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
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
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
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.
Biographies of mathematicians are from the
Mathematics archive at the University of St. Andrews, and are
used with permission.