**Alexander von Brill** was a German mathematician who worked in algebraic geometry. He also made mathematical models and was interested in the history of mathematics.

- Alexander Brill's school education was in Darmstadt where he attended elementary school and then a Gymnasium.
- In 1860 Brill entered the Technische Hochschule in Karlsruhe where he studied architecture and engineering science.
- Brill also moved to Giessen and was again taught by Clebsch.
- Brill needed to find ways to support himself financially during his studies at both Karlsruhe and Giessen and he did this by taking on duties as a substitute teacher and also by tutoring private pupils.
- Remaining in Giessen after his graduation to undertake research, Brill submitted his habilitation thesis in 1867.
- After the thesis was accepted Brill was appointed a privatdozent in Giessen, a post he held for two years.
- However, Paul Gordan remained at Giessen and his interests were similar to those of Brill.
- Brill's models, which represented surfaces by delicately interlaced circles or quadrilaterals, were not as sturdy as wooden or even plaster models, but cost considerably less.
- These cardboard models were described by Brill in Carton-Modelle von Flächen zweiter Ordnung, construirt nach Angabe Ⓣ(Cardboard models of surfaces of the second order, constructed as specified) (1874).
- Brill had met Max Noether, who was two years younger, when the two were both working at Giessen and they had become good friends.
- Alexander and Anna Brill had three sons, Alexander Brill, Eduard Brill (1877-1968) and August Brill.
- Alexander became President of the Imperial Pay Board, Eduard became an architect, craftsman and Director of a Craft School, and August became a manufacturer.
- Brill held the position in Darmstadt until 1875 when he was appointed as the professor of mathematics at the Technische Hochschule in Munich.
- Brill and Klein both had a great interest in teaching and Brill, like Klein, participated in the movement to reform the teaching of mathematics.
- It is clear that Brill was much influenced by being a colleague of Klein's for five years and the influence would show up in many different ways throughout Brill's career.
- At Munich a laboratory for the design, production, and pedagogical application of models was set up by Brill and Klein.
- Brill published Mathematische Modelle angefertigt im mathematischen Institut des Königlichen Polytechnikums zu München Ⓣ(Mathematical models made in the mathematics department of the Royal Polytechnic of Munich) (1880) and looked for a way to make his production of mathematical models more commercial.
- Von Dyck assisted Klein and Brill in the construction of models such as the tractrix of revolution, geodetic lines on an ellipsoid of revolution, Kummer's surface, Dupin's cyclide, the spherical catenary and twisted cubics.
- These mathematical models, constructed of silk threads in brass frames, became a major feature of Ludwig Brill's business.
- By 1890 he was selling 16 series of models, seven of which were the original ones constructed at the Technische Hochschule in Munich under the direction of Brill, Klein and von Dyck.
- Around this time the firm was taken over by Martin Schilling of Leipzig and by 1911 their catalogue contained about 400 mathematical models inspired by Brill's early work in this area.
- The production of mathematical models was part of Brill's efforts in teaching but he also published impressive research papers and books.
- Although Klein left Munich in 1880, Brill was to remain there for a few more years, taking up the chair of mathematics in the University of Tübingen in 1884.
- Brill held this chair until he retired in 1918 at the age of 76, but continued to live and do mathematics in Tübingen after his retirement until his death at age 92.
- Brill also wrote on determinants, elliptic functions, special curves and surfaces.
- Professor Brill sets out the Hertzian system, and illustrates it by examples.
- It is curious to note that the example chosen of non-holonomous systems, in which the constraints are expressible by a differential equation unintegrable per se, is as simply dealt with by direct application of Newton's second law, which avoids what Professor Brill terms the "delicate considerations and special precautions" necessary in applying Lagrange's equations.
- In 1912 Brill published Das Relativitätsprinzip.
- As is well known Brill together with Max Noether are the twin-stars of German geometricians who did the important pioneer work concerning the geometry on algebraic curves.
- In other words, the student will have a fairly good start in algebraic geometry after he has mastered Brill's lectures.
- Brill states that in former years he put more stress upon the projective point of view, while in later years he returned more and more to the standpoint of the first discoverers in this field, of Descartes, Newton, Cramer, Euler, in so far as the graphical or geometric form relations are concerned.
- What Brill presents is, as one might expect, very penetrating and illuminating.
- Brill, one of the remaining representatives of an important period of geometric development, has given enough of an algebraic, function theoretic treatment of algebraic geometry to stimulate the student for further reading and research in this direction.
- In 1928 Brill published his lectures on theoretical mechanics in the book Vorlesungen über Allgemeine Mechanik Ⓣ(Lectures on general mechanics).
- Professor Brill's work is to be recommended as an exceptionally well written introduction to dynamics.
- Finally let us comment on Brill's personality.
- Among the honours given to Brill throughout his long life we mention his election to the Reale Accademia dei Lincei, the Bavarian Academy of Sciences, the German Academy of Scientists Leopoldina, the Reale Istituto Lombardo di Scienze e Lettere, and the Göttingen Academy of Sciences.
- Brill gave his last public lecture on 4 March 1930 when he spoke to the Tübingen Dienstagsgesellschaft about his work on Kepler.

Born 20 September 1842, Darmstadt, Germany. Died 8 June 1935, Tübingen, Germany.

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Astronomy, Origin Germany

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