The scientific activity of Vladimir Varicak (1865-1942), professor of mathematics at the University of Zagreb, was mainly in non-Euclidean geometry and its applications to Einstein’s theory of relativity. His lecture delivered in 1911 at the German Mathematical Society in Karlsruhe has been published in 1912 in Jahresberichte der Deutschen Mathematiker Vereinigung, and translated from German into Polish (Warszaw, 1913), Russian (St. Petersburg, 1914), French (Paris, 1914).

His most important work is the monograph Darstellung der Relativitätstheorie im dreidimensionalen Lobatschefskijschen Raume, Zagreb, 1924, which has been been cited by many authors to these days. In 2007, the book has been translated into English (Vladimir Varićak: Relativity in three dimensional Lobachevsky space, Publisher A. F. Kracklauer, 2007, ISBN-13: 978-1847533647).

The original and arguably most complete book on the nonEuclidean formulation of relativity theory. Published in 1924 in German, it is now rare, but still current. Recent work in this area has greatly increased its utility; it should be of interest to all concerned with theoretical physics or application of modern geometry. Source.

The results of his work have been cited also in Wolfgang Pauli’s Relativitätstheorie. Vladimir Varićak was the main contributor to the the theory of rapidity (in the Theory of Relativity) in his writings from 1910 to 1924.

One of his students at the University of Zagreb was Vilim Feller, that is, William Feller, a famous Croatian – American mathematician. Vladimir Varicak was a Dean of the Mudroslovni fakultet (Faculty of Philosophy), as well as a Rector of the University of Zagreb, and since 1903 he was a full member of the Academy of Sciences and Arts in Zagreb. Since 1911, Varicak was also very interested in the life and work of Rudjer Boskovic, distinuished Croatian scientist from the 15th century. He was a collaborator of Croatian Encyclopaedia (A-E), which contains 4 four of his articles (while it is to be assumed that he has prepared many more).

A few citations (source Sibe Mardesic: Matematika u Hrvatskoj – Mathematics in Croatia):

Ich will nun des naeheren auf die Parallele zwischen der nichteuklidischen Geometrie und der relativitaetstheorie zu sprechen kommen. Diese Parallele ist Herrn unsympathisch. Ich darf darum wohl an die Arbeiten von Varicak erinnern, aus denen zu schliessen ist, dass jeder Formel der Einstein-Minkowski-schen Welt dreier, reeller Raum – und einer imaginaraen Zeitkoordinaten eine Formel in einer nichteuklidischen Weit von vier reellen Raum-Zeitkoordinaten entspricht. Ich hatte allerdings mit meiner parallele etwas ganz anderes gemeint, als diese mathematisch sehr interessante Entdeckung aussagt.

E. Gehrcke: Nochmals ueber die Grenzen des relativitaetsprinzips, Verhandlingen der Deuthschen Physikalischen Gesellschaft, 13 1911, str. 996.

Yet just now, 1912, this space of ours is being proved non-euclidean by the principle of relativity. Says Vladimir Varicak in a wonderful lecture. “Ueber die nichteuklidische Interpretation der Relativtheorie”: “I postulated that the phenomena happened in a Lobachevski space, and reached by very simple geometric deduction the formulas of the relativity theory. Assuming noneuclidean terminology, the formulas of the relativity theory become not only essentially simplified, but capable of a geometric interpretation wholly analogous to the interpretation of the classic theory in the euclidian geometry. And this analogy often goes so far, that the very wording of the theorems of the classic theory may be left unchanged”.

G.B. Halsted, Non-Euclidean Geometry, Science, New York, 1913, str. 597.

This is an interesting and lucid analysis of Lobatschiefsky space displaying its properties in such a form as to present their intimate relationship with the ideas of relativity.

Nature, London, 6. Dec. (1924) 820.

I problemi posti dalla fisica teoretica sono all’ordine del giorno specialmente per quanto riguarda la teoria della relativita di Einstein. In questa importane pubblicazione l’illustre professore di matematica dell’Universita di Zagabria, ha trattato l’arduo argomento con una intellegibita incontestabile, con logica rigorosa e con metodo scientifico convincente.

Bollettino delle opere scientifiche, Bologna, agosto (1926) 12.

Vladimir Varicak was the third president of the Croatian Shorthand Society (Hrvatsko stenografsko društvo) in Zagreb from 1918 to 1930. Many thanks to Mr. Josip Hanjš (president of the Croatian Shorthand Society) for this information (2015). Two sketches of Varićak’s letters to Albert Einstein are preserved, but nobody can decipher their content, since Varicak wrote them using a little known Gabelsberg’s shorthand system.