression, an 18th-century technology that was already mastered by Gauss before 1794. Standard econometric models do not learn. It is hard to believe that something as complex as 21st-century finance could be grasped by something as simple as inverting a covariance matrix.

Perhaps Cardano's curious combination of a mystical and a scientifically rational personality allowed him to catch these first glimmerings of what developed to be one of the most powerful of mathematical conceptions. In later years, through the work of Bombelli, Coates, Euler, Wessel, Argand, Gauss, Cauchy, Weierstrass, Riemann, Levi, Lewy, and many others, the theory of complex numbers has flowered into one of the most elegant and universally applicable of mathematical structures. But not until the advent of the quantum theory, in the first quarter of this century, was a strange and all-pervasive role for complex numbers revealed at the very foundational structure of the actual physical world in which we live-nor had their profound link with probabilities been perceived before this. Even Cardano could have had no inkling of a mysterious underlying connection between his two greatest contributions to mathematics-a link that forms the very basis of the material universe at its smallest scales.

Nereden başlayacağımı bilmiyorum: tereddüt-ler içindeyim. Kimse de yardım etmiyor. Asistan başıma di-kildi. Benden iki satır fazla bilmenin gururu içinde. OysaGauss’un yanında benim gibi o da bir hiç. Farkında değil.

Educability, then, is the principal ingredient of intelligence—which means that in order to be called intelligent, machines must show that they are capable of learning. The fourth objection—“that intelligence in machinery is merely a reflection of that of its creator”—can thus be countered by recognizing its equivalence to “the view that the credit for the discoveries of a pupil should be given to his teacher. In such a case the teacher would be pleased with the success of his methods of education, but would not claim the results themselves unless he had actually communicated them to his pupil.” The student, on the other hand, can be said to be showing intelligence only once he has leaped beyond mere imitation of the teacher and done something that is at once surprising and original, as the infant Gauss did. But what kind of machine would be able to learn in this sense? [...] Indeed, at this point in the report, one begins to get the sense that Turing’s ambition is as much to knock mankind off its pedestal as to argue for the intelligence of machines. What seems to irk him, here and elsewhere, is the automatic tendency of the intellectual to grant to the human mind, merely by virtue of its humanness, a kind of supremacy.

Gauss si mise a parlare del caso, il nemico di ogni scienza, quello che lui aveva sempre voluto sconfiggere. Se si osserva da vicino, ogni evento cela l'infinita raffinatezza della trama della causalità. Se ci si tiene abbastanza lontani, si può scorgere tutto il disegno. Libertà e caso sono una questione della media distanza, un effetto dello spazio interposto. Riusciva a seguirlo? Più o meno, disse Eugen stanco, guardando l'orologio da tasca. Non era molto preciso, dovevano essere fra le tre e mezzo e le cinque del mattino. Ma le leggi della probabilità non sono vincolanti, proseguì Gauss, premendosi le mani sulla schiena dolorante. Non sono leggi di natura, sono possibili delle eccezioni. Per esempio: un intelletto così speciale come il suo, oppure le vincite ai giochi d'azzardo che, innegabilmente, finiscono sempre nelle tasche di qualche imbecille. A volte supponeva perfino che anche le leggi della fisica non fossero altro che semplici fatti statistici. In quanto tali, ammettono delle eccezioni: i fantasmi, per esempio, o la trasmissione del pensiero. Eugen domandò se stesse scherzando. Non lo so neanch'io, disse Gauss, chiuse gli occhi e si abbandonò a un sonno profondo.

Gauss sospirò. Non è giusto, disse Bartels in tono di rimprovero, che un bambino sia sempre triste. Rifletté, quell'osservazione gli sembrava interessante. Perché era triste? Forse perché vedeva la madre spegnersi lentamente. Perché il mondo si rivela molto deludente, appena ci si rende conto di quanto sia sottile la sua trama, di che rozzo tessuto sia l'illusione, e quanto raffazzonate le sue cuciture. Perché solo i segreti e l'oblio rendono la vita sopportabile. Perché non si può sopravvivere senza il sonno che strappa dalla realtà. Non riuscire a fare finta di niente è tristezza. Lo stato di veglia è tristezza. Conoscere, mio povero Bartels, è disperazione. Perché, Bartels? Perché il tempo scorre sempre via.

Gauss si alzò, sorseggiò dal suo bicchiere e disse che non si sarebbe mai aspettato di trovare qualcosa di simile alla felicità e, a essere sinceri, non è che ci credesse davvero. Aveva piuttosto l'impressione che si trattasse di un errore di calcolo, uno sbaglio di cui sperava che nessuno si sarebbe mai accorto. Prese di nuovo posto e si meravigliò degli sguardi increduli con cui gli altri lo fissavano. A bassa voce, chiese a Johanna se avesse detto qualcosa di sbagliato. Nooo, ma cosa dici, rispose lei. Era proprio il discorso che sognavo per il mio matrimonio.

Lo sapeva già, ora lui le avrebbe detto che in futuro non ci sarebbe stata alcuna differenza fra quelle regioni, che presto nessuno avrebbe mosso un dito per quello per cui adesso si sacrificava la vita. Ma tutto ciò cosa cambiava? Una certa confidenza con il futuro è una forma di codardia. Credeva davvero che la gente sarebbe diventata più intelligente? Un po' sì, rispose Gauss. Per forza di cose. Ma viviamo in questo momento! Purtroppo, disse.

Gauss spinse indietro la sedia e provò ad abituarsi all'idea di doversi risposare. Aveva dei figli e non sapeva come crescerli. Ignorava del tutto come si tenesse una casa e i servitori erano cari. Senza far rumore, aprì la porta. Di questo si tratta, pensò. Continuare a vivere anche quando tutto è finito. Disporre, organizzare, ogni giorno, ogni ora, ogni minuto. Come se avesse ancora senso. Si tranquillizzò un po' quando sentì arrivare la madre. Pensò alle stelle. Alla breve formula che riassume tutti i movimenti in una sola frase. Per la prima volta si rese conto che non l'avrebbe mai trovata. Lentamente si fece buio. Esitante, si avvicinò al telescopio.

Tutti pensano di essere artefici della propria vita. Uno crea e scopre, accumula beni, trova delle persone che ama più della propria vita, fa figli, forse intelligenti, ma forse anche cretini, vede morire le persone che ama, invecchia e rimbecillisce, si ammala e viene sepolto. Uno pensa di aver deciso tutto da solo. Solo la matematica dimostra che uno sceglie sempre le strade già battute. Tirannia, basta solo sentire la parola! Anche i prìncipi sono semplicemente poveri diavoli che vivono, soffrono e muoiono come tutti gli altri. La vera tirannia è quella delle leggi di natura. Ma è la ragione a formare le leggi!, disse Humboldt. La vecchia scemenza kantiana. Gauss scosse il capo. La ragione non forma un bel niente e capisce ben poco. Lo spazio è curvo e il tempo si dilata. Chi traccia una retta e la segue fino alla fine troverà una buona volta il suo termine. Indicò il sole basso sulla finestra. Nemmeno i raggi di quella stella che si sta spegnendo sono linee diritte. Volendo, il mondo può essere misurato, ma questo non significa affatto che ci si capisca qualcosa.

Progetti, sbuffò Gauss. Chiacchiere, piani, intrighi. Tiritere con dieci prìncipi e cento accademie prima di poter appoggiare un barometro da qualche parte. Quella non era scienza. Ah, esclamò Humboldt, e cos'era allora la scienza? Gauss tirò dalla pipa. Un uomo da solo seduto alla sua scrivania. Un foglio di carta, tutt'al più un cannocchiale davanti alla finestra con un cielo terso. E quest'uomo che non si arrende fino a quando non capisce. Forse quella era scienza.

Alla luce di una lampada a olio Gauss passava ore e ore a osservare il pendolo. Nella stanza non penetravano suoni. Così come il viaggio sul pallone con Pilâtre gli aveva mostrato cosa fosse lo spazio, adesso in qualche modo sarebbe riuscito a comprendere l'inquietudine insita nel cuore della natura. Non era necessario arrampicarsi sulle montagne o impelagarsi nella giungla. Chi osservava quell'ago guardava l'interno del mondo.

Kolmogorov – Poincaré – Gauss – Euler – Newton, are only five lives separating us from the source of our science.

[On Gauss studies on the methods of least squares] ... and he was a wizard in using it in every thinkable way.

[About Gauss studies on the methods of least squares] ... and he was a wizard in using it in every thinkable way.

The second basic function of algebra is to convert expressions into more useful ones. Gauss’s

El origen de Gauss, Príncipe de la Matemática, no era en verdad real. Hijo de padres pobres; había nacido en una miserable casucha en Brunswick, Alemania, el 30 de abril de 1777.

Dorothea se trasladó a Brunswick en 1769. Teniendo 34 años (1776) contrajo matrimonio. El año siguiente nació su hijo, cuyo nombre bautismal era Johann Friederich Carl Gauss.

Terminados sus largos cálculos, Gerhard quedó asombrado al oír que el niño le decía: "La cuenta está mal, debe ser..." Al comprobar las operaciones se pudo ver que las cifras encontradas por el pequeño Gauss eran exactas.

compró el mejor manual de Aritmética que pudo encontrar y se lo entregó a Gauss. El muchacho hojeó rápidamente el libro. "Es superior a mí, dijo Büttner, nada puedo enseñarle".

Gauss comenzó a escribir su diario científico (Notizenjournal). Éste es uno de los documentos más preciosos de la historia de la Matemática.

We tranquilized a salamander lightly, placed it on a plastic shelf be-tween the poles of a strong electromagnet, and attached electrodes to measure the EEC As we gradually increased the magnetic field strength, we saw no change—until delta waves appeared at 2,000 gauss. At 3,000 gauss, the entire BEG was composed of simple delta waves, and the animal was motionless and unresponsive to all stimuli. Moreover, as we decreased the strength of the magnetic field, normal EEG patterns returned suddenly, and the salamander regained consciousness within seconds, This was in sharp contrast to other forms of anesthesia.

we can’t use Gauss’s law here. However, since this is a conductor, we can make use of a slightly more subtle argument

La conclusion, si existía, solía ser que el mundo es el mundo y las cosas son como son. La libertad de expresión y la tolerancia eran el mejor invento desde los rifles Gauss para mantener callada a la gente.

Now it is plainly not an essential part of this method in general that the tests were made by the observation of natural objects. For the immense progress which modern mathematics has made is also to be explained by the same intense interest in testing general propositions by particular cases — only the tests were applied by means of particular demonstrations. This is observation, still, for as the great mathematician Gauss has declared — algebra is a science of the eye, only it is observation of artificial objects and of a highly recondite character.

[About Gauss' studies on the methods of least squares] ... and he was a wizard in using it in every thinkable way.

He can’t know I spent the last meditation imagining Carl Gauss whispering sweet nothings to me while he proved the existence of algebra . . . right?

Maxwell toma la ley de Gauss para el magnetismo y la electricidad, la ley de Ampere modificada y la ley de Faraday, y crea sus famosas cuatro ecuaciones. Con ellas Maxwell demuestra que electricidad y magnetismo tienen un origen común: es la fuerza electromagnética.

Bhargava says he was able to accomplish this by reading old Sanskrit manuscripts preserved by his grandfather, Purshottam Lal Bhargava, who was the head of the Sanskrit department at the University of Rajasthan. In their library reserves he found the work of seventh-century Indian mathematician Brahmagupta, and he realized, using Brahmagupta’s work, that he could crack a problem unresolved for two centuries. Essentially, when two numbers, which are both the sum of two perfect squares, are multiplied together, what is arrived at is the sum of two perfect squares. He found a generalization of this principle in Brahmagupta’s work that helped him simplify the expansive Composition Law introduced by the German Carl Friedrich Gauss in 1801.

Replying two weeks later he states his opinion of Fermat’s Last Theorem. “I am very much obliged for your news concerning the Paris prize. But 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.

He (Gauss) lives everywhere in mathematics

The 1990s might well be described as the “decade of book burnings in the name of democracy.” That the good name of democracy should be so vilely abused in this regard constitutes a scandal which would undoubtedly cause the former propaganda minister of Nazi Germany to blush with envy. In the final decade of the 20th century, thousands upon thousands of books were confiscated by the authorities and quietly consigned to destruction. The names of revisionist authors whose books have been confiscated, banned or destroyed by the authorities in the finest totalitarian tradition are Ingrid Weckert, (Feuerzeichen), American author John Sack, (Eye for an Eye), Ernst Gauss, et. al., (Foundations of Contemporary History), Serge Thion, (Historical or Political Truth? The Power of the Media: The Faurisson Case), Steffen Werner, (The Second Captivity), John C. Ball, (The Ball Report), and miscellaneous titles by Germar Rudolf, Arthur Butz, Roger Garaudy, Jürgen Graf, and Otto-Ernst Remer.

To start with, the idea of "children," in the everyday sense of the term, learning "rigorous science and mathematics" is palpably absurd.'] In the course of history a few actual children have managed the trick-Pascal, Gauss, and Galois come to mind-but such talent is as rare as that of Mozart or Mendelssohn. Even Newton was unacquainted with rigorous science and mathematics before the age of twenty!

Holy-Center-Approaching is soon to be the number one Zonal pastime. Its balmy heyday is nearly on it. Soon more champions, adepts, magicians of all ranks and orders will be in the field than ever before in the history of the game. The sun will rule all enterprise, if it be honest and sporting. The Gauss curve will herniate toward the excellent. And tankers the likes of Närrisch and Slothrop here will have already been weeded out.

Sociologia, psihologia și economia noastră - cu alte cuvinte, civilizația - par incapabile să estimeze valoarea celor care nu se remarcă. Aceștia sunt înregistrați în mediocritatea inteligenței medii a normei americane. Iată de ce ”succesul” se bucură de o importanță atât de exagerată: e singura cale de a ieși din rândurile normei. Mass-media te scoate de acolo numai ca să-ți filmeze lacrimile după o tragedie, furia, sau ca să-ți ceară părerea; după care ești aruncat înapoi în oala în care fierbe mediocritatea nediferențiată. Media poate adula, celebra, mexagera, dar nu poate imagina și de aceea nu poate să vadă. S-o spunem repede și direct: nu există mediocritatea sufletului. Cele două concepte nu se ating. Vin din lumi diferite: ”sufletul” este singular și specific; ”mediocritatea” te descrie conform statisticilor sociale - norme, curbe, date, comparații. S-ar putea să fii considerat mediocru în toate categoriile sociologice, chiar și în propriile aspirații și realizări, dar manifestarea mediocrității tale sociale are aroma ei unică în orice curbă a lui Gauss. Nu există măsură care să le cuprindă pe toate.

At last two days ago I succeeded, not by dint of painful effort but so to speak by the grace of God. As a sudden flash of light, the enigma was solved.....For my part I am unable to name the nature of the thread which connected what I previously knew with that which made my success possible.

Casi todo lo concerniente a la vida social es producto de choques y ciertos saltos raros pero trascendentales; y pese a ello, casi todo lo que se estudia sobre la vida social se centra en lo «normal», especialmente en los métodos de inferencia de la campana de Gauss, la «curva de campana», que no nos dicen casi nada. ¿Por qué? Porque la curva de campana ignora las grandes desviaciones, no las puede manejar, y sin embargo nos hace confiar en que hemos domesticado la incertidumbre. A este fraude lo denominaremos GFI, «gran fraude intelectual».

Why did Hipparchus look upward and name the stars while tens of thousands of others slept? What compelled Archimedes to calculate the mathematical properties of spirals and spheres, or Gauss to approach infinity and presume to grapple with it? They had imaginative and audacious minds, certainly. But they also had passion and energy; they took joy in discovering something new. Nature rewards the enthusiastic and curious with excitement in the chase and the thrill of discovery, rewards the intellectually playful with the exuberant pleasures of play. Exuberance in science drives exploration and sustains the quest; it brings its own Champagne to the discovery.

The lore of creativity is rife with such accounts. Carl Gauss, an eighteenth- and nineteenth-century mathematician, worked on proving a theorem for four years, with no solution. Then, one day, the answer came to him “as a sudden flash of light.” Yet he could not name the thread of thought that connected his years of hard work with that flash of insight.