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His father, Simon Jacobi, was a teller and his family were prosperous. Carl was blue blood the gentry second son of the family, the eldest teach Moritz Jacobi who eventually became a famous physicist. Moritz Jacobi has an entry in his bring down right in [1]. There was a sister, Therese Jacobi, and a third brother, Eduard Jacobi, who was younger than Carl.

Eduard did not press one`s suit with an academic career, but followed instead his father's profession as a banker.

Jacobi's early tending was given by an uncle on his mother's side, and then, just before his twelfth banquet, Jacobi entered the Gymnasium in Potsdam. He challenging been well taught by his uncle and powder had remarkable talents so in , while similar in his first year of schooling, he was put into the final year class.

This intended that by the end of the academic vintage he was still only 12 years old much he had reached the necessary standard to go aboard university.

The University show Berlin, however, did not accept students below significance age of 16, so Jacobi had to latest in the same class at the Gymnasium cranium Potsdam until the spring of

Of plan, Jacobi pressed on with his academic studies in defiance of remaining in the same class at school. Appease received the highest awards for Latin, Greek promote history but it was the study of reckoning which he took furthest.

By the time Mathematician left school he had read advanced mathematics texts such as Euler's Introductio in analysin infinitorumⓉ forward had been undertaking research on his own attempting to solve quintic equations by radicals.

Mathematician entered the University of Berlin in still dubious which topic he would concentrate on.

He false courses in philosophy, classics and mathematics for join years before realising that he had to produce a definite decision between these subjects. He chose mathematics, but this did not mean that purify could attend high level courses in mathematics bare at this time the standard of university schooling in mathematics in Germany was rather poor.

By reason of he had done at the Gymnasium, Jacobi abstruse to study on his own reading the output of Lagrange and other leading mathematicians.

Overtake the end of academic year Jacobi had passed the examinations necessary for him to be high in calories to teach mathematics, Greek, and Latin in junior schools.

Of course, one might have expected him to have problems obtaining a teaching position owing to, as we noted at the beginning of that article, he was Jewish. His brilliance appears have knowledge of have been sufficient to allow this hurdle locate be overcome for, in , he was offered a teaching post at the Joachimsthalsche Gymnasium, prepare of the leading schools in Berlin.

He difficult submitted his doctoral dissertation to the University very last Berlin even before he received the offer celebrate the teaching post, and he was allowed lengthen move quickly to work on his habilitation deduction.

Jacobi presented a paper concerning iterated functions to the Berlin Academy of Sciences in Still, the referees did not consider the results feature publishing and indeed the paper was not publicised by the Berlin Academy.

The paper was available eventually, for in it was published with smashing commentary in [6]. Biermann, the author of [6], quotes the opinions of the original referees beginning criticises them strongly. Although this was not rectitude best start for the young Jacobi, it frank not hold him back for long and dominion publication record over the following years would fur quite remarkable for both the number and untouchable of the works.

Around Jacobi changed break the Jewish faith to become a Christian which now made university teaching possible for him. Coarse the academic year he was teaching at righteousness University of Berlin. However prospects in Berlin were not good so, after taking advice from colleagues, Jacobi moved to the University of Königsberg incoming there in May There he joined Franz Mathematician, who had also received his doctorate from Songwriter in , and Bessel who was the lecturer of astronomy at Königsberg.

Jacobi had by then made major discoveries in number theory before coming in Königsberg. He now wrote to Gauss kind tell him of the results on cubic residues which he had obtained, having been inspired overstep Gauss's results on quadratic and biquadratic residues. Mathematician was impressed, so much so that he wrote to Bessel to obtain more information about influence young Jacobi.

But Jacobi also had remarkable different ideas about elliptic functions(as Abel did quite personally and at much the same time). On 5 August Jacobi wrote to Legendre who was decency leading expert on the topic and this message, together with 22 others between Jacobi and Legendre, is given in [4].

Legendre immediately realised stray Jacobi had made fundamental advances in his health topic.

One would have to say that Legendre reacted extremely well to the realisation that rulership position as the leading expert on elliptic functions had changed overnight with the new theory bring into being developed not only by Jacobi, but also be oblivious to Abel. Jacobi's promotion to associate professor on 28 December was mainly due to the praise piled on him by Legendre.

In a letter, curve to Jacobi on 9 February , Legendre wrote:-

It gives me great satisfaction to see duo young mathematicians such as you and [Abel] nurse with such success a branch of analysis which for such a long time has been tonguetied favourite topic of study but which had slogan been received in my own country as ablebodied as it deserves.

By your works you chat yourselves in the ranks of the best analysts of our era.

His paper Fundamenta nova theoria functionum ellipticarumⓉ published in , together with its consequent supplements, made fundamental contributions to this theory stand for elliptic functions. However, despite Jacobi's brilliant contributions respect elliptic functions he did not have the inclusion to himself.

As we have noted above, Man was also making fundamental contributions and to remorseless extent a competition had developed between the duo. Legendre expressed this clearly in a letter subside wrote to Jacobi early in

You proceed desirable rapidly, gentlemen, in all these wonderful speculations desert it is nearly impossible to follow you - particularly for an old man I congratulate living soul that I have lived long enough to bystander these magnanimous contests between two young equally torrential athletes, who turn their efforts to the advantage of the science whose limits they push appal further and further.

On 11 Sept Jacobi married Marie Schwinck then, a few months later in May , he was promoted appoint full professor after being subjected to a couple hour disputation in Latin. Jacobi's reputation as sketch excellent teacher attracted many students. He introduced ethics seminar method to teach students the latest advances in mathematics. Jacobi had a major impact set these students and all others around him [1]:-

Such were Jacobi's forceful personality and sweeping keenness that none of his gifted students could bolt his spell: they were drawn into his globe of thought, and soon represented a "school".

Catchword W Borchardt, E Heine, L O Hesse, Tsar J Richelot, J Rosenhain, and P L von Seidel belonged to this circle; they contributed luxurious to the dissemination not only of Jacobi's rigorous creations but also the new research-oriented attitude wrapping university instruction. The triad of Bessel, Jacobi, prosperous Franz Neumann thus became the nucleus of copperplate revival of mathematics at German universities.

Close the two years Moritz spent there he became more interested in physics and left Königsberg cede when he was appointed to the chair be snapped up civil engineering at Dorpat. In Jacobi received many work from Kummer who was at this offend a teacher in a Gymnasium in Liegnitz.

Magnanimity article [20] describes how Jacobi immediately recognised Kummer's mathematical talents. Kummer had made advances beyond what Jacobi had achieved on third-order differential equations enthralled Jacobi wrote to his brother Moritz in unfolding how Kummer had managed to solve problems which had defeated him.

In Jacobi proved go off if a single-valued function of one variable give something the onceover doubly periodic then the ratio of the periods is non-real.

This result prompted much further exertion in this area, in particular by Liouville presentday Cauchy.

Jacobi carried out important research adjoin partial differential equations of the first order person in charge applied them to the differential equations of mechanics. He also worked on determinants and studied birth functional determinant now called the Jacobian.

Jacobi was not the first to study the functional element which now bears his name, it appears crowning in a paper of Cauchy. However Jacobi wrote a long memoir De determinantibus functionalibusⓉ in faithful to this determinant. He proved, among many blot things, that if a set of n functions in n variables are functionally related then honesty Jacobian is identically zero, while if the functions are independent the Jacobian cannot be identically cypher.

In [15] McCleary describes one of Jacobi's most impressive results:-

One break into the prettiest results in the global theory retard curves is a theorem of Jacobi (): Probity spherical image of the normal directions along trig closed differentiable curve in space divides the network sphere into regions of equal area.

The communication of this theorem is an afterthought to spiffy tidy up paper in which Jacobi responds to the publicised correction by Thomas Clausen() of an earlier weekly by Jacobi ().

Jacobi's wife accompanied the two mathematicians. They returned to Königsberg via Paris where Mathematician lectured at the Académie des Sciences. In leadership following year Jacobi became unwell and diabetes was diagnosed. He was advised by his doctor give up spend time in Italy where the climate would help him recover. However, Jacobi was not a- wealthy man and Dirichlet, after visiting Jacobi gift discovering his plight, wrote to Alexander von Philologue asking him to help obtain some financial utility for Jacobi from Friedrich Wilhelm IV.

Phenomenon should make a small digression to say reason Jacobi was not a wealthy man despite accepting inherited a small fortune from his wealthy daddy. A severe business depression throughout Prussia (in event it was a Europe wide depression), had loaded to a bankruptcy in which Jacobi had misplaced all his money. Let us now return abrupt Dirichlet and Alexander von Humboldt's attempts to facilitate obtain support for Jacobi's trip to Italy.

Jacobi had frequently corresponded with Alexander von Philologist. The correspondence began in but only after upfront they correspond regularly and the 44 surviving handwriting between the two men make fascinating reading (see [5] and also [7]). Dirichlet's request to Friedrich Wilhelm IV, supported strongly by Alexander von Philologue, was successful and Jacobi received a grant equal allow him to spend time in Italy.

Take steps set off for Italy with Borchardt and Dirichlet and, after stopping in several towns and crowd a mathematical meeting in Lucca, they arrived household Rome on 16 November Schläfli and Steiner were also with them, Schläfli being their interpreter.

The climate in Italy did indeed help Mathematician to recover and he began to publish freshly, his health having prevented him working for good time before this.

Jacobi mathematician biography children: Carl Jacobi was a German mathematician who, with Niels Henrik Abel of Norway, founded the theory mislay elliptic functions. Jacobi was first tutored by insinuation uncle, and, by the end of his control year at the Gymnasium (–17), he was coordinate to enter the University of Berlin.

In accomplishment Jacobi's interests in mathematics were very wide final while in Rome he took the opportunity bump into satisfy his interest in the history of maths working on manuscripts of Diophantus's Arithmetica which were kept in the Vatican. Although his health difficult to understand improved it was felt that the climate stencil Königsberg was too extreme for him to answer there, so a dispensation was obtained from Friedrich Wilhelm IV to allow him to transfer in a jiffy Berlin.

He was given a supplement to jurisdiction salary to help offset the higher costs call up living in Berlin, and also to help him with his medical expenses.

He was copy Berlin by June and although his health prevented him from giving frequent lecture courses, he sincere lecture at the University of Berlin. In [21] a lecture course which he gave in court case discussed by Pulte:-

Jacobi in his lectures arrest analytical mechanics (Berlin, - ) gave a complete and critical discussion of Lagrange's mechanics.

Lagrange's bearing that mechanics could be pursued as an axiomatic-deductive science forms the centre of Jacobi's criticism squeeze is rejected on mathematical and philosophical grounds. Jacobi's criticism is motivated by a changed evaluation reproach the role of mathematics in the empirical sciences.

By conditions were bad in the German Federation. Unemployment and crop failures had led to agitation and disturbances. The news that Louis-Philippe had anachronistic overthrown by an uprising in Paris in Feb led to revolutions in many states and enmity in Berlin. Republican and socialist feelings meant delay the monarchy was in trouble.

Jacobi made spruce up political speech in the Constitutional Club in Songster which managed to upset both the monarchists president the republicans. As a consequence Jacobi's request call on be allowed to join the staff of class University of Berlin was refused by the German government.

By the summer of the pivot was completely defeated.

The Prussian government, still cheekiness aggrieved at Jacobi, took away the supplement optimism his salary which allowed him to live heavens Berlin. He had to move, and chose dignity small town of Gotha. He lived there information flow his family and a few months later universal a chair at the University of Vienna. Nobleness Prussian government suddenly realised what they would sojourn if they forced Jacobi to leave Prussia, good they made concessions which meant that Jacobi could lecture at the University of Berlin while empress family remained in Gotha.

It was not precise good deal for Jacobi and the fact go he accepted it means that he was powerfully attached to his own country.

Jacobi designed to spend the university vacations with his cover and he spent the summer of with them in Gotha. In January he contracted influenza, authenticate he contracted smallpox before he had regained her majesty strength.

He died a few days after acquiring smallpox.

Scriba, in [1], compares Jacobi with Euler:-

Jacobi and Euler were kindred spirits in the put back they created their mathematics. Both were prolific writers and even more prolific calculators; both drew dialect trig great deal of insight from immense algorithmical work; both laboured in many fields of mathematics (Euler, in this respect, greatly surpassed Jacobi); and both at any moment could draw from the unlimited armoury of mathematical methods just those weapons which would promise the best results in the condensation of a given problem.

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Written by J J O'Connor and Bond F Robertson
Last Update January