Gotthold Eisenstein

Ferdinand Gotthold Max Eisenstein ( born April 16, 1823 in Berlin, † October 11, 1852 ) was a German mathematician who worked primarily in number theory and elliptic functions.

Origin and Youth

He was the son of businessman and temporary plating manufacturer Johann Konstantin Eisenstein (1791-1875), born in Danzig, and by Helene Pollack (1799-1876), a native of Konigsberg, born in Berlin. A friend of the family woke up already at six year olds interest in mathematics ( "I could already understand the age of six the proof of a proposition. "). He was also musically interested, he played the piano and composed. After attending the preschool, he was sent to a boarding school outside of Berlin because of his poor health. In more rural Charlottenburg he attended from 1833 to 1837, the educational reform Cauersche Institute ( 1834 Pädagogium ), guided by the principles of Fichte and Pestalozzi's teaching and educational institution. 1837 to 1842 he was at the Friedrich- Wilhelm- Gymnasium or Friedrich Werder Gymnasium. From 1840 he attended lectures by Dirichlet at the University of Berlin. At high school, he was encouraged by the teacher Karl Heinrich Schell Bach, he read the works of Euler, Lagrange and Gauss. 1840 moved the father to England, but could never get a foothold. In the summer of 1842 he Eisenstein followed with the mother. They moved through England, Wales and Ireland. In Liverpool, his piano playing aroused admiration. He also studied at this time, Gauss's main work on number theory, the Disquisitiones. In Dublin he met the famous mathematician and physicist William Rowan Hamilton, who sent along to him a work on Abel's equation theory for the publication in Berlin. In mid-June 1843 he was back in Berlin, where his parents lived separately from now on. Eisenstein draws from 1843 until his death sixteen times in Berlin around, and living apart from the mother from 1846. 1843 presented the mother for him a request for assistance. He made the external High School, where he already then made ​​his " hypochondriac mood " attentive in his CV for mandatory and otherwise referred to recommendations of Dirichlet, Hamilton, Jacobi and the astronomer and secretary of the Berlin Academy Johann Franz Encke. In October he enrolled at the University of Berlin.

Study

January 1844 he filed a separate work on cubic forms in two variables with Leopold Crelle for publication, published in the journal most of his work. About him he learned in March 1844 Alexander von Humboldt know who promoted him, joined with him in exchange of letters and made numerous entries for him. He has received numerous grants from now on, the king and the Ministry of Culture and the Academy: a total of 5300 dollars, on average 250 dollars a year, which he left another 500 dollars to his parents after his death. However, the entries had to be replaced every two to three years. At the invitation of Gauss, who praised the work sent to him, he was in June in Göttingen. There he became friends with the mathematician Moritz Stern. Simultaneously published in Volume 27 and 28 of Crelle Journal 1844 25 works by him (specifically, 23, and 2 problems ), which got acquainted him with one blow. They concerned the cubic and biquadratic reciprocity law ( Gauss published in the Disquisitiones only the quadratic reciprocity ), works on cubic shapes, circular pitch, elliptic and Abelian functions. First honors followed: In 1845 he was a student in the third semester honorary doctorate from the University of Breslau, on a proposal from grief and Gauss proposed him for the Order Pour le Mérite. He made ​​the acquaintance of Leopold Kronecker, with whom he became friends. As this, however, left the university to start a career as a businessman, he is very isolated. His hypochondriac mood worsened and remained so until his death. Beginning of 1846 there was a priority dispute with Jacobi: He had not mentioned him in his work on the circular scale. Jacobi called him in a letter to Bessel a " liar and ( literary) thief ," which also had an impact on his sponsors ( Encke ) in Berlin. Gauss, however, the kargte else with praise, wrote on April 14, 1846 Humboldt that Eisenstein's talent on the kind was that " given in every century only a few " is. The 80 -year-old Humboldt tried every effort to influence acquisitions Jacobi counteract, but had been looking a different site of action and wrote to the Bavarian Crown Prince Maximilian and to Heidelberg.

Lectureship and end

1847 Habilitation Eisenstein and lectured at the University of Berlin as a Privatdozent. In the summer of 1847 there heard Bernhard Riemann Eisenstein on elliptic functions. Eisenstein wrote about Riemann: " When he was here I am literally running after him, but he seemed to avoid me," and attributed it to his own shyness and inaccessibility. In addition, he had six ( elliptic functions ) or two listeners (function theory ), and similarly in the following semesters. Eisenstein issued an anthology of his works, for the Gauss wrote the foreword.

In the revolutionary year of 1848, he attended democratic clubs, but did not mix in politics. He studied under Johannes Muller since 1847 besides medicine. In letters he complained about his isolation: Dirichlet would be very kind to him, but he felt only cold politeness. On March 19, he was Friedrich Krause and road during the barricades arrested at his house corner with the other inhabitants, because it was shot out of the house. Under mistreatment they were taken to Spandau in the citadel, but was released the next day. In this time he held at the University lectures on Analysis and mechanics.

In March 1849 Dirichlet gave a very good opinion of him for the Ministry of Culture. The ministry also asked about rumors circulating about his " moral behavior ". Apparently it was believed but rumors that he had participated in the revolution and cut his salary, which Humboldt could still partly resist, fearing a similar fate to that of Abel for him. The relationship with Crelle clouded over, as this without asking changes to its publications undertook, with whom he wanted to improve Eisenstein's style, but sometimes change the meaning of the after Eisenstein's opinion.

August 1850 applied for Dirichlet and Jacobi Eisenstein professor, but this was rejected. Officially announced to him with doubts about his teaching certificate. He was frequently ill and kept his lecture of for the few listeners partly from the bed of his room. He published his work on higher reciprocity laws and Irreduzibilitätskriterium. January 1851 he was elected member of the Berlin Academy of Sciences, after he had been proposed by Dirichlet, Jacobi and Encke. He was not included because two other candidates took the vacated seats. However, he was in 1851 appointed with grief at the suggestion of Gauss corresponding member of the Göttingen Academy of Sciences. March 1852 he was also a member of the Berlin Academy.

Having previously Niederlag in the years again and again due to illness, he suffered a hemorrhage end in July 1852 (tuberculosis ). At the instigation of Humboldt, he received 500 dollars for a one-year stay Sicily, but was too weak. He died at age 29 in October, and was buried in the cemetery at Blücherplatz. The 83 -year-old Humboldt gave him their last respects. The grave no longer exists. Humboldt was responsible for the financial support of parents who presented the letters from Humboldt to her son in 1869 available to donate proceeds from the sale for the Humboldt monument.

Work

In algebra, the Eisenstein criterion comes from him ( however, was already proved by Theodor Beautiful man). Named after him are, for example, Eisenstein numbers that Eisenstein series and the Eisenstein functions. Access to elliptic functions via Eisenstein series was later expanded by Weierstrass and Kronecker. Also on theta functions new aspects found in Eisenstein.

In number theory, he proved the cubic and biquadratic reciprocity law ( from the theory of the lemniscate ), gave a geometric proof of the quadratic reciprocity law ( Crelle Journal Vol 28, 1844, p 246) and won it the admiration of Gauss. In all of these laws is the characterization of the solutions of the respective equations ( Grade 3 and 4 ) in the " (mod p) arithmetic ." In his works on the Reziprozitätsgesetzen he is in competition with simultaneous work sorrow, whose ideal theory, he also used. He also tried to extend it to cubic forms Gauss's work on quadratic forms in the Disquisitiones.

Leopold Kronecker went on many ideas of his friend. André Weil shows in his book that the Eisenstein's theories are very relevant today.

Writings and work issues

• Mathematical treatises. Especially in the field of higher arithmetic of elliptic functions. With a preface by C. F. Gauss. Reimer, Berlin, 1847.
• Mathematical works. 2 vols. Chelsea Publ, New York, 1975, ISBN 0-8284-0280-9 (2nd edition, 1989, ISBN 0-8284-1280-4 ).