# Paul Alexander Dienes

### Quick Info

Tokaj, Hungary

Tunbridge Wells, Kent, England

**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).

### Biography

We note first that**Paul Alexander Dienes**was also known as

**Pál Sándor Dienes**. He seldom used his middle name, however, and is usually known as

**Paul Diene**s. He came from a wealthy family who were Presbyterians. He was the son of Barnabás Dienes (1852-1923), a jurist who owned local vineyards, and Ilona Pusztay (1860-1934), who was of Greek origin. Barna and Ilona Dienes were married in Debrecen on 7 October 1877. They had eight children: Klára Katalin Dienes (1878-1959); Rósza Ilona Etelka Dienes (1880-1971); Kálmán Dienes (1882-1954); Pál Sándor Dienes (1882-1952), the subject of this biography; Lajos Dienes (1885-1974: László Dienes (1889-1953), Barna Dienes (1895-1950); and Katalin Dienes (1900-1979). We note at this point that Kálmán became an engineer, Lajos became a bacteriologist, and Barna became a Presbyterian priest.

Paul Dienes was educated at the Debrecen Reformed College. This important college had been founded in 1538 and provided a good education, particularly strong in philosophy. 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). There he was taught by Lipót Fejér who also taught the student Valéria Anna Geiger (1879-1978). Valéria Geiger's [5]:-

... university work focused on studying mathematics and physics. Lipót Fejér, the doyen of Hungarian mathematics of that period, was in love with Valéria. 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. Valéria began her doctoral studies of philosophy by listening to Bernát Alexander's lectures, the leading philosopher of Budapest those days, just like Pólya and many contemporary intellectuals did. She received her degree in the same ceremony as Paul Dienes in 1905 at Pázmány Péter University, Budapest. They exchanged engagement rings during that ceremony. Paul received his doctorate in mathematics. Valéria's doctorate was in philosophy as a major subject with a first minor in mathematics and a second minor in aesthetics.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 and Valéria Dienes were married in December 1905. On 2 August 1907 he began teaching at the 10th District State High School High School where he taught mathematics, physics, philosophy, and French. He went to Paris with his wife in 1908 and, after working with Borel and Hadamard, published the 88-page

*Essai sur les Singularités des Fonctions Analytiques*Ⓣ with Gauthier-Villars in Paris in 1909. Valéria worked with the philosopher Henri-Louis Bergson (1859-1941) and became fascinated by the relations between dance and mathematics [4]:-

The couple had a common interest in epistemology and in the philosophy of mathematics and physics at a time when the university life of Paris was loud from the discussion of functional representations of physical quantities, duration, and measurable time. Einstein's definitions on simultaneity and thoughts on the relativity of length and time (1905) began to become more widely known these days in France, while Bergson's public lectures in the Collège de France went on about 'duration' and 'time'. The couple worked together on common analytical functional topics. Paul had a strong interest in the mathematical problems of the theory of relativity and vector space singularities. Reports on their work in this period were published in the 'Comptes Rendus' of the Académie des Sciences, and in several papers in Hungarian.Their joint papers include

*Sur les singularités algébrologarithmiques*Ⓣ (1909) and three papers on

*General theorems on algebraic and logarithmic singularity*(Hungarian) in 1911 and 1912.

As a school teacher in Hungary he gave lectures aimed at parents of the school children, organised charity events to raise money to support the education of children of poor parents, and arranged field trips for his students in the areas of thermodynamics and electrical engineering. 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*Ⓣ was published in that collection in 1913.

You can read extracts from reviews of

*Leçons sur les singularités des fonctions analytiques*Ⓣ at THIS LINK.

Paul and Valéria Dienes had two children, Gedeon Dienes (born in Budapest on 16 December 1914) and Zoltan Pál Dienes (born in Budapest on 11 September 1916). Gedeon Dienes learnt English, French, German, Swedish, Italian and Russian and became a secretary at the Foreign Office. He represented Hungary at the peace conference at the end of World War II. He later worked in the Publishing House of the Hungarian Academy of Sciences, then became interested in dance, writing articles in many languages and founding a Budapest dance company. Zoltan Dienes became a mathematician and has a biography in this archive.

Béla Kun was a Hungarian Communist revolutionary and politician who, with Soviet support, led a successful

*coup d'état*and proclaimed the Hungarian Soviet Republic. As People's Commissar of Foreign Affairs he was the effective leader of Hungary from March 1919 until August 1919. 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. After the Hungarian Soviet Republic was formed, he became the head of the committee appointed to run the University of Budapest and also took part in the organisation of the Marx-Engels Workers' University. In mid July 1919, the Romanian army attacked Hungary, and when the Red Army failed to come to their aid, Béla Ku fled the country. Counter-revolutionaries start to hunt down supporters of Béla Kun and execute them. Richard George Cooke (1895-1965) writes [9]:-

During the Government of Bela Kun, Dienes took an active part in educational work in relation to the University. When this Government fell in 1919, Dienes had to leave Hungary in haste, with his life in danger. He has given me entertaining and thrilling accounts of his escape, and of his activities in the first period after his exile; for example, he escaped from Hungary in a cargo boat on the Danube which was supposed to be carrying beer to Vienna, and he occupied one cask instead of the beer. He duly arrived in Vienna ...Let us give a few more details about his escape. 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. To raise this sum, all the family possessions had to be sold, including their large and very valuable library. He arrived in Vienna with nothing but the clothes he was wearing.

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. Valéria, Gedeon, Zoltan and Sari Chylinska joined Dienes in Vienna and they lived in a Montessori children's home. Paul and Valéria agreed to divorce, Valéria and the children went to Nice in France, where they lived in a commune run by Raymond Duncan, the brother of the dancer Isadora Duncan. Paul, after contacting Émile Borel and Jacques Hadamard, made his way to Paris with Sari in 1921. He asked Hadamard if he knew of any British or American university that would like to employ him to teach as "a representative of the Paris School of Mathematicians." By coincidence Hadamard was approached by W H Young a couple of weeks later asking if he knew anyone looking for a position who could teach in the Parisian style. Dienes moved to Wales and began teaching in Aberystwyth in October 1921.

In 1922 Dienes' divorce from Valéria became official and he married Sari in Neukematen, Austria on 26 July of that year. He had been looking at the fundamental ideas in the theory of relativity and published papers such as

*Sur la connection du champ tensoriel*Ⓣ (1922). He had made some criticisms and Einstein wrote to him in August 1922:-

Your attack on the mathematical theories by Weyl and Eddington only touches the formulation, not however the content. Weyl had treated the second-order quantities loosely negligently but in a manner that is easily demonstrated to be innocuous. I am sending you a small book in which you will find on pages 48-49 a proof Levi-Civita's and Weyl's train of thought sketched a little more precisely, against which there ought to be no objection, in which he avoids these inaccuracies so such objections do not arise anymore.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. After four years work, in 1931

*The Taylor Series. An Introduction to the Theory of Functions of a Complex Variable*was published. Norman Miller writes [16]:-

Professor Dienes has here performed a notable service to the mathematical world in assembling and ordering in a thoroughgoing manner the modern theories relating to Taylor series. From its title and subtitle one might suppose the book to be another elementary text book on complex function theory from the Weierstrass point of view. The title however is too modest. The book is a pioneer in its field and makes no inconsiderable demands on the maturity of its readers.Joseph Ritt writes [19]:-

This treatise conducts the reader from the elements of real variable theory into some of the furthest reaches of complex analysis. ... It would be difficult to overestimate the value, for advanced students, of these later chapters in Dienes' book. They reduce to didactic form a large section of the recent literature on complex analysis. ... this treatise ... is the work of a distinguished authority and will hold an important place in every mathematical library.You can read more extensive extracts from reviews of this book at THIS LINK.

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. Dienes' two sons, Gedeon and Zoltan, spent most of the year with their mother Valéria, but would spend the summers with Paul and Sari Dienes travelling in France, Germany, Hungary, Italy and Transylvania. Dienes kept his interest in music and dance and in 1930 he and his wife became friends with the composer Michael Tippett and with the classical Indian dancer Uday Shankar, brother of Ravi Shankar. 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). Although not formally Reuben Louis Goodstein's advisor, nevertheless he was much involved in helping Goodstein with his thesis

*An axiom-free equation calculus*(1946). 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. He became more interested in logic and wrote papers such as

*On ternary logic*(1945) which begins as follows:-

In this paper we give the complete list of the functions of one variable with some of their properties, and lists of functions corresponding to various properties of sum, product, implication, and equivalence. The range of the variables as well as that of functional values will be 0 (false), 1/2, 1 (true). As an application we consider Frege's, Russell's and Heyting's systems in ternary logic. The proofs are mostly omitted as obvious if sometimes laborious.Wilhelm Ackermann, reviewing this paper, writes [1]:-

It is well known that in a three-valued propositional calculus with the values 0, $\large\frac{1}{2}\normalsize$, 1 there is no unequivocal determination of the matrix system defining the logical connections due to the lack of a generally recognised interpretation. Usually, however, one will proceed in such a way that the logical functions for 0 and 1 retain the same values that they have in two-valued logic. Symmetry will be required for disjunction, conjunction and equivalence. The author now undertakes to list the various possibilities that then remain for negation, disjunction, conjunction, implication and equivalence and to group them according to their main properties. It is stated which types of conjunctions and disjunctions are associative, which disjunctions with regard to which conjunctions satisfy one or the other of the two distributive laws, and for which definition of negation, conjunction and disjunction De Morgan's formulas apply.Dienes retired in 1948 and turned to writing poetry. The book of his poems,

*The Maiden And The Unicorn: A Cycle Of Poems*, was published in 1954, two years after his death. His friend, the composer Michael Tippet, said of his poetry [9]:-

The first thing to remember about him was that he had a philosophical and mathematical discipline as the core of his mind, but music had an almost Schopenhauerian significance for him .... I think, therefore, that his poetry represented an attempt at an amalgam of these various sensibilities, so that the sound pattern of the verse seems to overbalance the pattern of the sense. It is possible that I, as someone with a musical discipline, and abiding interest, though no aptitude, for philosophy, can savour Dienes's poetry better than most.Dienes died of a heart attack in March 1952. Cooke writes [9]:-

Dienes had a most charming personality, and was much loved by both his colleagues and his students.

### References (show)

- W Ackermann, Review: On Ternary Logic, by Paul Dienes,
*The Journal of Symbolic Logic***15**(3) (1950), 225. - Anon, Review: The Taylor Series. An Introduction to the Theory of Functions of a Complex Variable, by Paul Dienes,
*The Military Engineer***50**(335) (1958), 242. - Anon, Review: The Taylor Series. An Introduction to the Theory of Functions of a Complex Variable, by Paul Dienes,
*Nature***130**(3275) (1932), 188. - A G Benedek and A Tuska, Paul Dienes: a forgotten character in the history of math or a missing link in the family tree of embodied mathematics?,
*HMTM*(May 2022). - A G Benedek, Embodied Conceptions of Mathematical Understanding in the Twentieth Century: the emergence of Zoltan P Dienes's principles and their origin.

https://core.ac.uk/download/pdf/159127121.pdf - R Berlind and S Dienes, Sari Dienes,
*Art Journal***53**(1), Art and Old Age (1994), 38-39. - Biography of Paul Dienes,
*Dienes family Home Page*.

http://www.dienes.hu/?page_id=40 - R Borus (ed.), A század nagy tanúi (RTV- Minerva, Budapest, 1978).
- R G Cooke, Obituary: Paul Dienes,
*Journal of the London Mathematical Society*(2)**35**(1960), 251-256. - P Dienes, On Ternary Logic,
*The Journal of Symbolic Logic***14**(2) (1949), 85-94. - P Dienes, A new treatment of the theory of inference,
*The Monist***40**(3) (1930), 462-476. - H F, Review: The Taylor Series. An Introduction to the Theory of Functions of a Complex Variable, by Paul Dienes,
*Journal of the Institute of Actuaries (1886-1994)***63**(1) (1932), 110-111. - G B Jeffrey, Review: The Taylor Series. An Introduction to the Theory of Functions of a Complex Variable, by Paul Dienes,
*The Mathematical Gazette***16**(221) (1932), 358. - P E B Jourdain, Review: Leçons sur les Singularités des Fonctions analytiques, by Paul Dienes,
*The Mathematical Gazette***7**(107) (1913), 177. - S Mac Lane, Review: Logic of Algebra, by Paul Dienes,
*The Journal of Symbolic Logic***4**(2) (1939), 100. - N Miller, Review: The Taylor Series. An Introduction to the Theory of Functions of a Complex Variable, by Paul Dienes,
*The American Mathematical Monthly***39**(7) (1932), 418-420. - N Nielsen, Review: Leçons sur les Singularités des Fonctions analytiques, by Paul Dienes,
*Nyt tidsskrift for matematik***27**(AFDELING B) (1916), 67. - F E Relton, Review: The Taylor Series. An Introduction to the Theory of Functions of a Complex Variable, by Paul Dienes,
*Science Progress in the Twentieth Century (1919-1933)***27**(105) (1932), 154. - J F Ritt, Review: The Taylor Series. An Introduction to the Theory of Functions of a Complex Variable, by Paul Dienes,
*Bulletin of the American Mathematical Society***38**(11) (1932), 792-793. - B Rosser, Review: Logic of Algebra, by Paul Dienes,
*Bulletin of the American Mathematical Society***46**(1940), 15. - Sari Dienes,
*Sari Dienes Foundation*.

http://saridienes.org/life/index.html - L C Young, Review: Logic of Algebra, by Paul Dienes,
*The Mathematical Gazette***23**(256) (1939), 426.

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Written by J J O'Connor and E F Robertson

Last Update July 2022

Last Update July 2022