**Paul Diene**s was a Hungarian mathematician who, because of his political views, had to escape from Hungary in 1920. He spent most of his career in Wales and England, was a highly effective Ph.D. supervisor, and wrote the influential book *The Taylor Series* (1931).

- He seldom used his middle name, however, and is usually known as Paul Dienes.
- Paul Dienes was educated at the Debrecen Reformed College.
- After graduating from the Debrecen Reformed College, Dienes began studying mathematics and physics at the Pázmány Péter University in Budapest (it was later renamed the Eötvös Lóránd University).
- He happened to introduce Paul Dienes to her, with the remark that Paul Dienes was a mathematical genius, an introduction that led to their marriage.
- She received her degree in the same ceremony as Paul Dienes in 1905 at Pázmány Péter University, Budapest.
- Paul received his doctorate in mathematics.
- While undertaking research, Dienes had spent some time in Paris studying with Émile Borel and Jacques Hadamard at Université Paris IV-Sorbonne.
- The degree ceremony in Budapest was held on 24 June 1905 and Dienes was awarded a doctorate for his thesis Additions to the theory of analytic functions (Hungarian).
- Paul had a strong interest in the mathematical problems of the theory of relativity and vector space singularities.
- Valéria Dienes was friendly with the poet and writer Mihály Babits (1883-1941) and a close friendship developed between Paul Dienes and Babits.
- Dienes took part in school groups led by Babits discussing method of education.
- It was not only school teaching that Dienes undertook at this time for he was appointed as a docent at the University of Budapest in 1908, a docent at the University of Cluj-Napoca in 1912, and at the University of Budapest in 1916.
- Émile Borel had approached Dienes to see if he would publish his Budapest lectures as a monograph in the series "Collection of Monographs on the Theory of Functions, published under the direction of M Émile Borel," and Dienes' Leçons sur les singularités des fonctions analytiques Ⓣ(Lessons on singularities of snalytic functions) was published in that collection in 1913.
- Gedeon Dienes learnt English, French, German, Swedish, Italian and Russian and became a secretary at the Foreign Office.
- Zoltan Dienes became a mathematician and has a biography in this archive.
- Dienes had been a strong supporter of Béla Kun and, together with Babists, had argued for him in lectures to students and in protests in cafes.
- When this Government fell in 1919, Dienes had to leave Hungary in haste, with his life in danger.
- To avoid being captured, Dienes had hidden in a cupboard in a friends' apartment.
- His food was brought regularly by Sari Chylinska (1898-1992) who had studied dance with Valéria Dienes in Budapest from 1915 to 1918.
- She and Dienes became romantically involved.
- Valéria tried to arrange for Dienes to be taken out of the country and was put in touch with the captain of a river boat.
- He agreed to smuggle Dienes out of the country but only if he received a large sum of money.
- After Dienes arrived in Vienna in 1920 he failed to find an academic position and only managed to do a little film work being in crowd scenes in a film.
- Paul, after contacting Émile Borel and Jacques Hadamard, made his way to Paris with Sari in 1921.
- Dienes moved to Wales and began teaching in Aberystwyth in October 1921.
- In 1923 W H Young resigned from Aberystwyth and Dienes left to take up a lectureship in Swansea, Wales.
- Paul and Sari Dienes set up home in Sketty, on the outskirts of Swansea.
- Evan Davies had begun his university studies in 1921 at Aberystwyth and was taught there by both Dienes and W H Young.
- When both left in 1923, Evan Davies followed Dienes to Swansea where his research advisor was Dienes who advised him to work on the absolute differential calculus.
- In 1926 G H Hardy and Archibald Richardson approached Dienes suggesting he write a book on Taylor series.
- It would be difficult to overestimate the value, for advanced students, of these later chapters in Dienes' book.
- In 1929, before Dienes had finished writing his book on Taylor series, he had left Swansea to take up a readership at Birkbeck College in the University of London.
- In 1937 Paul and Sari Dienes separated.
- In addition to Evan Davies, Dienes supervised the Ph.D. studies of a number of outstanding students including: H S Allen, who wrote the thesis Maximum matrix rings (1942); Ralph Henstock (1923-2007), who wrote the thesis Interval Functions and their Integrals (1948); Abraham Robinson, who wrote the thesis The Metamathematics of Algebraic Systems (1949); and Paul Vermes (1897-1968), who wrote the thesis Gamma matrices and their applications to infinite series (1947).
- He also wrote the joint paper On the effective range of generalised limit processes (1938) with Richard George Cooke and encouraged him to write the book Infinite matrices and sequence spaces (1950) which contains a wealth of original results by Cooke and by Dienes.
- Dienes was appointed to the newly created Chair of Mathematics at Birkbeck College in 1945.
- Dienes retired in 1948 and turned to writing poetry.
- Dienes died of a heart attack in March 1952.

Born 24 November 1882, Tokaj, Hungary. Died 23 March 1952, Tunbridge Wells, Kent, England.

View full biography at MacTutor

Origin Hungary

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive