His name is sometimes written Lueroth, following the common printing convention for umlauted characters.
He began his studies in astronomy at the University of Bonn, but switched to mathematics when his poor eyesight made taking astronomical observations impossible.
He received his doctorate in 1865 from Heidelberg University, for a thesis on Pascal's theorem.
[2] Following up on Carl Friedrich Gauss's work on statistics, Lüroth discovered the t-distribution usually credited to William Sealy Gosset.
In modern terms, the calculation that led Lüroth to the t-distribution was the computation of a Bayesian interval.