He undertook research at the university for his doctorate advised by Lajos Schlesinger and submitted his thesis The Gauss-type medium arithmetico-geometricum in 1903. For this work he received his doctoral degree and, in addition, in 1904 he was awarded a secondary school teaching certificate in mathematics and physics. Between 1903 and 1904 he worked as a trainee teacher, then as a substitute at the National College in Kolozsvár. In 1904-1905 he undertook his military service.
Between 1905 and 1906 Dávid studied in Göttingen, attending courses by David Hilbert and Felix Klein, and then in Paris. Returning to Hungary, he first became an associate teacher at the Unitary College of Kolozsvár (1906-1907), and was later appointed to be a teacher at the Reformed College of Székelyudvarhely (1908-1912). He habilitated at the University of Kolozsvár in 1910, with his thesis About the Theory of Algebraic Numbers and Functions. To give lectures at the university, he had to commute between Székelyudvarhely and Kolozsvár, thus he desired to become a teacher in a university town, which he only achieved somewhat later. In 1911 Lajos Schlesinger left Kolozsvár when he was appointed as a Professor at the University of Giessen in Germany. Schlesinger invited Dávid to take part in writing commentaries on the works of Gauss for the Mathematics Seminars in Göttingen and Giessen. In 1914, he filled a vacancy which had occurred for a substitute teacher at the Higher Vocational School of the 8th District of Budapest, so he moved to the Hungarian capital.
He was known to be accurate, scrupulous and ambitious in his work. He possessed professional skills and was a devoted teacher. His work was highly efficient and he was held in high esteem both by his colleagues and his pupils. He gave several lectures at the sessions of the Society of Mathematics and Physics.
In 1916, on the recommendation of Lipót Fejér and Manó Beke (1862-1946), the University of Budapest supported his habilitation as private professor in analysis. In 1918, he was the first to give lectures at the university on the history of mathematics, focusing on the history of analysis. Between 1919 and 1929 he worked as a professor of the so-called "Paedagogium", the Teacher Training College of state civil schools in Budapest. He became engaged in the study of different issues of education and dealt with educational reforms. It was during this time that he had his interest awakened in research into Farkas Bolyai and János Bolyai.
Today Dávid he is best known for his work as a devoted Bolyai researcher. His most significant book, entitled A két Bolyai élete és munkássága Ⓣ was published in 1923. Based on this book, he had several articles about the two Bolyais, which he intended to be distributed abroad. As early as 1924, Lajos Dávid pointed out that the work of János Bolyai contained the seeds of the theory of relativity. Besides, the writing of Lajos Dávid is an important source-book because of the accuracy of its data. A second edition of this book was published in 1979.
Dávid was a dedicated professional in teacher training. From 1925 on, he worked as a lecturer in mathematics at the University of Debrecen, where he became a public associate professor in 1929, and a full professor in 1933 (until 1940). His focus again shifted to the study of arithmetic and geometric means, the history of mathematics, the Bolyai research, and the popularization of mathematics.
In Debrecen, Hungary, he was entrusted with organizing a Mathematics Seminar at the Institute, launching an institute library, and training the next generation of researchers with academic degrees. The first research group in the history of mathematics in Hungary was established under his guidance. It is to his merit that the book series titled Közlemények a debreceni Egyetem Matematikai Szemináriumából Ⓣ (1927-1940), containing 15 doctoral theses, started to appear. Many of the topics concerned related to Dávid's projects, to the research of the Bolyais and to the Gauss-type 'medium arithmetico-geometricum'.
There were only a few to assist him at the Mathematics Seminar, so Lajos Dávid himself held lectures on a very wide variety of topics: descriptive geometry, infinite series, infinitesimal calculus and geometry, analysis, the practical solution of equations, the theory of differential equations, surface theory, probability theory, and practical mathematics. To help effective learning, he wrote course books, e.g. Practical Differential Geometry I, and Plane Curves. In addition to this heavy teaching load, he also held lectures for medical students.
He was very well liked by his students. He delivered his entertaining lectures in a vivid and familiar style. He assigned significance to mathematical applications, both the mechanical and economic aspects. Also when there was no teaching at the university, he kept in touch with his students and accompanied them on trips, or received them at his home and replied to their letters during the summer vacations.
In addition, he dealt with the didactics of mathematics on an academic level, and he delivered lectures at the Teacher Training Institute of the University, as well. He was of the belief that "a professor should not only be convinced in what he professes, but, at the same time, he should also be able to make his students be convinced of that too, that is, a professor should be a real teaching master."
He was a member of the teachers' commission of enquiry, and was also a government delegate on the occasion of secondary-school graduation exams. He wrote some essays on reforms concerning teaching in secondary schools, emphasizing the close affinity of people to what is concrete as a natural guiding principle in the process of forming secondary-school education.
Between 1940 and 1944, he worked as a professor and director of the Institute of Mathematics at the University of Kolozsvár, Transylvania. During this time, he wrote his book entitled Bolyai-geometria az Appendix alapján Ⓣ, a good many copies of which were later pulped, and only a few copies have survived. In 1944, he returned to Hungary, but after this he became neglected, did not get any respected position, nor the qualification consonant with his scientific reputation. He was not awarded the Degree of Doctor of Science. He worked at the Institute of Geophysics, then at the National Museum. In 1950 he was forced into retirement. On the 150th Anniversary of the birth of János Bolyai his books were not exhibited. He went on with studying his favourite subject, the Bolyai research, with the help of his godson Lászlo Kalmár, but at the Mathematics Congress in 1960 he only participated as a member of the audience.
He published 55 books, and left behind 10 more, unpublished. A list of his publications is given at THIS LINK.
A list of his doctoral students, together with the titles of their theses are given at THIS LINK.
Let us list here what are considered to be his six major works:
- Theorie des Gauss'schen verallgemeinerten und speziellen arithmetisch-geometrischen Mittels, Mat. und Naturwiss. Ber. aus Ungarn 25 (1907), 152-171.
- Az algebrai iteráció elméletéhez, Mat. és Termtud. Ért 26 (1908), 230-240.
- A két Bolyai élete és munkássága, Bp. (1923), pp. 202; 2nd Enhanced Edition, Gondolat (1979), pp. 335.
- Bolyai geometria az Appendix alapján (Minerva, Kolozsvár, 1944), pp. 188; Reprint, Bolyai János Katonai Muszaki Foiskola, Bp.(1992).
- Debreceni régi matematikusok, A debreceni Tisza István Tud. Társaság II. Oszt. Munkái 2 (1927) 4., 35-54.
- Gauss, KöMal 3 (1927), 133-148.
Article by: Tünde Kántor, University of Debrecen