Riesz, Frigyes
(Győr, January 22nd, 1880 – Budapest, February 28th, 1956)

One of the most significant personalities among Hungarian mathematicians, creator of functional analysis.
At the beginning he studied engineering at the Technical University of Zurich,
but he soon realised that he was much more interested in mathematics than in technical subjects. So he continued to study at the Royal Hungarian University of Sciences
in Budapest. For him the lectures of Gyula Kőnig and József Kürschák meant the most. Then he learnt for a year in Göttingen
and attended the lectures of David Hilbert and Hermann Minkowski. He obtained his PhD degree and diploma of secondary school teacher of mathematics and physics in Budapest.
His life was basically influenced by his invention known in the mathematician world as the RieszFischer thesis. His theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space. It was the mathematical basis for proving the equivalence of matrix mechanics and wave mechanics which is of fundamental importance in early quantum theory.
His student, Ákos Császár, academician described this result as follows: This invention of Frigyes Riesz, to say the least of it, had a decisive influence on the development of the whole 20th century mathematics. Its basic idea, which is that from many aspects functions behave similarly to space vectors, is the last source and starting-point of an enormous and still intensively developing branch of mathematics called functional analysis, and there are innumerable possibilities of its application both in mathematics and physics, among others it is one of the basic aids of quantum mechanics.
Today the world considers Frigyes Riesz, M. Fréchet and Banach as founders of functional analysis, the gigantic theory joining the methods of algebra, analysis and geometry.
In 1912 Riesz was appointed assistant and shortly after full professor of the University of Kolozsvár. (today Cluj, Romania)
In 1920 the Peace Treaty of Trianon shrunk Hungary to its third, Transylvania became part of Romania. The University of Kolozsvár in 1920 was transferred to Szeged,
where there had previously been no university. 
Frigyes Riesz and Alfréd Haar also moved to Szeged. Mostly due to their persistent working Szeged became a research centre of mathematics, abroad it is still talked about as the Hungarian Göttingen. In 1922 Riesz set up the János Bolyai Mathematical Institute together with Haar. The Institute was named after the famous Hungarian mathematician whose birthplace was Kolozsvár. Riesz became editor of the newly founded journal of the Institute Acta Scientiarum Mathematicarum which quickly became a major source of mathematics.
By that time Riesz had become famous even in far-away countries, and scholarship holders came to visit him in Szeged even from abroad.
In 1945 Riesz was appointed to as professor of the Loránd Eötvös University of Sciences.
Memberships: Correspondent (1916) and full (1936) member of the Hungarian Academy of Sciences;
president and later honorary president of section III of the Hungarian Academy of Sciences; honorary president of the János Bolyai Mathematical Society;
associate member of the Academy of Sciences of Paris; external member of the Bavarian Academy of Sciences and the Swedish Royal Association of Physiography.
Honours:
- Grand Prize of the Hungarian Academy of Sciences (1945), Kossuth Prize (1949, 1953).
References:
- M Bernkopf, The Development of Functional Spaces, Archive for History of Exact Sciences 3 (1966-67), 1-96.
- Frigyes Riesz: necrologue (Russian), Uspekhi matematicheskikh nauk 12 (4) (76) (1957), 155-166.
- P R Halmos, The work of Frigyes Riesz (Hungarian), Mat. Lapok 29 (1-3) (1977/81), 13-20.
- E Kreyszig, Friedrich Riesz als Wegbereiter der Funktionalanalysis, Elem. Math. 45 (5) (1990), 117-130.
- B Szökefalvi-Nagy, Life and personality of Frigyes Riesz (Hungarian), Mat. Lapok 29 (1-3) (1977/81), 1-5.
- Frigyes Riesz URL: http://www-history.mcs.st-andrews.ac.uk/Biographies/Riesz.html
Functional analysis
A branch of mathematical analysis, studies infinite dimensional vector spaces and mappings between them. The elements of these spaces are very often themselves functions, as for example, the space of continuous functions on an interval. Its historical roots rests on the study of transformations, such as the Fourier transformations, and on the study of integral and differential equations. This usage of the term functional goes back the variation calculus, implying a function whose argument is a function.
König, Gyula
(Györ, 16th December 1849 - Budapest, 8th April 1913)
He studied medicine in Vienna and mathematics in Heidelberg. He earned his doctorate in 1870.
Next year he returned to Budapest. He became a professor at the Teacher's College in Budapest in 1873 and was appointed professor in the following year at the Technical University of Budapest.
König made the most important contributions to teaching, rather than to research. He raised the level of mathematics teaching at the Technical University to a high standard.
He published many research papers on a wide range of topics in mathematics, but his greatest significance comes from his excellent textbooks he wrote. When he retired from his position in 1905, he continued to lecture particularly on topics that he was interested in. He spent the last part of his life working on his own approach to set theory, logic and arithmetic, which was published in 1914, one year after his death.
He also contributed to the Hungaian Academy of Sciences, which he was elected to in 1889.
Császár, Ákos
(1924 - )
He obtained his teacher's degree in physics and mathematics at the Péter Pázmány University of Sciences then he became a lecturer of Frigyes Riesz at the Lóránd Eötvös University where he taught for forty years. Since 1990 he has been the chairman of the Department of Mathematical Sciences of the Hungarian Academy of Sciences.
He introduced the idea of colour topogenic spaces, by means of which he established the synthesis of neighbouring spaces and uniform spaces. His monograph written on this was published in French in 1960.
Many students have learnt and learn even today from his lecture notes and textbooks written with the utmost accuracy: Introduction into the general topology (1970), Real analysis Vol. I and II (1983). As early as his twenties he described the body surrounded by flat plates, which has been named after him since then. The highly effective solution and the elementary way of discussion drew high attention all over the world.
Haar, Alfréd
(18851933)
He was one of the founders of the mathematical school of Szeged and a member of the Hungarian Academy of Sciences. He achieved significant results in different fields of mathematical analysis. In his doctoral thesis he discusses Haar's orthogonal function system, which, among others, has a role in the theory of the Fourier series. He made his mark as a scholar in functional theory, in variation calculation and in the theory of sets; his quantity concept introduced into the theory of topologic groups is the invariant quantity of continuous groups.
Main building and Library (Korb and Giergl 1906-1907) of the University of Kolozsvár