**Eduard Study** was a German mathematician who became a leader in the geometry of complex numbers. He also worked on invariant theory.

- Eduard was christened Christian Hugo Eduard Study on 16 April 1862 but he always used the name Eduard.
- Rather remarkably, he sent the twelve year old Eduard on this holiday on his own.
- Eduard attended the Coburg Gymnasium where his two favourite subjects were mathematics and biology and, after graduating from school in 1880, he entered the University of Jena to study with the biologist Ernst Häckel (1834-1919).
- After studying at the University of Jena for a year, Study decided that he wanted to move towards mathematics and in order to do this he went to the University of Strasbourg to work with Theodor Reye.
- Study solved all the problems in the first volume of this book during the academic year 1881-82 when he was at Strasbourg.
- We should note that Study, almost certainly because of his upbringing, worked in a very solitary manner.
- Despite the fact that Study chose to prove a generalisation of one of the problems that had been set, Philipp von Seidel criticised his solution as clumsy.
- After the award of his doctorate, Study returned to the University of Leipzig where he worked on his habilitation thesis encouraged by Felix Klein to whom he expressed his "very special thanks".
- In 1885 Study was appointed as an assistant in mathematics at the University of Leipzig where, in addition to Klein, he met David Hilbert who had just arrived there.
- Dr Study approves, or rather he knows, only one field of mathematics and that is the theory of invariants, very exclusively the symbolic theory of invariants.
- Klein suggested that both Hilbert and Study should visit Erlangen and discuss their research with Paul Gordan who was the leading expert on invariant theory.
- Klein then told both Study and Hilbert that they should visit Paris.
- They both went in early 1886, Study arriving first.
- In a letter written to Study, Klein continued to insist that he must have personal contact with Gordan and Noether.
- In Paris, Camille Jordan gave a dinner for Study and Hilbert to which George-Henri Halphen, Amédée Mannheim and Gaston Darboux were invited.
- Although they considered him very old (he was 64), he was "extraordinarily friendly and hospitable" and discussed the big problems of invariant theory which interested Study.
- Study returned to Germany and reported in person to Klein about his Paris visit.
- However, Klein was disappointed that Study did not speak as much about mathematics as he had expected.
- Back at Leipzig, Study habilitated and gave various lecture courses: Einleitung in die analytische Geometrie der Ebene und des Raumes Ⓣ(Introduction to the analytic geometry of the plane and space) (Summer semester 1886); Einführung in die Theorie der Wärmeleitung, in Verbindung mit der Theorie der Fourier'schen Reihen und Fourier'schen Integrale Ⓣ(Introduction to the theory of heat conduction, in conjunction with the theory of Fourier series and Fourier integrals) (Winter semester 1886); Einleitung in die neuere Algebra und deren geometrische Anwendungen Ⓣ(Introduction into modern algebra and their geometric applications) (Summer semester 1887); Einleitung in die Ausdehnungslehre und Quaternionentheorie Ⓣ(Introduction to the theory of extension and quaternions) (Summer semester 1887); Neuere Algebra Ⓣ(Newer algebra) (Winter semester 1887); Mechanische Theorie der Wärme Ⓣ(Mechanical theory of heat) (Winter semester 1887); and Principien der Mathematik (Zahlbegriff und geometrische Axiome) für Fortgeschrittenere Ⓣ(Principles of mathematics (concept of number and geometric axioms) for more advanced students) (Summer semester 1888).
- Study spent a month, from 15 January 1887 to 15 February 1887, at Erlangen where he had discussions with Gordan.
- This was at Klein's suggestion but this time Study was keen to go.
- Study had first met Engel in July 1885 just after he had returned from a ten month visit to Sophus Lie in Oslo.
- From that time on, Study corresponded with both Engel and Lie concerning his mathematical results.
- In July 1888, Study left Leipzig and moved to the University of Marburg where he became a privatdocent.
- The reader will miss in Study's book Elliott's philatelic detail, Capelli's combinatorial skill, Hilbert's and Alfred Young's steam-rolling genius, but will find instead a breadth of conceptual view and philosophical insight that displays Continental mathematical thought in its finest hour.
- Study became more and more unhappy at Marburg.
- This led to a degree of rivalry between Study and the other lecturers and he came to dislike the lecturing side of his job.
- Around this time, however, Study began work on writing a book on spherical trigonometry having already published the paper Über die sphärische Trigonometrie Ⓣ(On spherical trigonometry) in 1891.
- Study was interested but not confident that he would be a strong applicant.
- Again Study was to move after three years, this time to a full professorship at Greifswald.
- Study held the chair at Bonn until he retired in 1927.
- Study became a leader in the geometry of complex numbers.
- Study demonstrated what he considered to be a thorough treatment of a problem.
- With Corrado Segre, Study was one of the leading pioneers in the geometry of complex numbers.
- Study, employing the identities of the theory, sought to demonstrate that geometric theorems are independent of coordinates.
- Other areas which Study worked on were straight lines in elliptic space, with his student at Bonn J L Coolidge, and he simplified the method of differential operators.
- Study remained in Bonn after his retirement at the end of the summer semester of 1927, being made professor emeritus at this time.
- One final fact about Study is of interest.

Born 23 March 1862, Coburg, Germany. Died 6 January 1930, Bonn, Germany.

View full biography at MacTutor

Origin Germany

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