**Jacob Lüroth** was a German mathematician who worked on rational curves and the invariance of dimension. He discovered the *Student t*-distribution before Gosset.

- Jacob attended the Lyceum in Mannheim where he showed himself to be a gifted linguist.
- Lüroth took part in observing and was given much encouragement by Schönfeld.
- In the autumn of 1862, Lüroth passed the matriculation examination for the University of Bonn and he began to study astronomy with Friedrich Wilhelm Argelander (1799-1875).
- He had worked on a star catalogue in collaboration with Eduard Schönfeld who had advised Lüroth that Bonn was an excellent place to study astronomy.
- Lüroth began to make astronomical observations but he soon realised that his poor eyesight was not going to give him a future in that subject so his interest turned to mathematics.
- After graduating from Heidelberg, Lüroth went to Berlin where he spent 1865-66 attending lectures at the University from several leading mathematicians including Karl Weierstrass.
- He had collaborated with Paul Gordan at Giessen on the theory of abelian functions and their joint monograph on that topic was published around the time Lüroth arrived in Giessen.
- It was working with Clebsch in Giessen that directed Lüroth's research towards geometry and function theory.
- Lüroth habilitated at the University of Heidelberg in the summer of 1867 after submitting the thesis Zur Theorie der windschiefen Flächen Ⓣ(On the theory of wind-swept surfaces) and he was appointed to the teaching staff.
- He worked there until 1868 and initially Lüroth was appointed to help Dienger out but, after Dienger left, he became a candidate to fill the vacant professorship and in January 1869 he was appointed as a full professor of mathematics at the Technische Hochschule in Karlsruhe.
- Lüroth spent twelve years at Karlsruhe, then in 1880 he moved to Munich, teaching at the Technische Hochschule there for three years.
- In 1883 Lüroth moved again, this time being appointed to the University of Freiburg.
- Because he had a remarkable memory, Lüroth was effortlessly at home in almost all areas of mathematics, including applied mathematics, many branches of astronomy, geodesy and even more remote areas of knowledge.
- As we have mentioned above, Lüroth was taught by Hesse and Clebsch and because of their influence he continued to develop their work on geometry and invariants.
- In 1869 Lüroth discovered the "Lüroth quartic" and it appears in his paper Einige Eigenschaften einer gewissen Gattung von Kurven vierter Ordnung Ⓣ(Some properties of a certain class of fourth-order curves) which was published in the first volume of Mathematische Annalen in 1869.
- The Lüroth quartic is a nonsingular quartic plane curve which contains the ten vertices of a complete pentalateral.
- Lüroth's work on this curve came out of an investigation he was carrying out into when a ternary quartic form could be represented as the sum of five fourth powers of linear forms.
- In 1883 Lüroth published his method on constructing a Riemann surface for a given algebraic curve.
- Lüroth also worked on the big problem of the topological invariance of dimension.
- Jacob Lüroth, Johannes Thomae, Enno Jürgens, Eugen Netto, as well as Cantor himself, addressed this problem ....
- Lüroth assumed a one-to-one correspondence between two coordinate manifolds of different dimension and arrived at a contradiction but only for certain special cases of particular choices of dimension.
- Although Lüroth made some useful progress, this difficult problem was not completely solved until the work of L E J Brouwer in 1911.
- Among his other work, Lüroth undertook editing.
- Karl von Staudt's ideas of geometry interested Lüroth and he further developed von Staudt's complex geometry in papers such as Über das Rechnen mit Würfen Ⓣ(On calculating with throws) (1873) and Das Imaginäre in der Geometrie und das Rechnen mit Würfen.
- Lüroth carried on with Gauss's analysis of the linear normal model by considering the joint distribution of the parameters.
- This statistical test was rediscovered by William Gosset, who coincidently was born in the year that Lüroth made his discovery, and its discovery is now attributed to Gosset who published it under the name 'Student' in 1908.
- Lüroth received many honours for his contributions.
- Lüroth continued to work at Freiburg despite his health deteriorating due to heart problems.
- What efforts Lüroth has spent on encouraging an appreciation of the work of his late friend, Ernst Schröder who, for a long time, stood alone with his efforts to introduce a conceptual notation in Germany.
- And to Julius Weingarten, who was still brought in his final years to Freiburg im Breisgau, where a position as visiting professor, was given at the university essentially due to Lüroth, which gave the lonely scholar in his last years a desired sphere.

Born 18 February 1844, Mannheim, Germany. Died 14 September 1910, Munich, Germany.

View full biography at MacTutor

Astronomy, Origin Germany

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