Riesz, Frigyes

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

Riesz, Frigyes

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, Web link 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 Web link in Budapest. For him the lectures of Gyula Kőnig and József Kürschák meant the most. Then he learnt for a year in Göttingen Web link 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 Riesz–Fischer 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) Web link 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, Web link where there had previously been no university. Web link

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; Web link president and later honorary president of section III of the Hungarian Academy of Sciences; honorary president of the János Bolyai Mathematical Society; Web link associate member of the Academy of Sciences of Paris; external member of the Bavarian Academy of Sciences and the Swedish Royal Association of Physiography.

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