Biography

Žarko Mijajlović

IN THE SECOND HALF OF THE 19TH CENtury, the groundworks were laid for the emergence of Serbian mathematics. Universally recognized as the most influential mathematicians of that time, Henri Poincaré and David Hilbert, introduced new mathematical concepts and new style of abstract mathematical thinking. New mathematical theories with multiple applications in technics and physics were emerging, and old theories were receiving novel grounding. Mihailo Petrović, Poincaré’s doctoral student, began his academic career armed with such knowledge and a European understanding of science and culture. As a young man, he was already well-formed as a mathematician and moreover, very productive academically. Tending to analysis, he already knew well the works of mathematicians of the French school in that area and in his works he was already discussing the most topical issues in the field of differential equations and theory of functions.

Petrović returned from Paris in 1894, at the exact time his former professor, Dimitrije Nešić, retired. He therefore applied for the vacancy to become a professor at the University. Another application was submitted by Petar Vukićević, a slightly older fellow student at the Faculty of Philosophy. Petrović was chosen for the post, having obtained one vote more than Vukićević. Vukićević subsequently became a gymnasium professor and probably due to the defeat of his application, he ceased to engage in academic work or pursue an academic career. At that time, the Grande école (Grand School) was consistently adhering to the principle of numerus clausus which limited the number of professorship posts, often to the detriment of development of the Grand School and science in Serbia as such. Petrović once said the following regarding his election for the post: “If I had not obtained that one additional vote for my application for a Grand School professor, I would have never pursued mathematics as my profession. I would have lived on Serbian rivers, not on a boat, but on a dinghy.”

Upon his return to Belgrade, Petrović encountered several mathematicians engaging in scholarly work: Ljubomir Klerić, Dimitrije Nešić, Petar Živković, Dimitrije Danić and Bogdan Gavrilović. Among them, Professor Bogdan Gavrilović was held in particularly high regard and he soon became a close friend and fellow colleague of Petrović. Gavrilović was, among other things, a writer of excellent university textbooks on linear algebra and analytical geometry, about which Radivoj Kašanin said the following: “Both textbooks, but particularly the latter one, would have been to the credit of every nation and at that time many nations far bigger and happier than us did not have such works.” At approximately the same time two other scholars with Doctoral degree in mathematics were also residing in Belgrade, namely Đorđe Petković and Petar Vukićević, pursuing their careers as gymnasium professors.

In his scholarly work, Mihailo Petrović upheld the highest standards of the most developed European countries. During a brilliant upward career span, in only four years, by the beginning of the 20th century, Petrović had published some thirty papers in leading European mathematical journals. This success brought a great reputation to Petrović and he soon received major recognition. Already in 1897, less than thirty years old, he became a correspondent member of the Serbian Royal Academy and in 1899 a regular member. With the new century, Serbia enthroned its king of mathematics. He became an honorary member of several foreign academies of arts and sciences, namely those in Bucharest, Prague, Warsaw and Krakow. He was elected a correspondent member of the Yugoslav Academy of Sciences in Zagreb and became a member of numerous European learned societies.

In terms of his academic work, Petrović belongs to a specific time. Due to the rising voluminousness of mathematical knowledge, it was difficult, if not impossible, for an individual to be well acquainted with all of the mathematical knowledge of the time. The era of universal mathematicians and scientists was slowly passing. Henri Poincaré was certainly one of the last homo universalis of science in the sense of the understanding and breadth of academic work in mathematics, mechanics and philosophy he displayed and he was one of the professors of Mihailo Petrović. Judging by his later scholarly work, we can conclude that the spirit of universalism in his professor was inculcated in Petrović as well. He equally excelled, and achieved first-rate results in, several mathematical fields: differential equations, numerical analysis, theory of functions of a complex variable and geometry of polynomials. His interest also expanded to natural sciences, chemistry, physics and biology, and he published academic work in these fields too. Further, it is considered that Petrović was a founder of new academic disciplines, namely mathematical phenomenology and spectral theory.

The influence of Mihajlo Petrović on the development of mathematics in Serbia was enormous. He was spiritus movens of Serbian mathematics and has strongly contributed to the spirit of contemporary European science in Serbia. Moreover, he knew how to gather people together, awaken their interest and motivate them. This is solely an opinion of Serbian mathematical public, but also the fact we is established in world-class reference journals. Thus The Oxford Handbook of the History of Mathematics gives prominent space to academic biography of Mihailo Petrović. It emphasizes that Petrović, as the most prominent Serbian mathematician at that time, set the directions of development of the Serbian mathematical school on the foundation of French mathematics.

In his academic career, Petrović published some four hundred papers, of which three hundred were in mathematics. Furthermore, he published twelve books and there are fourteen manuscripts based on his lectures, crafted either by students or himself. The academic career of Mihailo Petrović was tied to the Grand School, which became a University in 1905 and subsequently to the University of Belgrade, until the end of his professional life. As he once said himself, he had spent a total of fifty-five years in the Mansion of Miša Anastasijević, where the gymnasium he attended was located, along with the Grand School, first as a pupil, and later as a student and a professor. The Department of Mathematics of Faculty of Philosophy was the main site of Petrović’s scholarly and pedagogical work.

During one period, from when Belgrade University was established in 1905 until Milutin Milanković became a professor of applied mathematics in 1909, Petrović was the sole professor of mathematics at the Faculty of Philosophy. For this reason, it happened that in one school year he practically taught all subjects, as illustrated by the versatility and number of manuscript books that have been preserved, that is, student notes on his lectures. They included subjects in linear algebra, analytical geometry in a plane and in a space, differential equation and its applications, ordinary and partial differential equations, and theory of functions and algebraic equation. Judging by the manuscripts, the lectures of professor Petrović were not structured in the form of strict definitions, theorems and proofs and were not difficult to follow. It seems that they contained exactly the material which the students were supposed to learn. He published three university textbooks: Computing with Number Intervals, 1932, Elliptic Functions, 1937 and Integration of Differential Equation by Use of Series, 1938. He also published the textbook Leçons sur les spectres mathematiques, Paris, 1928, which he followed when he gave lectures at Sorbonne in Paris in 1927–1928.

When we talk about Petrović’s teaching work at the University, we have to say that along with his colleague, Professor Bogdan Gavrilović, Petrović elevated Serbian mathematics to the European level. Milutin Milanković emphasizes that the two of them laid the foundations of Serbian mathematics. Petrović did it in terms of academic work, and Gavrilović in terms of organizational work, helping the Grand School to grow into the University of Belgrade. Gavrilović and Petrović were complementary in their interests in mathematics. While the focus of Petrović’s work was on analytical methods, Gavrilović focused more on linear algebra and geometry. Petrović mostly published scholarly works, while Gavrilović wrote valuable monographic textbooks in algebra and geometry. Unlike Petrović’s papers, Gavrilović’s works, perhaps undeservedly, have not left a major trace in the mathematical community of Belgrade, even less internationally, since they were all published in Serbian. This was also at least partially due to the rule that papers in Academia’s Gazette, where Gavrilović published, had to be published in Serbian. On the other hand, the majority of Petrović’s papers were published in French and in leading European journals. Whatever the case may be, Petrović and Gavrilović, each in his own way, have enormously contributed to the development of mathematics in Serbia and to the creation of an atmosphere in which, from a provincial town, Belgrade has developed into one of the centers of academic work.

It is interesting that the aforementioned complementarity of Petrović and Gavrilović was not exhausted in the field of education and science, but also extended to their everyday life. Petrović was a great fisherman, Gavrilović was a gardener who bred peaches. Petrović was a world traveler, while Gavrilović mostly spent his spare time at his country estate in Grocka. Gavrilović had a family and lots of children, while Petrović never married and did not leave direct heirs. Gavrilović was close to the royal family, while Petrović was not, primarily due to his friendship with Prince Đorđe Karađorđević, who fell out of grace with the King. Consequently, Gavrilović was the chancellor of the University of Belgrade and the president of the Academy (1931–1937), while the candidacy of academic circles of Petrović for this post in 1927 and 1931 was not accepted or approved by the authorities. Most authors attribute this to King’s animosity towards him. However, it has to be said that Petrović did not encounter obstacles in his academic work or any other activities. On the contrary, he enjoyed a great reputation both among the general public and among government representatives as a great scientist and a great expert. He was winning important state commissions, for example he was the main cryptographer of the Serbian and the Yugoslav Army and represented his country in international commissions and delegations in the areas of education and fisheries. It is possible that his unconventional life has contributed to the failure of his nomination to become the chancellor and the president of the Academy. Similarly to mythological divinity Janus, Petrović had two faces. One was turned towards mathematics, philosophy and the spiritual world, the other looked towards faraway roads, fisherman’s adventures and tavern gatherings. It is possible that some parts of the government could not reconcile this other side of Petrović with the image of a chancellor who almost daily wades in his fisherman’s boots through Danube backwaters, hunting for fish and subsequently playing violin to entertain folks in a tavern. However, there are anecdotes that also suggest that even gentlemen of the highest station at the time were not able to resist the charm of “a fisherman’s ball” which Petrović was often organizing. Jelenko Mihailović recorded an interesting anecdote from 1903 involving the famous Finance Minister Lazar Paču and Mika’s great catch, a beluga “weighing 200 kilos.” Even though the Minister received 10 kilograms of “ajvar” (caviar) from this catch, it was not enough and the same evening he brought the entire government, headed by the Prime Minister, to tavern “Jasenica” to have dinner prepared by Mika Alas. The posts of the chancellor and the president of the Academy, even though they are high posts, are nonetheless only administrative posts and Petrović did not much regret not occupying them. It is possible that he himself did not want to take on that kind of responsibility because it would interfere with the life he was leading and loving.

Notwithstanding the aforementioned differences, Petrović and Gavrilović shared the same love for science, students and university. They were colleagues and the bedrock of the Mathematical Club between the two World Wars. Their relationship was characterized by friendship. Apart from the Mathematical Club, they also often met in taverns and fishermen’s adventures. When Milutin Milanković became a professor at the University of Belgrade, he immediately joined the two of them in every way, both academically and socially. The three scientists were academic and moral stalwarts on which mathematical sciences in Serbia relied until the Second World War and the emergence of a new academic generation. Even though they were great individualists in science, for example none of them had a co-author or a visible collaborator for their papers, they were tied to one another through their work at the University and through their friendship. Milanković wrote about it with a lot of sympathy in his biographical novella Mika Alas – Notes on a Life of a Great Mathematician Mihailo Petrović. The words of Radivoj Kašanin, Petrović’s doctoral student and Gavrilović’s assistant and descendant at the Mathematical Department of the Faculty of Technology, can also serve as an illustration: “In addition to their high educational qualifications and original academic work, the three of them had also possessed a feature I appreciate most and consider a human quality of the highest rank: appreciation of younger generations, understanding of young people, selfless and sincere assistance to the young, talented people in their advancement. They knew how to rejoice and enjoy when young people rise to prominence. I was lucky to develop and work alongside these great authorities in science and morality. To take pride in their friendship. I do not believe that anywhere else there existed such an atmosphere as the one that was created by Gavrilović, Petrović and Milanković.”

Already in 1894, the Library of the Mathematical Seminar was set up, offering broad possibilities for scholarly work to generations of mathematicians of at the University of Belgrade. Until the First World War, Bogdan Gavrilović and Mihailo Petrović were in charge of the Library. Other mathematicians subsequently also joined. When in 1938 the Mathematical Department moved to a new building next to the building of the Faculty of Philosophy, located in the Mansion of Miša Anastasijević, the Library also moved to the same building. Unfortunately, only two days before the liberation of Belgrade, on October 18, 1944, the enemy army in retreat burned the Library and it was destroyed. Only a couple of books borrowed by individuals survived out of the entire library.

The story about the life of Mihailo Petrović is inseparable from the story about development of the Belgrade University and mathematical sciences in Serbia. The Faculties within the Grand School developed in 1900 into autonomous entities of the Grand School and acquired an organization they would keep until after the Second World War. The same year, the Seminar for Mathematics, Mechanics and Theoretical Physics opened and professors from the Faculty of Philosophy and Technology gave lectures on mathematics, mechanics and astronomy. The most prominent among them were Mihailo Petrović and Bogdan Gavrilović. After many years of preparation and delays, in 1905 the Grand School was transformed into a University as “the highest self-managing body for higher professional education and the pursuit of science.” The newly established University consisted of four Faculties: Faculty of Philosophy, Law, Technology and Theology. At the Faculty of Philosophy, one of the first eight full professors was Mihailo Petrović. Until 1909, lectures in theoretical mathematics at the Faculty of Philosophy were held by Mihailo Petrović and occasionally Bogdan Gavrilović as an honorary professor. The same year, at their proposal, the University of Belgrade invited Milutin Milanković from Vienna to take the post of professor of applied mathematics.

In the meantime, science at the University of Belgrade had become advanced so, that the first Doctoral dissertation in mathematical sciences was defended at the University, under the supervision of professor Petrović. A Doctoral dissertation in the field of differential equations was defended in 1912 by Mladen Berić, an assistant to a teacher at the First Belgrade Gymnasium and a teaching assistant to professor Petrović. Already the following year, Sima Marković defended his Doctoral dissertation on the topic of Riccati differential equation, supervised by professor Petrović. This has marked the emergence of the Belgrade Mathematical School. Unfortunately, the work at the University of Belgrade has often been interrupted due to wars. In academic year 1912/13 the University was closed due to the Balkan wars. In academic 1913/14 the University reopened, but the First World War suddenly interrupted its work and students and professors had to go to war. In August 1914, soon after the war started, a part of the Mansion of Miša Anastasijević was torn down due to bombing. The enemy ransacked the deserted and demolished building. Mihailo Petrović himself participated in the war as a reserve officer.

After the war ended, in early 1920s, the University experienced an accelerated growth for a short period of time. The number of professors increased and among others, mathematicians Nikola Saltikov and Anton Bilimović came from Russia, giving a strong boost to the the Department of Mathematics at the Faculty of Philosophy. Even though Mladen Berić and Sima Marković became lecturers at the Department of Mathematics, they left the University in the mid 1920s. Berić had private reasons to do so, while Marković had to leave because of politics. Even though professor Petrović placed his hopes on his best students, he did not have good fortune with them.

In the mid 1920s, a new generation of mathematicians came of age: Tadija Pejović, Radivoje Kašanin, Jovan Karamata and Miloš Radojčić. They were all graduate and doctoral students of Mihailo Petrović. In the 1930, Dragoslav Mitrinović, Danilo Mihnjević, Konstantin Orlov, Petar Muzen and Dragoljub Marković also defended their doctoral dissertation in front of professor Petrović as their Doctoral supervisor. The figure shows all mathematicians at the University of Belgrade in 1926. The Faculty of Philosophy, the Department for Theoretical Mathematics, consisted of: full professors Mihailo Petrović and Nikola Saltikov, lecturer Tadija Pejović and administrative assistants Jovan Karamata and Miloš Radojčić; the Department of Applied Mathematics consisted of: full professors Milutin Milanković and Anton Bilimović, associate professor Vojislav Mišković and lecturer Vjačeslav Žardecki. At the Faculty of Technology, the Department for Mathematics consisted of: full professors Bogdan Gavrilović and Petar Zajončkovski, lecturer Radivoj Kašanin; the Department of Applied Mathematics consisted of: Ivan Arnovljević and Jakov Hlitčijev. All professors and lecturers of theoretical and applied mathematics at the University belonged to the Mathematicians’ Club of the University of Belgrade. This seminar actually represents the mathematical school of the Belgrade University and the main gathering place of all Belgrade mathematicians. It can be said that it was the golden era of Serbian mathematics. The club did not have any special rules, except that meetings were held once a month and that at those meetings, papers and academic discussions of the Club’s members were featured.

The mathematical heirs of professor Petrović, connected with him through his supervision of their doctoral dissertations, constitute mathematical genealogy made up of around 800 mathematicians. Of that number, around 500 are Serbian mathematicians, the rest are foreigners. The descendants are grouped into eight generations, whereas several last generations encompass some of leading contemporary Serbian mathematicians. If we look closely at the genealogy, we will notice four major clusters, the roots of which are made up of: Tadija Pejović, Jovan Karamata, Dragoslav Mitrinović and Konstantin Orlov. They are all to be credited for introduction of new fields of research in Serbian mathematics or creation of their own mathematical schools. Professors Pejović, Karamata and Orlov have created a powerful mathematical node at the Department of Mathematics of the Faculty of Mathematics and Natural Sciences in Belgrade, a precursor of today’s Faculty of Mathematics. A Doctoral student of Professor Karamata, Professor Bogoljub Stanković, has created his own mathematical school in Novi Sad, while professor Mitrinović should be credited for development of academic mathematical work in Niš and at the Faculty of Electrical Engineering in Belgrade.

Thanks to an endowment by Luka Ćelović Trebinjac and at the initiative of Anton Bilimović, with the support of Mihailo Petrović and Milutin Milanković, a new journal was launched in 1932 entitled Publications de l’Institut Mathématique Université de Belgrade. The papers were published in Russian, English, French and German. Belgrade mathematicians thus gained a venue to present their academic papers to the worldwide mathematical public. Seven volumes of the journal were published up to World War II. In each volume, Petrović published at least one paper. The last prewar issue, number VIII, printed on the eve of the Second World War, was destroyed in the enemy bombing of Belgrade in 1941. In addition to mathematicians from the University of Belgrade, world-class mathematicians at the time, as well as contemporaries, were publishing in the journal Publications, including, for example, Elie Cartan, Waclaw Sierpinski, Paul Montrel, Josip Plemelj, Đuro Kurepa and Paul Erdös.

At the beginning of the 20th century, Petrović expressed great interest in the practical side of mathematics. He was deeply preoccupied with the problem of the appearance, and manner of appearance, of mathematics in natural sciences, that is, the way in which mathematics can be applied to a research of natural phenomena. Similarly to Leibnitz, who tried to invent characteristica universalis, a universal and formal language that would be able to express all mathematical, scientific and metaphysical notions, Petrović tried to invent a universal method that would be used to solve problems in other sciences. The fundamental place in his discussions was accorded to analogies. He was searching for and citing examples of completely disparate phenomena that can be described by the same differential equations. These efforts produced an original work he is noted for – namely, mathematical phenomenology. He published three books on the topic, two in Serbian and one in French, presenting his theory.

Mihailo Petrović had a rich, interesting and unconventional life. It is difficult to fully enumerate, let alone describe in detail, all the things Petrović engaged in. In addition to his interest in various areas of mathematics, Petrović appears in many other, often unexpected fields. He wrote laws and drafted international agreements, but was also an inventor, holding successful and executed patents. Petrović is considered by many to be one of Serbia’s most important philosophers and inventors of an original theory in natural philosophy, namely mathematical phenomenology. His style of writing was beautiful and interesting and some of his novels are among favorite Serbian pieces of youth literature. He wrote academic papers in and studied other natural sciences, primarily astronomy, theory of relativity and chemistry. He created a coding system and was the main cryptographer of the Serbian and Yugoslav Army. He played violin and conducted the musical band “Suz” which up to the onset of the Second World War provided one of the main loci of bohemian life of Belgrade. Finally, he was a great and passionate fisherman, and a great world traveler and seafarer who sailed northern and southern seas. A great mathematician and world traveler died quietly, dreaming about a new and great ocean journey. Mihailo Petrović died in Belgrade on June 8, 1943 at his home in Kosančićev venac street no. 22.

Many Serbian and foreign authors have written about the life and works of Mihailo Petrović. The author who most certainly wrote the most valuable works about him was Dragan Trifunović, a historian of mathematics and a professor of the University of Belgrade. He wrote and edited a large number of books about Petrović and the times in which he lived. Trifunović is to be credited not only for the fact that in the past half century, Petrović’s name has been accorded a high and prominent place in Serbian mathematics, but also for discovery of numerous less well known details of his life. The Collected Works of Mihailo Petrović, an edition published by the Institute for Textbook Publishing and Teaching Aids, also contains, in addition to all known works by Petrović, complete and comprehensive academic analysis of his work and various contributions by distinguished Serbian mathematicians. Thanks to the engagement of the Serbian Academy of Arts and Sciences and the courtesy of the aforementioned publishing house, The Collected Works have been digitalized and are accessible to the public concerned at the Virtual Library of the Faculty of Mathematics in Belgrade and its digital endowment dedicated to Mihailo Petrović.