# Anton Davidoglu

### Quick Info

Born
30 June 1876
Died
27 May 1958
Bucharest, Romania

Summary
Anton Davidoglu was a Romanian mathematician who studied for his doctorate in Paris. He was the founder of the Academy of Advanced Commercial and Industrial Studies in Bucharest, and laid the foundations of mathematical education of economists in Romania.

### Biography

Anton Davidoglu was the son of Cleante Davidoglu and Profira Mooc. Cleante Davidoglu was a medical doctor who served the villages around Bârlad, a town in the east of Romania not far from the border with Moldova. He had studied medicine in Paris and was awarded a doctorate in medicine in 1868. He later became head of the Bârlad hospital. Anton had an older brother, named Cleante Davidoglu after his father. Cleante Davidoglu Jr. (1871-1947) had a career in the military and became a famous Romanian major general during World War I. The paternal grandfather of the two Davidoglu boys was a seller of salep, a flour made from orchids used to make winter drinks, their great-grandfather was a professional cavalrymen in the Ottoman army, and their great-great grandfather was an infantryman in the Ottoman army.

Anton Davidoglu had both his primary and secondary education in his hometown of Bârlad and, being an outstanding pupil, he decided to go Paris for his university education instead of continuing to study at one of the two Romanian universities. He could have studied mathematics at the University of Bucharest where at least three of the mathematics staff had doctorates from Paris, but he chose to go the Paris to be taught by world leading mathematicians. He enrolled at the École Normale Supérieure but also attended lectures at Faculty of Science of the Sorbonne where he was taught by Jacques Hadamard who had just taken up a position at the Sorbonne after leaving a chair of mathematics in Bordeaux. Davidoglu graduated with a first degree in 1897 having impressed his teacher Hadamard.

Davidoglu then continued his studies at the École Normale Supérieure, undertaking research for his doctorate. He submitted his thesis Sur l'équation des vibrations transversales des verges élastiques to the University of Paris and was examined on 24 November 1900 by a committee chaired by Émile Picard and which included Henri Poincaré. The thesis begins with the following introduction:-
The present work contains the study of an equation of the fourth order which one meets in mathematical physics. We carried out this study using the method of successive approximations. In his classical memoirs on second order equations, M Picard, applying it to particular types of problems, obtained very important results with remarkable simplicity. This method of successive approximations occurs naturally in the question which occupies us, when we consider integrals as functions of a certain parameter.

The first part contains the study of the equation
$(1) \; \Large\frac{d^4 y}{dx^4}\normalsize = k \phi (x)y.$
M Picard's methods apply to this equation; difficulties appear when we want to establish the existence of an infinite series of exceptional values of k. An extension of Sturm's theorem for second order equations is useful for the representation of an arbitrary function by means of exceptional integrals of equation (1).

In the second part we study an asymptotic expansion of the integrals of equation (1) with respect to k. We have taken great advantage of a memoir by M Horn on second order equations, but we have not yet managed to represent the exceptional values of k asymptotically. For that, it would be necessary to solve asymptotically an equation that we form.

Some communications of the above have been made to the Academy of Sciences.
The differential equations that Davidoglu was studying in this thesis relate to the transverse vibrations of nonhomogeneous elastic bars. In 1900-01, he published two papers related to work from his thesis, namely Sur une application de la méthode des approximations successives (1900), and Sur les intégrales périodiques des équations différentielles binomes (1901), see [4] and [5].

The problem of computing the number of solutions of a system of polynomials had been studied at the end of the 19th century by Leopold Kronecker and Émile Picard. Davidoglu was advised by Émile Picard and, as he says in the Introduction above, applied Picard's results. He gave theorems on the number of roots of multiplicity greater than 2.

The author of [1] notes:-
Thus, Anton Davidoglu became the sixth Romanian with a doctorate in mathematics at the Sorbonne, after Spiru Haret (1851-1912) in 1878, David Emmanuel (1854-1941) in 1879, Constantin Gogu (1854-1897) in 1882, Nicolae Coculescu (1866 -1952) in 1895 and Gheorghe Țițeica (1873-1939) in 1899.
The author of [1] writes:-
Appreciated properly by the examining committee and the specialists of the time, the doctoral thesis brought Anton Davidoglu temporary joy followed by a long-term sadness! Young and inexperienced, Anton Davidoglu did not immediately publish the remarkable results in his thesis and thus, despite the importance of his results, he will not appear among the founders of the theory of integral equations, these being considered to be only Erik Ivar Fredholm (1866-1927) and Vito Volterra (1860-1940) whose fundamental independent results were published exactly as in Anton Davidoglu's thesis! Those who knew Anton Davidoglu directly claimed that this very sad scientific event marked his entire scientific career as well as his publishing activity, totalling only 12 articles!
We are somewhat puzzled by this statement since Davidoglu's thesis appears to have been published in Annales scientifiques de l'École Normale Supérieure (3) 17 (1900), 359-444, see [3].

Davidoglu left Paris after successfully defending his doctoral thesis, and returned to Romania. In 1902 he was appointed as an associate professor in the Department of Differential and Integral Computing at the Faculty of Sciences of the University of Bucharest. In 1903 he published Quelques démonstrations nouvelles des théoremes fondamentaux de l'analyse , see [6], which has the following introduction:-
The beginnings of Analysis offer the peculiarity of requiring a considerable effort at the beginning from those who are studying science for the first time. It is in fact known that a whole series of theorems concerning the notions of upper and lower limits is needed before tackling Rolle's theorem which is the foundation of the matter. It is this last theorem that I establish, so to speak, directly in Section (1); we will see, in fact, that very little is required to give the demonstration, which is done more analytically. The following Sections (2) and (3) contain the direct proofs of two theorems that are usually deduced from the first. These theorems are as follows: "Any function of a variable x whose derivative is identically zero in an interval ab is a constant in this interval"; and "Any function of a variable x whose derivative is constantly positive (negative) in the interval ab increases (decreases) in this interval (the statement remains true if the derivative becomes zero there without however being constantly zero there".
In 1905 he was promoted to full professor of differential and integral calculus at the Faculty of Sciences in Bucharest where he succeeded Iacob Lahovary (1846-1907). It is worth saying a few words about Lahovary. He had attended the School of Officers in Bucharest, they continued his education in Paris being awarded a mathematics degree from the Sorbonne in 1870. He had a military career, reaching the rank of general by 1900, but also in parallel had a career as a mathematician, becoming a professor at the Departments of Infinitesimal Calculus and Mechanics at the University of Bucharest. His colleagues at the University of Bucharest included David Emmanuel, Spiru Haret, O Gogu, and Dimitrie Petrescu; Davidoglu and all his colleagues taught the exceptional student Gheorghe Țițeica.

Bucharest University of Economic Studies was founded on 6 April 1913 and called at that time the Academy of Higher-level Commercial and Industrial Studies. Davidoglu was appointed to serve as the first Rector of the new institution and became a founding member. This was a difficult time with the two Balkan Wars taking place in 1912 and 1913. Romania took no part in the first but was involved in the second 1913 war against Bulgaria. Romania was neutral for the first two years of World War I, but entered the war on the side of the Allies in August 1916. This political situation certainly made the Commercial Academy's beginnings quite difficult. As well as acting as Rector, Davidoglu also served as a professor teaching financial mathematics and insurance. This means that Davidoglu is considered today as the founder of the Romanian School of Financial and Actuarial Mathematics.

After Romania entered World War I, their armies made initial advances but German troops counterattacked and by November 1916 the Germans were approaching Bucharest. Davidoglu fled to Petrograd (now St Petersburg), in Russia, where he remained for the duration of the war. While there he learnt Russian and made contacts with Russian mathematicians; he continued these contacts after the war was over and he returned to his various positions in 1918 at the University of Bucharest and at the Commercial Academy.

As a teacher, Davidoglu was highly regarded and respected by his students although he had exceptionally high standards setting examinations that were exceedingly challenging. He taught many students who went on to become leading Romanian mathematicians, including Theodor Angheluta, Petre Sergescu, Grigore C Moisil, Tiberiu Popoviciu and Caius Iacob all of whom have a biography in this archive. At the University of Bucharest he regularly taught courses on ordinary differential equations and partial derivatives. He also gave special courses in mathematical analysis at the Faculty of Science, dealing with existence theorems and the calculus of variations.

Nicholas Georgescu-Roegen (1906-1994) became a well-known mathematician, statistician and economist. Born in Constanta in Romania, he attended the lyceum in his home town, graduating in 1923 and entered the University of Bucharest where he studied mathematics. He writes about the mathematics course (see [9]):-
The requirement for the 'licence' was four courses per year for three years. There were no graduate courses. After the licence anyone could submit a dissertation for a doctor's degree. The curriculum was specifically classical; for example, it included a full year of elliptic functions but not a single lecture on modern algebra or topology. There was little variation from year to year. An exception: while I was in my last year, Anton Davidoglu, who ordinarily taught mathematical analysis, offered at his pleasure a special seminar on the singularities of differential equations. What I learnt from his masterly exposition helped me arrive at the peculiar results of my 1936 paper 'The Pure Theory of Consumer's Behaviour'. Curiously, in 1926 I did not think that it could be of value to me.
Although Davidoglu did not publish any books directly, in fact two books were published based on lecture notes taken by students at courses he gave. The course he gave on infinitesimal analysis at the Bucharest Faculty of Science was attended by his student Racliş Neculai Rodolphe (1896-1966). Rodolphe followed his professor Davidoglu in going to Paris to study for his doctorate which was awarded by the Sorbonne in 1930 for his thesis The principal solution of Poincaré's finite difference equation. Rodolphe's notes of Davidoglu's course formed the basis of Davidoglu's book Curs de analiza infinitezimala published in 1931. The second of Davidoglu's books was based on a course he gave at the Commercial Academy. In this case the notes of his course on insurance theory were taken by his student Ilie Niculescu and published as Curs de teoria asigurarilor in 1935.

The author of [1] writes:-
Although few in number but dense in content and full of new ideas, Anton Davidoglu's works inspired many Romanian or foreign mathematicians in their research and were cited in reference works in the field such as Émile Picard's 'Treatise on Analysis'. Anton Davidoglu became and remained a significant landmark in the development of the Romanian higher mathematical and economic education. Founder of the Academy of Advanced Commercial and Industrial Studies in Bucharest, Anton Davidoglu laid the foundations of the mathematical education of economists.
Davidoglu retired from his positions at the Bucharest Faculty of Science and at the Commercial Academy on 1 January 1941. In the years before his retirement, he had served as dean of the Faculty of Science. In 1956 Hadamard, at this time 90 years old, attended the Fourth Congress of Romanian Mathematicians held in Bucharest. He remembered his excellent Romanian student from nearly sixty years earlier, and asked:-
How is my eminent student Davidoglu?
In 1976 Romania issued a stamp in honour of Anton Davidoglu's 100th birthday. See THIS LINK.

### References (show)

1. Anton Davidoglu (1876-1958), Outstanding Members, Departamentul de Matematici Aplicate, Academia de Studii Economice din Bucureti.
https://asemath.ase.ro/membri-marcanti/
2. A Bellow, C S Calude and T Zamfirescu (eds.), Mathematics Almost Everywhere: In Memory Of Solomon Marcus (World Scientific Publishing Company, 2018).
3. A Davidoglu, Sur l'équation des vibrations transversales des verges élastiques, Annales scientifiques de l'École Normale Supérieure (3) 17 (1900), 359-444.
http://archive.numdam.org/article/ASENS_1900_3_17__359_0.pdf
4. A Davidoglu, Sur une application de la méthode des approximations successives, Comptes rendus de l'Académie des Sciences 130 (1900), 1241-1243.
5. A Davidoglu, Sur les intégrales périodiques des équations différentielles binomes. Bulletin de la Société des Sciences de Bucarest-Roumanie 10 (6) (1901), 524-526.
https://www.jstor.org/stable/pdf/43770590.pdf?ab_segments=0%2FSYC-6168%2Fcontrol&refreqid=fastly-default%3Ae4e5352aa965a00d2907dc4a1a717b41
6. A Davidoglu, Quelques démonstrations nouvelles des théoremes fondamentaux de l'analyse, Bulletin de la Société des Sciences de Bucarest-Roumanie 12 (5/6) (1903), 341-346.
7. N Georgescu-Roegen, From Bioeconomics to Degrowth: Georgescu-Roegen's 'New Economics' in Eight Essays (Taylor & Francis, 2011).
8. J M Gowdy, K Mayumi (eds.), Bioeconomics and Sustainability: Essays in Honor of Nicholas Georgescu-Roegen (Edward Elgar Publishing, 1999).
9. J A Kregel (ed.), Recollections of Eminent Economists (Palgrave Macmillan, 1989).
10. P G Partington, Who's who on the postage stamps of Eastern Europe (Scarecrow Press, 1979).
11. P P Teodorescu, Treatise on Classical Elasticity: Theory and Related Problems (Springer Netherlands, 2013).