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He completed his magnum opus , Disquisitiones Arithmeticae , in , at the age of 21—though it was not published until Gauss's intellectual abilities attracted the attention of the Duke of Brunswick , [10] [5] who sent him to the Collegium Carolinum now Braunschweig University of Technology , [10] which he attended from to , [14] and to the University of Göttingen from to Gauss was so pleased with this result that he requested that a regular heptadecagon be inscribed on his tombstone.

The stonemason declined, stating that the difficult construction would essentially look like a circle. The year was productive for both Gauss and number theory.

He discovered a construction of the heptadecagon on 30 March. On 8 April he became the first to prove the quadratic reciprocity law. This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic.

The prime number theorem , conjectured on 31 May, gives a good understanding of how the prime numbers are distributed among the integers.

On 1 October he published a result on the number of solutions of polynomials with coefficients in finite fields , which years later led to the Weil conjectures.

Gauss remained mentally active into his old age, even while suffering from gout and general unhappiness.

In , Gauss published his influential Dioptrische Untersuchungen , [19] in which he gave the first systematic analysis on the formation of images under a paraxial approximation Gaussian optics.

In , he became an associated member of the Royal Institute of the Netherlands; when that became the Royal Netherlands Academy of Arts and Sciences in , he joined as a foreign member.

In , Gauss selected the topic for Bernhard Riemann 's inaugural lecture "Über die Hypothesen, welche der Geometrie zu Grunde liegen" About the hypotheses that underlie Geometry.

Two people gave eulogies at his funeral: Gauss's son-in-law Heinrich Ewald , and Wolfgang Sartorius von Waltershausen , who was Gauss's close friend and biographer.

Highly developed convolutions were also found, which in the early 20th century were suggested as the explanation of his genius.

Gauss was a Lutheran Protestant , a member of the St. Albans Evangelical Lutheran church in Göttingen. Waldo Dunnington , described Gauss's religious views as follows:.

For him science was the means of exposing the immortal nucleus of the human soul. In the days of his full strength, it furnished him recreation and, by the prospects which it opened up to him, gave consolation.

Toward the end of his life, it brought him confidence. Gauss's God was not a cold and distant figment of metaphysics, nor a distorted caricature of embittered theology.

To man is not vouchsafed that fullness of knowledge which would warrant his arrogantly holding that his blurred vision is the full light and that there can be none other which might report the truth as does his.

For Gauss, not he who mumbles his creed, but he who lives it, is accepted. He believed that a life worthily spent here on earth is the best, the only, preparation for heaven.

Religion is not a question of literature, but of life. God's revelation is continuous, not contained in tablets of stone or sacred parchment.

A book is inspired when it inspires. The unshakeable idea of personal continuance after death, the firm belief in a last regulator of things, in an eternal, just, omniscient, omnipotent God, formed the basis of his religious life, which harmonized completely with his scientific research.

Apart from his correspondence, there are not many known details about Gauss's personal creed. Many biographers of Gauss disagree about his religious stance, with Bühler and others considering him a deist with very unorthodox views, [31] [32] [33] while Dunnington though admitting that Gauss did not believe literally in all Christian dogmas and that it is unknown what he believed on most doctrinal and confessional questions points out that he was, at least, a nominal Lutheran.

In connection to this, there is a record of a conversation between Rudolf Wagner and Gauss, in which they discussed William Whewell 's book Of the Plurality of Worlds.

In this work, Whewell had discarded the possibility of existing life in other planets, on the basis of theological arguments, but this was a position with which both Wagner and Gauss disagreed.

Later Wagner explained that he did not fully believe in the Bible, though he confessed that he "envied" those who were able to easily believe. Two religious works which Gauss read frequently were Braubach's Seelenlehre Giessen, and Süssmilch 's Gottliche Ordnung gerettet A ; he also devoted considerable time to the New Testament in the original Greek.

Gauss's religious consciousness was based on an insatiable thirst for truth and a deep feeling of justice extending to intellectual as well as material goods.

He conceived spiritual life in the whole universe as a great system of law penetrated by eternal truth, and from this source he gained the firm confidence that death does not end all.

Gauss declared he firmly believed in the afterlife , and saw spirituality as something essentially important for human beings.

Though he was not a church-goer, [39] Gauss strongly upheld religious tolerance , believing "that one is not justified in disturbing another's religious belief, in which they find consolation for earthly sorrows in time of trouble.

On 9 October , [41] Gauss married Johanna Osthoff — , and had two sons and a daughter with her. He then married Minna Waldeck — [41] [42] on 4 August , [41] and had three more children.

Gauss had six children. With Johanna — , his children were Joseph — , Wilhelmina — and Louis — With Minna Waldeck he also had three children: Eugene — , Wilhelm — and Therese — Eugene shared a good measure of Gauss's talent in languages and computation.

His mother lived in his house from until her death in Gauss eventually had conflicts with his sons. He did not want any of his sons to enter mathematics or science for "fear of lowering the family name", as he believed none of them would surpass his own achievements.

They had an argument over a party Eugene held, for which Gauss refused to pay. The son left in anger and, in about , emigrated to the United States.

Later, he moved to Missouri and became a successful businessman. Wilhelm also moved to America in and settled in Missouri, starting as a farmer and later becoming wealthy in the shoe business in St.

It took many years for Eugene's success to counteract his reputation among Gauss's friends and colleagues. Gauss was an ardent perfectionist and a hard worker.

He was never a prolific writer, refusing to publish work which he did not consider complete and above criticism. This was in keeping with his personal motto pauca sed matura "few, but ripe".

His personal diaries indicate that he had made several important mathematical discoveries years or decades before his contemporaries published them.

Scottish-American mathematician and writer Eric Temple Bell said that if Gauss had published all of his discoveries in a timely manner, he would have advanced mathematics by fifty years.

Though he did take in a few students, Gauss was known to dislike teaching. It is said that he attended only a single scientific conference, which was in Berlin in However, several of his students became influential mathematicians, among them Richard Dedekind and Bernhard Riemann.

On Gauss's recommendation, Friedrich Bessel was awarded an honorary doctor degree from Göttingen in March Before she died, Sophie Germain was recommended by Gauss to receive an honorary degree; she never received it.

Gauss usually declined to present the intuition behind his often very elegant proofs—he preferred them to appear "out of thin air" and erased all traces of how he discovered them.

Gauss supported the monarchy and opposed Napoleon , whom he saw as an outgrowth of revolution. Gauss summarized his views on the pursuit of knowledge in a letter to Farkas Bolyai dated 2 September as follows:.

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

In his doctorate in absentia, A new proof of the theorem that every integral rational algebraic function of one variable can be resolved into real factors of the first or second degree , Gauss proved the fundamental theorem of algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

Mathematicians including Jean le Rond d'Alembert had produced false proofs before him, and Gauss's dissertation contains a critique of d'Alembert's work.

Ironically, by today's standard, Gauss's own attempt is not acceptable, owing to the implicit use of the Jordan curve theorem. However, he subsequently produced three other proofs, the last one in being generally rigorous.

His attempts clarified the concept of complex numbers considerably along the way. It appears that Gauss already knew the class number formula in Piazzi could only track Ceres for somewhat more than a month, following it for three degrees across the night sky.

Then it disappeared temporarily behind the glare of the Sun. Gauss heard about the problem and tackled it. After three months of intense work, he predicted a position for Ceres in December —just about a year after its first sighting—and this turned out to be accurate within a half-degree when it was rediscovered by Franz Xaver von Zach on 31 December at Gotha , and one day later by Heinrich Olbers in Bremen.

Gauss's method involved determining a conic section in space, given one focus the Sun and the conic's intersection with three given lines lines of sight from the Earth, which is itself moving on an ellipse, to the planet and given the time it takes the planet to traverse the arcs determined by these lines from which the lengths of the arcs can be calculated by Kepler's Second Law.

This problem leads to an equation of the eighth degree, of which one solution, the Earth's orbit, is known. The solution sought is then separated from the remaining six based on physical conditions.

In this work, Gauss used comprehensive approximation methods which he created for that purpose. One such method was the fast Fourier transform.

While this method is attributed to a paper by James Cooley and John Tukey , [55] Gauss developed it as a trigonometric interpolation method.

His paper, Theoria Interpolationis Methodo Nova Tractata , [56] was only published posthumously in Volume 3 of his collected works.

This paper predates the first presentation by Joseph Fourier on the subject in Zach noted that "without the intelligent work and calculations of Doctor Gauss we might not have found Ceres again".

Though Gauss had up to that point been financially supported by his stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure mathematics to be important enough to deserve support.

Thus he sought a position in astronomy, and in was appointed Professor of Astronomy and Director of the astronomical observatory in Göttingen , a post he held for the remainder of his life.

The discovery of Ceres led Gauss to his work on a theory of the motion of planetoids disturbed by large planets, eventually published in as Theoria motus corporum coelestium in sectionibus conicis solem ambientum Theory of motion of the celestial bodies moving in conic sections around the Sun.

In , the live-action comedy film Mr. His most recent appearance was in DreamWorks Animation 's The Boss Baby , where he briefly appears on the cover of a comic book.

In the s, UPA turned its attention to television, and began producing the series Mister Magoo for the character.

The cartoons suffered from varying character designs and choppier animation, due to rushed production schedules.

Magoo's nephew Waldo voiced, as in most of the theatrical cartoons, by Jerry Hausner was seldom seen with his uncle, now appearing in his own episodes, introduced by a brief phone conversation from Magoo's point of view, which acted as a teaser.

The Waldo episodes also featured a slick-talking con man named Presley, and always ended with a return to Magoo saying, "Oh, that Waldo and Presley.

What'll they be up to next? Hee hee hee! Magoo's houseboy Cholly i. Cholly was an Asian stereotype with huge buck teeth and comically fractured English pronunciation.

Despite his stereotyped appearance and voice, he nonetheless usually plays straight man to Magoo's shenanigans, rather than being a source of humor on his own.

He is the "sane" one of the pair. His resourcefulness often saves Magoo from danger. Still other cartoons featured Tycoon Magoo, voiced by Mel Blanc , and his bumbling assistant Worcestershire.

It was the first ever animated Christmas special made for television and the first hour-long animated TV special and is considered to be a holiday classic of the s, ranking alongside A Charlie Brown Christmas and How the Grinch Stole Christmas!

Magoo , which placed Magoo as an actor in other well-known stories. In the late s, Mr. This series was made under license by the DePatie—Freleng studio, as UPA had by this time ceased in-house cartoon production.

Nickelodeon 's Weinerville anthologizes most of his shorts. Magoo was portrayed by Leslie Nielsen in a live-action Mr. Magoo feature film.

It failed to find critical or popular success, and some support groups for the disabled , including the National Federation of the Blind , protested it on behalf of the blind and sight-impaired.

A Mexican-U. Magoo helped advertise the General Electric line of products throughout the s and s, [14] sometimes under the name J.

Quincy Magoo. Magoo became the spokesman of the optical retail store Sterling Optical. Magoo also was featured in a series of commercials for Stag Beer in the s.

Also in the s, the Polaner company sold its line of preserves in jars decorated with images of Mr. Magoo which, when empty, could then be used as drinking glasses.

ASI Entertainment [16] has used Mr. Magoo cartoons to "warm up" audiences when testing television comedy pilots. Magoo's catchphrase was "Oh Magoo, you've done it again!

Magoo is an alumnus of Rutgers University , Class of The reason behind this is that his creators wanted him to be "a college alumnus who was still fired up with the old school spirit [and they felt] Rutgers was the embodiment of the 'old school tie' in America.

Another television series, simply titled Mr. Magoo , began airing in Magoo looks younger rather than being elderly and has a pet dog name Mr.

Cat because it meows who replaces McBarker. The following Mr. This page showed certain incenses, spell materials, chalks, and all sorts needed to be used.

Kit sighed. Kit worked steadily, occasionally asking for a little help with drawing a line or bringing something over. Kit was surprised at his compliance, but supposes it was to be expected.

Finally, he took a deep breath, leaned against the wall, and wiped his brow. This could take some time. Kit began his chant, and it became clear that in just a few seconds he no longer had to remember; the spell was leading.

Before long, the God and the Goddess appeared in human form. They looked like the Morphis only more perfected and elegant.

Kit came to a stop, then looked at them. He bowed. I shall do you the same curtesy of bluntness. Will you, and what is the price? The two considered him for a moment longer before the Goddess spoke in a gentle kind voice "The sacrifice as you may know serves as a reminder to the Morphis people to be at peace with the world" he paused "You may also know that the Morphis people value life, value family, as do we" she paused again, watching Kit "We have watched the promised sacrifice, Mahana, and have watched you Kristofer, we find both your spirits and hearts to be pure.

As such we shall send a new reminder of peace" she said "Your soon to be wife shall bare a child of the gods that you will raise as your own, this child will grow to be a great leader and will reunite the Morphis people and bring peace and prosperity to them again.

It is your duty Kristofer and Mahanas to protect this child from the devils that will try to destroy it". He looked down. These are our terms" the God spoke.

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