Gotthold Eisenstein: Difference between revisions
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==Early life== |
==Early life== |
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From an early age, he demonstrated talent in [[mathematics]], and also in [[music]]. As a young child he learned to play [[piano]], and he continued to play and compose for the instrument throughout his life. |
Gotthold Maximilian Eisenstein was the last survivor of six children of a Jewish mercantile family in Berlin. From an early age, he demonstrated talent in [[mathematics]], and also in [[music]]. As a young child he learned to play [[piano]], and he continued to play and compose for the instrument throughout his life. |
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He suffered various health problems throughout his life, including [[meningitis]] as an infant, a disease which took the lives of all five of his brothers and sisters. In 1837, at the age of 14, he enrolled at Friedrich Wilhelm [[Gymnasium (school)|Gymnasium]], and soon thereafter at Friedrich Werder Gymnasium in Berlin. His teachers recognized his talents in mathematics, but by 15 years of age he had already learned all the material taught at the school, and he began to study [[differential calculus]] from the works of [[Leonhard Euler|Euler]] and [[Joseph-Louis Lagrange|Lagrange]]. |
He suffered various health problems throughout his life, including [[meningitis]] as an infant, a disease which took the lives of all five of his brothers and sisters. In 1837, at the age of 14, he enrolled at Friedrich Wilhelm [[Gymnasium (school)|Gymnasium]], and soon thereafter at Friedrich Werder Gymnasium in Berlin. His teachers recognized his talents in mathematics, but by 15 years of age he had already learned all the material taught at the school, and he began to study [[differential calculus]] from the works of [[Leonhard Euler|Euler]] and [[Joseph-Louis Lagrange|Lagrange]]. |
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==Five remarkable years== |
==Five remarkable years== |
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| ⚫ | In 1843 Eisenstein returned to Berlin, where he passed his graduation exams and enrolled in the University the following autumn. In January 1844 he had already presented his first work to the [[Berlin Academy]], on cubic forms in two variables. The same year he met for the first time with [[Alexander von Humboldt]], who would later become Eisenstein's patron. Humboldt managed to find grants from the King, the government of [[Prussia]], and the Berlin academy to compensate for Eisenstein's extreme [[poverty]]. The monies, always late and grudgingly given, were earned in full measure by Eisenstein: in 1844 alone he published over 23 papers and two problems in [[Crelle's Journal]], including two proofs of the law of [[quadratic reciprocity]], and the analogous laws of [[cubic reciprocity]] and [[Quadratic reciprocity#Generalizations|quartic (biquadratic) reciprocity]]. |
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| ⚫ | Eisenstein's papers began to appear in 1843 and came out rapidly; in a short lifetime he published 50 papers, principally in the theory of numbers and elliptic functions. In 1843 Eisenstein returned to Berlin, where he passed his graduation exams and enrolled in the University the following autumn. In January 1844 he had already presented his first work to the [[Berlin Academy]], on cubic forms in two variables. The same year he met for the first time with [[Alexander von Humboldt]], who would later become Eisenstein's patron. Humboldt managed to find grants from the King, the government of [[Prussia]], and the Berlin academy to compensate for Eisenstein's extreme [[poverty]]. The monies, always late and grudgingly given, were earned in full measure by Eisenstein: in 1844 alone he published over 23 papers and two problems in [[Crelle's Journal]], including two proofs of the law of [[quadratic reciprocity]], and the analogous laws of [[cubic reciprocity]] and [[Quadratic reciprocity#Generalizations|quartic (biquadratic) reciprocity]]. |
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| ⚫ | In June 1844 Eisenstein visited [[Carl Friedrich Gauss]] in [[Göttingen]]. In 1845, [[Ernst Eduard Kummer|Kummer]] saw to it that he received an [[honorary doctorate]] at the [[University of Breslau]]. [[Carl Gustav Jakob Jacobi|Jacobi]] also encouraged the distinction, but later relations between [[Carl Gustav Jakob Jacobi|Jacobi]] and Eisenstein were always rocky, due primarily to a disagreement over the order of discoveries made in 1846. In 1847 Eisenstein [[habilitated]] at the University of Berlin, and he began to teach there. [[Bernhard Riemann]] attended his classes on [[elliptic functions]]. |
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| ⚫ | In June 1844 Eisenstein visited [[Carl Friedrich Gauss]] in [[Göttingen]], who was literally carried away by the genius of young Eisenstein. In 1845, [[Ernst Eduard Kummer|Kummer]] saw to it that he received an [[honorary doctorate]] at the [[University of Breslau]]. [[Carl Gustav Jakob Jacobi|Jacobi]] also encouraged the distinction, but later relations between [[Carl Gustav Jakob Jacobi|Jacobi]] and Eisenstein were always rocky, due primarily to a disagreement over the order of discoveries made in 1846. In 1847 Eisenstein [[habilitated]] at the University of Berlin, and he began to teach there. [[Bernhard Riemann]] attended his classes on [[elliptic functions]]. |
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==Imprisonment and death== |
==Imprisonment and death== |
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In 1848, Eisenstein was imprisoned briefly by the [[Prussia]]n army for his revolutionary activities in Berlin. Eisenstein always had republican sympathies, and while he did not actively participate in the revolution of 1848, he was arrested on 19 March of that year. Although he was released just one day later, the harsh treatment he suffered damaged his already delicate health. But his association with the Republican cause led to his official stipends being revoked, despite Humboldt's tenaciously coming to his defense. |
In 1848, Eisenstein was imprisoned briefly by the [[Prussia]]n army for his revolutionary activities in Berlin. Eisenstein, according to his own account, merely visited the so-called "democratic clubs" several times, but did not join them during the revolution of 1848. He was only mildly involved. Eisenstein always had republican sympathies, and while he did not actively participate in the revolution of 1848, he was arrested on 19 March of that year. Although he was released just one day later, the harsh treatment he suffered damaged his already delicate health. But his association with the Republican cause led to his official stipends being revoked, despite Humboldt's tenaciously coming to his defense. |
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Despite his health, Eisenstein continued writing paper after paper on quadratic partitions of [[prime numbers]] and the laws of [[reciprocity (mathematics)|reciprocity]]. In 1851, at the instigation of Gauss, he was elected to the [[Academy of Göttingen]]; one year later, this time at the recommendation of Dirichlet, he was also elected to the [[Academy of Berlin]]. |
Eisenstein longed for companionship and did not get along well with his family. Drichlet, Jacobi, Stern, Gauss, Encke and others tried to cheer him up. Despite his health, Eisenstein continued writing paper after paper on quadratic partitions of [[prime numbers]] and the laws of [[reciprocity (mathematics)|reciprocity]]. In 1851, at the instigation of Gauss, he was elected to the [[Academy of Göttingen]]; one year later, this time at the recommendation of Dirichlet, he was also elected to the [[Academy of Berlin]]. |
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He died of [[tuberculosis]] at the age of 29. Humboldt, then 83, accompanied his remains to the cemetery. He had recently obtained, too late, as it turned out, the funding necessary to send Eisenstein on holiday to [[Sicily]]. |
He was never very healthy and was hypochondriac. He died of [[tuberculosis]] at the age of 29. Humboldt, then 83, accompanied his remains to the cemetery. He had recently obtained, too late, as it turned out, the funding necessary to send Eisenstein on holiday to [[Sicily]]. |
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[[Carl Friedrich Gauss|Gauss]] |
Gauss deeply mourned his early death. Eisenstein worshiped Gauss and Gauss looked on him almost as a son; he was his favorite mathematician. Moritz Cantor quotes [[Carl Friedrich Gauss|Gauss]] as having said, "there have been only three epoch-making mathematicians: [[Archimedes]], [[Isaac Newton|Newton]], and Eisenstein".<ref>{{cite web | title = Review of ''Archimedes: What Did He Do Besides Cry Eureka?'' |author=Sandifer, Ed| publisher =[[Mathematical Association of America]] | url = http://www.maa.org/reviews/archim.html|accessdate=2007-07-23}}</ref> Gauss's choice of Eisenstein, who specialized in [[number theory]] and [[mathematical analysis|analysis]], may seem puzzling to many, but Eisenstein proved several results that eluded even Gauss, such as the theorem on [[biquadratic reciprocity]]. |
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In another occasion when Rudolf Wagner asked Gauss if he really considers Eisenstein to be so important, Gauss replied: "Yes, One of the greatest talents of ''all'' times. He did things which give testimony of the most refined and rarest concepts". <ref>Gauss, Titan of Science, by G. Waldo Dunnington, p 308</ref> |
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== See also == |
== See also == |
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Revision as of 03:26, 28 December 2010
Ferdinand Eisenstein | |
|---|---|
| Born | April 16, 1823 |
| Died | October 11, 1852 (aged 29) |
| Nationality | German |
| Alma mater | University of Berlin |
| Scientific career | |
| Fields | Mathematics |
Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) was a German mathematician. He specialized in number theory and analysis, and proved several results that eluded even Gauss. Like Galois and Abel before him, Eisenstein died before the age of 30. He was born and died in Berlin, Germany.
Early life
Gotthold Maximilian Eisenstein was the last survivor of six children of a Jewish mercantile family in Berlin. From an early age, he demonstrated talent in mathematics, and also in music. As a young child he learned to play piano, and he continued to play and compose for the instrument throughout his life.
He suffered various health problems throughout his life, including meningitis as an infant, a disease which took the lives of all five of his brothers and sisters. In 1837, at the age of 14, he enrolled at Friedrich Wilhelm Gymnasium, and soon thereafter at Friedrich Werder Gymnasium in Berlin. His teachers recognized his talents in mathematics, but by 15 years of age he had already learned all the material taught at the school, and he began to study differential calculus from the works of Euler and Lagrange.
At 17, still a student, Eisenstein began to attend classes given by Dirichlet and others at the University of Berlin. In 1842, before taking his final exams, he traveled with his mother to England, to search for his father. In 1843 he met Hamilton in Dublin, who gave him a copy of his book on Niels Henrik Abel's proof of the impossibility of solving fifth degree polynomials, a work which would stimulate Eisenstein's interest in mathematical research.
Five remarkable years
Eisenstein's papers began to appear in 1843 and came out rapidly; in a short lifetime he published 50 papers, principally in the theory of numbers and elliptic functions. In 1843 Eisenstein returned to Berlin, where he passed his graduation exams and enrolled in the University the following autumn. In January 1844 he had already presented his first work to the Berlin Academy, on cubic forms in two variables. The same year he met for the first time with Alexander von Humboldt, who would later become Eisenstein's patron. Humboldt managed to find grants from the King, the government of Prussia, and the Berlin academy to compensate for Eisenstein's extreme poverty. The monies, always late and grudgingly given, were earned in full measure by Eisenstein: in 1844 alone he published over 23 papers and two problems in Crelle's Journal, including two proofs of the law of quadratic reciprocity, and the analogous laws of cubic reciprocity and quartic (biquadratic) reciprocity.
In June 1844 Eisenstein visited Carl Friedrich Gauss in Göttingen, who was literally carried away by the genius of young Eisenstein. In 1845, Kummer saw to it that he received an honorary doctorate at the University of Breslau. Jacobi also encouraged the distinction, but later relations between Jacobi and Eisenstein were always rocky, due primarily to a disagreement over the order of discoveries made in 1846. In 1847 Eisenstein habilitated at the University of Berlin, and he began to teach there. Bernhard Riemann attended his classes on elliptic functions.
Imprisonment and death
In 1848, Eisenstein was imprisoned briefly by the Prussian army for his revolutionary activities in Berlin. Eisenstein, according to his own account, merely visited the so-called "democratic clubs" several times, but did not join them during the revolution of 1848. He was only mildly involved. Eisenstein always had republican sympathies, and while he did not actively participate in the revolution of 1848, he was arrested on 19 March of that year. Although he was released just one day later, the harsh treatment he suffered damaged his already delicate health. But his association with the Republican cause led to his official stipends being revoked, despite Humboldt's tenaciously coming to his defense.
Eisenstein longed for companionship and did not get along well with his family. Drichlet, Jacobi, Stern, Gauss, Encke and others tried to cheer him up. Despite his health, Eisenstein continued writing paper after paper on quadratic partitions of prime numbers and the laws of reciprocity. In 1851, at the instigation of Gauss, he was elected to the Academy of Göttingen; one year later, this time at the recommendation of Dirichlet, he was also elected to the Academy of Berlin.
He was never very healthy and was hypochondriac. He died of tuberculosis at the age of 29. Humboldt, then 83, accompanied his remains to the cemetery. He had recently obtained, too late, as it turned out, the funding necessary to send Eisenstein on holiday to Sicily.
Gauss deeply mourned his early death. Eisenstein worshiped Gauss and Gauss looked on him almost as a son; he was his favorite mathematician. Moritz Cantor quotes Gauss as having said, "there have been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein".[1] Gauss's choice of Eisenstein, who specialized in number theory and analysis, may seem puzzling to many, but Eisenstein proved several results that eluded even Gauss, such as the theorem on biquadratic reciprocity. In another occasion when Rudolf Wagner asked Gauss if he really considers Eisenstein to be so important, Gauss replied: "Yes, One of the greatest talents of all times. He did things which give testimony of the most refined and rarest concepts". [2]
See also
- Eisenstein's criterion
- Eisenstein ideal
- Eisenstein integer
- Eisenstein prime
- Eisenstein series
- Eisenstein theorem
- Real analytic Eisenstein series
Publications
- Eisenstein, Gotthold (1975), Mathematische Werke (in German), New York: AMS Chelsea Publishing, ISBN 978-0-8284-1280-3, MR0427029 Weil's review
References
- ^ Sandifer, Ed. "Review of Archimedes: What Did He Do Besides Cry Eureka?". Mathematical Association of America. Retrieved 2007-07-23.
- ^ Gauss, Titan of Science, by G. Waldo Dunnington, p 308
- O'Connor, John J.; Robertson, Edmund F., "Gotthold Eisenstein", MacTutor History of Mathematics Archive, University of St Andrews
- Schappacher, Norbert (1998), "Gotthold Eisenstein. 16 April 1823--11 October 1852", Mathematics in Berlin, Basel, Boston, Berlin: Birkhäuser, pp. 55–60, MR1648677
- Warnecke, Heinz (1988), "Gotthold Eisenstein (1823--1852)---ein mathematisches und hochschulpädagogisches Talent aus Berlin", Wissenschaftliche Zeitschrift der Humboldt-Universität zu Berlin. Mathematisch-Naturwissenschaftliche Reihe, 37 (2): 187–193, ISSN 0863-0631, MR975243
- Weil, André (1976), "Review: Gotthold Eisenstein, Mathematische Werke", Bulletin of the American Mathematical Society, 82 (5): 658–663, ISSN 0002-9904
External links
- Gotthold Eisenstein at the Mathematics Genealogy Project
- The life of Gotthold Ferdinand Eisenstein by M.Schmitz (PDF format)
- Ferdinand Eisenstein by Larry Freeman (2005), Fermat's Last Theorem Blog.