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

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

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. 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 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.

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 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 is said to have claimed, "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.

See also

* Eisenstein's criterion
* Eisenstein ideal
* Eisenstein integer
* Eisenstein prime
* Eisenstein series
* Eisenstein theorem
* Real analytic Eisenstein series

References

1. ^ Sandifer, Ed. "Review of Archimedes: What Did He Do Besides Cry Eureka?". Mathematical Association of America. http://www.maa.org/reviews/archim.html. Retrieved 2007-07-23.

External links

* O'Connor, John J.; Robertson, Edmund F., "Ferdinand Eisenstein", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Eisenstein.html .
* Ferdinand Eisenstein at the Mathematics Genealogy Project
* The life of Gotthold Ferdinand Eisenstein by M.Schmitz (PDF format)
* André Weil's review of Eisenstein's collected work, Bulletin of the American Society of Mathematics.
* Ferdinand Eisenstein by Larry Freeman (2005), Fermat's Last Theorem Blog.