Tiberiu Popoviciu is one of the greatest Romanian mathematicians. [acad. C. Iacob – link soon]
He is the most important mathematician given by Transylvania, after János Bolyai. [acad. C. Iacob – link soon]
He has set the foundations of the Numerical Analysis in Romania. [acad. M. Nicolescu – link soon]
He appears in the select History of Approximation Theory (Technion University, Israel).
He became corresponding member of the Romanian Academy in 1948, at 42 years age, and full member of the Romanian Academy 13 years later.
He has obtained some important, deep results, from various fields of Mathematics (Numerical Analysis, Approximation Theory, Mathematical Analysis, Algebra):
- he used for the first time the modulus of continuity for obtaining estimations for the remainders in approximation formulas (1937)
- he prefigured the de Casteljau algorithm (1937)
- he introduced for the first time the test functions criterion for the convergence of linear positive operators (1950) – some call it the Popoviciu-Bohman-Korovkin theorem, others Bohman-Korovkin-Popoviciu theorem;
- he obtained early contributions on B-spline functions: he obtained for the first time the (now called) Marsden recurrence identity, and the (now called) Boehm’s knot insertion formula (1933, 1934)
- early results on the cardinal spline interpolation (1942)
- the generalization of the Leibniz formula for the product of two functions to divided differences (1933)
- introduction and study of convex functions of higher order (1933)
- a mean value formula for the divided differences of a function
- results on interpolation, quadrature, etc
- inequalities that bear his name (on variances, on convex functions, and others)
- results in functional equations
- algebra (a result regarding the number of partitions of n)
- to be completed
He is the founder of the Institute of Numerical Analysis (1951), which now bears his name (in Romanian Institutul de Calcul “Tiberiu Popoviciu”)
He was a visionary mathematician, and foreseen the increasing importance of the numerical computing. He integrated at the Institute the (abstract) Calculus, Numerical Calculations and Electronic Computing. In Romanian, “Calcul” may be associated to all the three mentioned notions
- Numerical Analysis (“calcul matematic”),
- Practice/Industrial Mathematics (“calcul practic”), over 100 contracts with economic agents were carried out using the computers built here;
- Computing technique (“calcul electronic”), three electronic computers were built here. The third computer was designed to support hardware implemented instructions for floating point computations (real numbers represented in floating point arithmetic on 48 bits).
The mathematicians from the Institute, together with their PhD students, and the PhD students of their PhD students,… formed a powerful team, called the Cluj-Napoca Team on Numerical Analysis and Approximation Theory (“Şcoala Clujeană de analiză numerică şi teoria aproximării”), known not only in Romania, but also abroad. It amounts to over 400 people.
He is one of the founders of the IT hardware and software in Romania, and the founder of the IT industry in Cluj-Napoca.
Under his vision, initiative and guidance, several talented mathematicians and engineers were gathered after 1957 (when the Institute received legal personality, and could hire engineers and physicists), who have built some of the first electronic computers in Romania:
- MARICA, in 1959 an experimental computer with relays;
- DACICC-1, in 1963 – the third electronic computer built in Romania, but the first one containing transistors (not fully transistorized), and the first one with internal memory (of ferites); Romania was the 11th country in the world that used transistors in computers.
- DACICC-200, in 1968 – the first Romanian computer with operating system and with compiler, and also with several advanced features: arithmetic instructions hardware supported, overlap features, etc; it has the best characteristics among the Romanian computers before the ‘70s, some of these characteristics remaining superior even to the first computers made later under license (200.000 op./sec, floating point representation in 48 bits, compared to 32 bits on IRIS, etc.).
The hardware section of the Institute was transferred in 1968 and formed the Institute for Computers – Cluj (Institutul pentru Tehnică de Calcul – ITC Cluj) and the Territorial Center for Computing (Centrul Teritorial de Calcul Cluj).
The IT industry in Cluj-Napoca has started from Tiberiu Popoviciu. However, it is worth noting that, according to Gh. Farkas, one of the leading engineers of the Institute, Popoviciu has risked his future when engaging the whole Institute resources for constructing some computers they wouldn’t know if would work…
Version of April 22, 2017.