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Gotthold Eisenstein worked on a variety of topics including quadratic and cubic forms, the reciprocity theorem for cubic residues, quadratic partition of prime numbers and reciprocity laws.Eisenstein suffered all his life from bad health. Even while he was at school he had health problems and after leaving school he travelled with his parents to England where they were looking for a better life. They tried Wales and Ireland before returning to Germany.
While in Ireland Eisenstein met Hamilton who gave him a copy of a paper that he had written on Abel's work on the impossibility of solving quintic equations. This stimulated Eisenstein to research in mathematics and on his return to Germany he enrolled at the University of Berlin.
Eisenstein was soon publishing mathematical works, mainly in Crelle's Journal where Abel had published his work. In fact volumes 27 and 28 of Crelle's Journal contain 25 of Eisenstein's papers.
In 1844 Eisenstein went to Göttingen for a short time and he met Gauss. At this time Eisenstein was working on a variety of topics including quadratic and cubic forms and the reciprocity theorem for cubic residues.
From 1846 to 1847 Eisenstein worked on elliptic functions and in the first of these years he was involved in a priority dispute with Jacobi. In 1847 Riemann attended lectures that Eisenstein gave in Berlin.
Eisenstein's health was always bad and it worsened after 1847. Soon he was to spend most of his time in bed although his amazing output of mathematics did not diminish as he published one treatise after another on quadratic partition of prime numbers and reciprocity laws.
Eisenstein spent a year in Sicily in an attempt to improve his health but after his return to Germany he died of pulmonary tuberculosis at the age of 29.
References (10 books/articles)
References elsewhere in this archive:
Tell me about Eisenstein's work on matrices and determinants
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