# Mór Réthy

### Born: 9 November 1846 in Nagykörös, Hungary

Died: 16 October 1925 in Budapest, Hungary

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**Mór Réthy**was born with the name Rothbaum but, in 1871, he changed his name as a sign of solidarity with the Hungarian culture. Unlike most contemporary scientists he didn't come from a well-to-do family. His father, a man of high morality, was an outstanding teacher at the elementary school of Nagykörös. However, he had a big family to care for so he was forced to give up teaching and he became a merchant.

Mór went to primary and to secondary school in his native town of Nagykörös. Later he attended the Technical Universities of Vienna and Budapest. Meanwhile he worked for a year as an officer at the Central Postal and Telegraph Service to support his father. He graduated with a degree in mathematics and descriptive geometry from the Technical University of Budapest in 1870. In the same year he married Etelka Finály, the sister of the famous classical-philology professor Henrik Finály. Following his graduation, Réthy worked for two years as a teacher of mathematics and descriptive geometry at the Modern Technical School of Körmöcbánya.

Thanks to a state bursary suggested by Baron Loránd Eötvös, he had the opportunity to continue his studies at the famous universities of Göttingen and Heidelberg. At Göttingen he had the good fortune to be able to admire Alfred Clebsch's lectures and his wonderful way of teaching. Unfortunately, although only 39 years old, Clebsch died of diphtheria in November 1872 and Réthy had to face up to his sudden death. His first paper on the diffraction of light was presented at Göttingen in 1872. The second part of his bursary was spent at Heidelberg University, where Kirchhoff, Königsberger and Schering assured him lifelong mental munition. Leo Königsberger and Réthy remained in a close contact: Réthy's nine letters from 1875 to 1898 can still be found in the Staatsbibliothek zu Berlin Handschriftabteilung. He obtained his doctoral degree from Heidelberg University in 1874.

Returning home after the award of his doctorate, he was appointed extraordinary professor at the University of Kolozsvár. His seminars in mathematics - on elliptic functions, complex functions and determinants - gave a new colour to contemporary mathematical life. During his stay at Kolozsvár problems concerning of navigation, including the question of constructing the most efficient propeller, were the focus of interest. Mór Réthy took part in very fruitful debates between outstanding mathematicians of his age and soon enriched the literature with two papers on the topic. In 1876 he was promoted professor in the Mathematical and Theoretical Physics Department at Kolozsvár.

In 1878 he was elected a corresponding member of the Hungarian Academy of Sciences. He was promoted to dean at Kolozsvár University, serving in this role on two separate occasions. From 1884 to 1886 he was the Head of the Department of Elementary Mathematics.

His whole life was interwoven with analysing, communicating and developing the work of the two Bolyais. This theme began to dominate contemporary mathematical thinking [2]:-

In 1886 Mór Réthy was invited to the Technical University of Budapest, where he first lectured on geometry. Then his interest turned to theoretical problems of physics and mechanics. From 1892 he was professor of the Analytical Mechanics and Theoretical Physics Department. Similarly to his years at Kolozsvár, he served two spells as dean of the Technical University of Budapest. In 1891 he became not only a founding member of the Mathematical and Physical Society (today named the János Bolyai Mathematical Society), but he worked as a committee member from its inception.The prelude was Mór Réthy's lecture delivered at Kolozsvár University in1874, which soon appeared in print. This paper throws light on Réthy's efforts to introduce and popularize absolute geometry. His aim was to kindle interest in reading the Appendix itself, and with this in mind, he gave reformulations of several basic definitions and concepts(Bolyai's definition of parallelism, the paracycle, parasphere, hypercycle, hypersphere)that are easier to follow than their originals in the Appendix. And he went a step further: starting from the fact that in absolute geometry in infinitely small segments of space the theorems of Euclidean geometry hold true, and relying on the recognition that spherical trigonometry is independent of Euclid's5^{th}postulate, Réthy built up Bolyai's trigonometry independently. Thus, he set the trend aiming at the simplest possible exploration of absolute trigonometry relying on the fewest possible axioms. Of the wealth of literature in this vein, let us only mention the articles by Pál Szász.

Another merit of Réthy is that he was the first to review and elaborate the hyperbolic constructions of the Appendix in detail.

Mór Réthy was one of the professors - Gyula König, Arpád Geötze, Jenö Hunyadi, Gyula Farkas etc. - who lectured both on mathematics and physics at a very high level. (As stated in [1]) Unfortunately he is often referred to as either a mathematician or a physician in spite of the fact that he embodied both. Another problem is that though he was born in 1846 his year of birth is often erroneously written 1848. Of course the correct data can also be found: Réthy, Mór; früher Rothbaum (1846-1925) Physiker und Mathematike.) His literary heritage is divided between mathematics and physics. Most of his work was published in Hungarian, but a great many papers were written in German or at least have been titled in English:

*Über ein Dualitätsprinzip in der Geometrie*Ⓣ (1872),

*The so-called non-Euclidean plane trigonometry of the three-dimensional homogeneous space*(1875, Hungarian),

*Die Fundamentalgleichungen der nicht-euklidischen Geometrie auf elementare Wege abgeleitet*Ⓣ (1876),

*A contribution to the theory of propeller and peripeller surfaces*(1876, Hungarian),

*To the theory of the propeller*(1877, Hungarian),

*Theorie d. Reflexion und Brechung; Ueber die Polarisation d. gebeugten Lichts*Ⓣ (1880),

*Endlich-gleichen Flächen*Ⓣ (1890 & 1891),

*Über endlich-gleichen Flächen*Ⓣ (1893),

*End-like equal areas*(1890 & 1893, Hungarian),

*Zum Beweise des Haupsatztes über die Endlichkeit zweier ebener Systeme*Ⓣ (1894),

*Flüssigkeitsstrahlen in incompressiblen reibenslosen Flüssigkeiten*Ⓣ (1894),

*Fluid currents*(1894, Hungarian),

*Über das Princip der kleinsten Action, (und über das von Hamilton)*Ⓣ (1896),

*Über schwere Flüssigstrahlen*Ⓣ (1898),

*An introduction to János Bolyai's "new, different world"*(1903, Hungarian),

*Das Ostwaldsche Princip vom Energieumsatz in der Mechanik*Ⓣ (1905).

In 1900 Mór Réthy became a full-member of the Hungarian Academy of Sciences. Regarding his results concerning hydrodynamics, because of his studies on end-like equal areas and finally his treaties on mechanical principles (and the fact that all of them created significant international interest) Mór Réthy was awarded the Marczibányi Prize by unanimous voting of the Committee of the Hungarian Academy of Sciences in 1904 [2]:-

At the last decades of the 19Endowed with extreme modesty and working capacity, Réthy was a person worthy of affection and an ardent servant of all Hungarian causes. His most significant essays deal with the legacy of the two Bolyais and the development of some of their results. Internationally, however, better known are Réthy's investigations in physics. His results concerning the shape of jets of incompressible fluids - where he applied deep tools of function theory - were the basis for many a further investigation. Also well known is Réthy's research into the Ostwald theory and into the classic "principles" of mechanics.

^{th}century the Hungarian Academy of Sciences decided to bring into being the second edition of the two Bolyais' immortal work: the

*Tentamen*. Some outstanding scientists took part in that time-consuming enterprise, but it was only Mór Réthy, who persisted in doing so from the beginning to the end:

At the time of the celebrations of János Bolyai's centenary Mór Réthy published an essay on the new different world of János Bolyai. At that time he wrote something very personal in his diary [7]:-Wolfgangi Bolyai de Bolya: Tentamen iuventutem studiosam in elementa matheseos purae elementaris ac sublimioris methodo intuitiva evidentiaque huic propria introducendi, cum appendice triplici(1897)(I. Conspectus arithmeticae generalis. Mandato Academiae scientiarum hungaricae suis adnotationibus adiectis ediderunt Julius König et Mauritius Réthy. - II. Elementa geometriae et appendices ... ediderunt Josephus Kurschák, Mauritius Réthy, Béla Tötössy de Zepethnek)Ⓣ

The last quarter of Mór Réthy's life was shadowed by personal and historical losses: the decease of his second son as a victim of World War I, his four-year-old granddaughter's death; at the University the change of the atmosphere for the worse, further the separation from Transylvania, Kolozsvár, and his beloved garden at Hója.The atmosphere of these celebrations led me back to the absolute geometry. Suddenly I have noticed that an error crept into the last sentence in the new edition of the Appendix. The remark concerning it originates from me.

In the last but one year of his life, on 24 July 1924, he was awarded a Jubilee doctorate from Heidelberg University.

**Article by:** R Oláh-Gál and M Rupp

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