Traian Lalescu (; 12 July 1882 â 15 June 1929) was a Romanian mathematician. His main focus was on integral equations and he contributed to work in the areas of functional equations, trigonometric series, mathematical physics, geometry, mechanics, algebra, and the history of mathematics.
He was born in Bucharest. His father, also named Traian, was originally from Cornea, CaraÃÂ-Severin and worked as a superintendent at the Creditul Agricol Bank. Lalescu went to the Carol I High School in Craiova, continuing high school in Roman, and graduating from the Boarding High School in IaÃÂi. After entering the University of IaÃÂi, he completed his undergraduate studies in 1903 at the University of Bucharest.
He earned his Ph.D. in Mathematics from the University of Paris in 1908. His dissertation, Sur les équations de Volterra, was written under the direction of ÃÂmile Picard. That same year, he presented his work at the International Congress of Mathematicians in Rome. In 1911, he published Introduction to the Theory of Integral Equations, the first book ever on the subject of integral equations.
After returning to Romania in 1909, he first taught Mathematics at the Ion Maiorescu Gymnasium in Giurgiu. He then taught until 1912 at the Gheorghe ÃÂincai High School and the Cantemir VodÃÂ High School in Bucharest. From 1909 to 1910, he was a teaching assistant at the School of Bridges and Roads, in the department of graphic statistics. A year later, he was appointed full-time professor of analytical geometry, succeeding Spiru Haret; he lectured at the School (which would later become the Polytechnic University of Bucharest) until his death. In 1916, he became the first president of Sportul StudenÃÂesc, the university's football club. Also that year, he was appointed tenured professor of algebra and number theory at the University of Bucharest, a position he held until his death. One of his PhD students there was Valeriu Alaci. In 1920, Lalescu became a professor and the inaugural rector of the Polytechnic University of TimiÃÂoara; for a year, he would commute by train for 20 hours between TimiÃÂoara and Bucharest to teach his classes. In 1921, he founded the football club Politehnica TimiÃÂoara.
His wife, Ecaterina, was a former student of his; they had four children—two sons and two daughters: Nicolae, Mariana, Florica, and Traian. She died in childbirth in 1921, at age 28. In 1920, Lalescu was elected to the Parliament of Romania as deputy for OrÃÂova, and then re-elected twice as deputy for CaransebeÃÂ. He presented in parliament a well-received report on the budget project for 1925. In the fall of 1927, he caught a double pneumonia; in 1928, he went for a vacation in Nice and for treatment in Paris, but he succumbed to the disease the next year, at age 46. In 1991, he was elected posthumously honorary member of the Romanian Academy.
In a 1900 issue of , Lalescu proposed the study of the sequence
It turns out that the Lalescu sequence is decreasing and bounded below by 0, and thus is converging. Its limit is given by
There are several institutions bearing his name, including Colegiul NaÃÂional de InformaticÃÂ Traian Lalescu in Hunedoara and Liceul Teoretic Traian Lalescu in ReÃÂiÃÂa. There are also streets named after him in Craiova, Oradea, ReÃÂiÃÂa, and TimiÃÂoara. The National Mathematics Contest Traian Lalescu for undergraduate students is also named after him.
A statue of Lalescu, carved in 1930 by Cornel Medrea, is situated in front of the Faculty of Mechanical Engineering, in TimiÃÂoara and another statue of Lalescu is situated inside the University of Bucharest.