Mathematician Gheorghe Țițeica

The history of the Romanian school of mathematics begins in the late 1810s, with the establishment, in 1818, of the Polytechnic University of Bucharest under the name of  Higher Technical School. Here and in other higher education institutions established later, entire generations of Romanian engineers and mathematicians were trained. One of the names that made history in the development of mathematics in Romania is Gheorghe Țițeica.

Steliu Lambru, 04.01.2025, 13:57

The history of the Romanian school of mathematics begins in the late 1810s, with the establishment, in 1818, of the Polytechnic University of Bucharest under the name of  Higher Technical School. Here and in other higher education institutions established later, entire generations of Romanian engineers and mathematicians were trained. One of the names that made history in the development of mathematics in Romania is Gheorghe Țițeica.

He was born in 1873, in Turnu Severin, a city on the Romanian bank of the Danube Gorge, and passed away in Bucharest in 1939, at the age of 66. From an early age, he showed a great interest in mathematics and the so-called “hard sciences”, that is, the formal sciences and the natural sciences that are based on methodological rigor, accuracy and objectivity. He was the first to be admitted to the Bucharest Normal School, the future PolytechnicUniversity, and studied mathematics at the Faculty of Sciences in Bucharest. Among the professors at the University of Bucharest, he was closest to mathematician and astronomer Spiru Haret, the most important reformer of the Romanian education system.

In 1895 he graduated in mathematics and the following year he went to study in Paris. He specialized in differential geometry. Țițeica wrote about networks in a space with “n” dimensions and introduced new classes of surfaces, curves and networks. He issued the “five-lei piece problem” or “Țițeica’s theorem”, and the concepts of “Țițeica surface” and “Țițeica curve”. He also dedicated himself to popularizing science and raising the level of mathematical education in Romania. One of his great passions was the “Gazeta Matematica” magazine and he was among the founders of the publication “Mathematics”.

Bogdan Suceavă is a mathematician and writer and an expert in the history of mathematics in Romania. He defines Țițeica’s study period in the West as decisive for his career and and the development of scientific education in Romania: “The first decades of “Gazeta Matematica” are linked to Gheorghe Țițeica’s name. He benefited from scholarships all his life. He grew up without a father. He graduated from the school in Bucharest and in 1896, and, when he arrived in Paris, the first thing he was recommended to do was study at the Ecole Préparatoire. On that first year, he met Henri Lebesgue, who six years later would become the author of a very important chapter in mathematical analysis. Țițeica, being of the human quality we know, followed two sets of courses, those at the École Préparatoire and those at the École Normale. The first year was hell. He coped at the highest level and the question is why was he recommended to take more courses? Between Bucharest and Paris there was a certain difference. In July 1897, he quickly passed the certification exams in differential and integral calculus, mechanics and astronomy, all in a single year. He was first in an extraordinary generation, occasion on which he received a scholarship, plus a fee exemption. This experience would be important at a formative level. He understood very quickly how things were, how he had to prepare, what level the French school was at and where the Romanian school was at, during that time. This was happening before 1900.”

Romania was moving at full speed towards the West and Romanian mathematics was one of the sciences in great expansion. And Țițeica’s generation sought to reduce the huge differences between Western society, the French one being the great model, and the Romanian one. As Bogdan Suceavă also noted, Țițeica met top mathematicians in France and learned from them everything that he brought to Romania: “Who did Gheorghe Țițeica work with? He worked with Gaston Darboux, who at that time was not only dean of the Faculty of Mathematics at the Sorbonne, he was also the author of a four-volume treatise on differential geometry in which the unifying theme is the following: how to choose the most appropriate benchmarks for various problems of differential geometry? The subject he studied was a whole philosophy, he was a very influential author who had many talented students, Țițeica being one of the best. He also studied with Henri Poincaré, Edouard Goursat, Charles Hermite, Émile Picard, Jules Tannery, Paul Émile Appell, the best mathematicians. After which, in 1899, he returned to Bucharest. He would write until 1937, over 100 works. In the last two years he did not work at all. He started collaborating with “Gazeta Matematica” while he was in Paris. The mathematics competition with the same name owes a lot to him. The editorials he wrote during that period described everything, including how the candidates behaved in the oral exams. It’s the kind of comments that no one would publish today, but which Țițeica, did.”

Gheorghe Țițeica could not have become anything other than a university professor, a member of some academies and an honorary doctor of some universities. He was also among the ranks of the Romanian Society of Mathematical Sciences, whose president he was.