prominent scientist from the University of Cluj
Mathematician and physicist Gyula FARKAS, the most frequently quoted professor of all universities in Cluj from the beginnings until today, was born on March 28, 1847 in the town called Sárosd (in western Hungary). He attended the secondary school in Gyor at the Benedictine Secondary School. In 1866 he was admitted to the Faculty of Law and to the Music Academy concurrently. During this period he published articles on the theory of music. Encouraged by the Physics professor Ányos Jedlik he turned his attention to Physics and transfered to the Natural Sciences and Chemistry specialization.
During the 1870-1874 period he worked as a professor at Székesfehérvár where he also taught music. He wrote a Physics textbook for the popular schools.
During 1874-1880, being a private teacher for the children of count Géza Batthány he went on a trip with the Batthány family in Italy and France, where he met famous mathematicians (Hermite, Villarceau etc.). These encounters prompted him to turn to Mathematics. During the 1881-1887 period he intensely studied Mathematics with the financial support of count Géza Batthány, subsequently applying for a doctorate in this specialization. After obtaining the doctoral degree he taught the Theory of Functions at the University of Budapest.
In 1887 he was appointed teaching professor at the University of Cluj with the Department of Theoretical Physics. He was Dean of the Faculty of Sciences seven times (1889-1890, 1892-1893, 1893-1894, 1896-1897, 1897-1898, 1898-1899, 1902-1903), Rector once (1907-1908) and deputy once (1908-1909).
He was elected corresponding member in the Hungarian Academy in 1898, and full member in 1914. In 1892 he was appointed the delegate of the Cluj University to Padua, on the occasion of celebrating the 300 years anniversary since Galilei had come to this University. He was awarded the title of Doctor Honoris Causa of the University of Padua.
Gyula Farkas’s most important achievement is a Theorem of Linear Inequalities Systems, today called, out of historical considerations, Farkas’ Lemma.In current language, this theorem can be formulated as follows:
The necessary and sufficient condition in an euclidian space for the inequality gx?0 is a consequence of the inequalities system g 1 x?0, g 2 x ? 0, . , g n x ? 0 is that the vector g is a linear combination with unnegative shares of the vectors g 1, g 2, . , g n . .
This theorem has been known and used in the world of science especially since 1951, when the book HW Kuhn - A. W. Tucker was released: Nonlinear programming, which is used to demonstrate the theory for the multipliers in the optimization theory (known today as the Kuhn-Tucker theorem). This Farkas’ Lemma is now quoted on a daily basis in the Mathematics research papers related to operational research.
Its great merit was to bring to Cluj renowned mathematicians such as Lipót Fejér, Frigyes Riesz, Alfred Haar, who had important contributions to the development of Mathematics in the period when they were teachers at Cluj. Their names cannot be left out of any serious book of Mathematics Analysis even today.
Gyula Farkas published in 1906 his first article related to the theory of relativity (Einstein's article in this field was published in 1905!). Fourier's Principle (described in 1789) was rediscovered in 1829 by Gauss. Gyula Farkas was the first who demonstrated with mathematical rigour this principle. He showed the usefulness of this principle in describing movement in a more general form than all his predecessors had done. He dealt with the theoretical problems of mechanics, thermodynamics, and electrodynamics. In his discoveries in Theoretical Physics physicist Farkas benefited from the help of mathematician Farkas.
"Nature uses mathematical language." - is what he wrote in a paper. In 1900 he published the book entitled Vektortan és az egyszerű inaequatiók tana (Theory of vectors and simple inequalities), which comprises his own achievements in the domain.
He popularized the achievements of Farkas Bolyai and János Bolyai. In 1902, he held a speech as Dean on occasion of unveiling the commemorative plate on the house where János Bolyai was born. He was one of the founders of the Society of Mathematics and Physics. He was chairman of the section of Natural Sciences in the Transylvanian Museum Association.
He wrote a series of course notes, some of which are still to be found nowadays in the Faculty of Mathematics and Informatics Library and they can be consulted and easily understood because he put great emphasis on an accurate and didactic exposition.
Farkas's influence is also identifiable in the works of Alfred Haar, Imre Fényes and Teofil Vescan.
Gyula Farkas retired in 1915 and withdrew to Pestszentlőrinc (town near Budapest) where he died on December 27, 1930.