**Eugen Netto** was a German mathematician who made major steps towards abstract group theory when he combined permutation group results and groups in number theory. He also worked on space-filling curves.

- Up to the age of eleven Eugen attended a school in Halle, but from that time he went to the Friedrich-Wilhelm Gymnasium in Berlin, an excellent school founded in 1797.
- Karl Ferdinand Ranke (1802-1876), a classical philologist, was the rector of the Friedrich-Wilhelm-Gymnasium from 1842 to 1876, so was the rector when Netto began his studies there.
- Netto was fortunate to have two outstanding teachers of mathematics at the Gymnasium in Karl Heinrich Schellbach and August Rudolph Luchterhandt.
- Both Luchterhandt and Schellbach were excellent mathematicians and exceptional teachers but it was Schellbach who showed Netto the excitement of mathematics and from that time on mathematics was clearly the only topic that he considered.
- After graduating from the Gymnasium in 1866, Netto entered the University of Berlin to study mathematics.
- Netto graduated from Berlin in 1870 having worked specifically under Weierstrass and Kummer.
- Netto had to submit three further minor theses in order to obtain his doctorate.
- There was no immediate university appointment for Netto, however, and he taught at the Friedrich-Werder Gymnasium in Berlin for nine years before being appointed as extraordinary professor at the University of Strasbourg in 1879.
- For the first few years teaching at this Gymnasium, Netto published relatively little, the only publication after his 1870 dissertation before 1877 was Zur Theorie der zusammengesetzten Gruppen Ⓣ(On the theory of composite groups) (1874).
- The Mathematics Seminar there was directed by Elwin Christoffel and Theodor Reye, and Netto took part in this seminar.
- After three years at the University of Strasbourg Weierstrass recommended that Netto be appointed an extraordinary professor at the University of Berlin and he took up the appointment in 1882.
- Netto held this post in Berlin until 1888 when he was appointed ordinary professor at the University of Giessen.
- Despite this, Netto's "proof" was widely accepted as providing a solution to the dimension problem until Jurgens' criticism in 1899 of Netto's proof.
- In the following year Netto showed that such a mapping cannot be a continuous function.
- These results by Cantor and Netto are starting points for the investigations of space-filling curves which are an active research area today.
- Netto made major steps towards abstract group theory when he combined permutation group results and groups in number theory.
- By this means an easy and attractive entrance into the theory of substitutions is gained, accessible even to the beginner, and it may fairly be said that Netto's book has largely contributed to spread the knowledge of this important branch of mathematics.
- This was only the first of a number of important books published by Netto.
- In particular, in 1877 Netto had given new proofs of the Sylow's theorems.
- In publishing so excellent a treatment of the subject Professor Netto has performed a service of value to the mathematical public.
- Beginning in 1910, Netto suffered from Parkinson's disease, which as the disease progressed forced him to withdraw increasingly from the public.

Born 30 June 1846, Halle, Germany. Died 13 May 1919, Giessen, Germany.

View full biography at MacTutor

Algebra, Group Theory, Origin Germany

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive