Ferdinand Eisenstein

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Ferdinand Gotthold Max Eisenstein.

Ferdinand Gotthold Max Eisenstein (April 16, 1823 – October 11, 1852) was a German mathematician.

Like Galois and Abel, Eisenstein died before his 30th birthday and, like Abel, he died of tuberculosis.

Biography

Eisenstein was born and died in Berlin. From an early age he showed talent in mathematics, and also in music. He learned to play the piano when he was very young, and continued playing and composing throughout his life.

He suffered from health problems throughout his life, including meningitis in childhood, a disease from which his five brothers and sisters died. In 1837, at the age of fourteen, he entered the Friedrich Wilhelm Gymnasium, later moving on to the Fiedrich Werder Gymnasium in Berlin. His teachers recognized his mathematical talent, but by the age of 15 he had already surpassed the knowledge he could obtain in school and began studying differential calculus from the works of Euler and Lagrange.

At 17, while still in school, he began attending classes by Dirichlet and other mathematicians at the University of Berlin. In 1842, before taking his final exams at school, he traveled with his mother to England (where his father was). In 1843 he meets Hamilton in Dublin; He gave him a copy of one of his works on Abel's work on the impossibility of solving fifth degree equations through rational and radical operations, which notably stimulated the young Eisenstein's interest in mathematical research.

In 1843 he returned to Berlin, took his graduation exams and in the fall entered the University. By January 1844 he had already presented his first work to the Berlin Academy, on cubic forms with two variables. In that year he met for the first time with Alexander von Humboldt, who from then on would be his protector. Considering Eisenstein's extreme poverty, Humboldt manages to obtain subsidies for him from the King, the Prussian government, and the Berlin Academy. These subsidies, always late and given reluctantly, were more than repaid by Eisenstein: in 1844 alone he published 23 works and two problems in the Crelle.

In June 1844 he visited Gauss in Göttingen. In 1845 Kummer ensures that Eisenstein receives an honorary doctorate from the University of Breslau. Jacobi also promoted this distinction, but the relations between him and Eisenstein would always be difficult; in particular, because of a question of discovery priorities that arose in 1846. In 1847 he obtained his habilitation from the University of Berlin, and began teaching there. Bernhard Riemann attended his classes on elliptic functions.

Eisenstein had Republican sympathies, and although he did not actively participate in the revolutionary events of 1848, he was arrested on March 19 of that year. Although he was released a day later, the mistreatment suffered further aggravated his delicate health. But in addition, suspicions of his alignment with the Republican cause caused his official subsidies to be withdrawn, although Humboldt continued to tenaciously support him.

Despite his state of health, Eisenstein continued to write a job after another on quadratic partitions of prime numbers and reciprocity laws. In 1851, at the request of Gauss, he is elected a member of the Gotinga Academy; one year later, on the recommendation of Dirichlet, he is also elected a member of the Berlin Academy.

He died of tuberculosis at 29 years of age. Humboldt, then 83 years old, accompanied his remains to the cemetery. He had raised, too late, the money necessary to send Eisenstein to a rest period in Sicily.

Contributions

In his short life, Eisenstein made numerous contributions to various fields of mathematics. The three main areas in which he made fundamental contributions were the theory of forms, generalizing the results obtained by Gauss with respect to quadratic forms; the laws of reciprocity, with the aim of generalizing Gauss's results on quadratic reciprocity; and elliptical functions, a field in which he made the most outstanding theoretical developments and which retain influence and relevance.

Publications

Alleged appointment of Gauss

Gauss in a conversation once commented that, 'there had only been three epoch-making mathematicians: Archimedes, Newton and Eisenstein. This is the origin of the quote sometimes attributed to Gauss about Eisenstein.

E. T. Bell in his 1937 book Men of Mathematics (page 237) states that Gauss said "There have only been three epoch-making mathematicians, Archimedes, Newton, and Eisenstein," and this has been widely cited in writings about Eisenstein. It is not a quote from Gauss, but (a translation of) the end of a sentence from the biography of Eisenstein by Moritz Cantor, one of Gauss's last students and a historian of mathematics, which summarized his memory of a comment made by Gauss on Eisenstein in a conversation many years earlier.

The original quote is the following: 

Seit 1847 was er Privatdocent an der Universität zu Breslau, seit dem 24. April 1852 ordertliches Mitglied der dortigen Akademie der Wissenschaften alss 24. April 1852 Since April 24, 1852 he was an ordinary member of the Academy of Sciences of Breslavia, in which he obtained his degree on July 1. Juli seine Antritsrede hielt, ein Vierteljahr später starb der geniale Mathematiker, den ein Gauß so sehr seiner Freundschaft gewürdigt hatte, daß erine Sammlung Eisenstein'scher Aufsätze, welche 1848, also noch währendses habe nur drei epochebildende Mathematiker gegeben: Archimed, Newton, Eisenstein.

Although it is doubtful that Gauss actually put Eisenstein on the same level as Newton, his writings demonstrate that Gauss held Eisenstein in very high regard. For example, a letter from Gauss to Humboldt, dated April 14, 1846, says that Eisenstein's talent is one that nature grants only a few times a century ("welche die Natur in jedem Jahrhundert nur wenigen erteilt").

Additional bibliography