**Isaac Jacob Schoenberg** was a Romanian-born American mathematician best known for his discovery of splines.

- Jacob and Rachel Schoenberg were Zionists and very active in the Zionist community in Iasi.
- Rachel Schoenberg was fluent as writing and speaking French and she taught Isaac the language.
- However, to understand physics required mathematics and very soon Isaac had become more interested in mathematics than in physics.
- In his first year, 1919-20, Schoenberg studied Victor Costin's course in 'Projective and Descriptive Geometry' and, in 1920-22, he studied the following courses leading to the degree of M.A.: 'Analytic Geometry', taught by Alexandru Myller; 'Algebra Including Galois Theory', taught by Simion Stoilow; 'Analysis', taught by Simion Sanielevic; 'The Theory of Analytic Functions', taught by Vera Myller-Lebedev; 'Mechanics', taught by Simion Sanielevici; and 'Astronomy', taught by Constantin Popovici.
- Taught by these excellent mathematicians, Schoenberg received his M.A. in Mathematics (with distinction) in 1922.
- It was the 'Analytic Number Theory' course, in which Schur had discussed Hermann Weyl's results on the uniform distribution of numbers mod 1, that gave Schoenberg the ideas which would eventually form his Ph.D. thesis.
- Göttingen was also very attractive since Edmund Landau was teaching there, so Schoenberg spent the whole of the academic year 1924-25 at Göttingen.
- By the time he returned to Göttingen in 1924, Alexander Ostrowski was teaching there and Schoenberg attended his course on 'Overconvergence of Power Series' and also the seminar that Ostrowski ran.
- Schoenberg had obtained his Baccalaureate in Romania and this was not recognised by Germany so he was not allowed to submit his thesis to a German university.
- Schoenberg presented his thesis Über die asymptotische Verteilung reeller Zahlen mod 1 Ⓣ(On the asymptotic distribution of real numbers mod 1) to the University of Iasi and was awarded his Ph.D. in June 1926.
- All High School graduates had to serve for a year in the army so Schoenberg spent six months at the Field Artillery School in Timisoara, a city that had been allotted by the Treaty of Trianon to Romania in 1920.
- At Göttingen Schoenberg had got to know Edmund Landau well and it was Landau who arranged a visit for Schoenberg to the Hebrew University of Jerusalem which he made in the spring semester of 1928.
- Schoenberg lectured in Hebrew in Jerusalem on Higher Algebra.
- Schoenberg became interested in estimating the number of real zeros of a polynomial and so began his very influential work on Total Positivity and Variation diminishing linear transformations...
- This went very well and Bliss arranged for Schoenberg to remain at Chicago for the year 1931-32 as his assistant.
- During these two years Schoenberg wrote seven papers, two of which were jointly written with Bliss.
- Schoenberg was acting assistant professor at Swarthmore College from January 1935 until June 1936.
- Something of Schoenberg's approach is seen in a new course called "Non-technical mathematics" which he introduced last year.
- Schoenberg is noted worldwide for his realisation of the importance of spline functions for general mathematical analysis and in approximation theory, their key relevance in numerical procedures for solving differential equations with initial and/or boundary conditions, and their role in the solution of a whole host of variational problems.
- Schoenberg's more than 40 papers on splines after 1960 gave much impetus to the rapid development of the field.
- Schoenberg made further outstanding contributions in a series of papers between 1950 and 1959 on the theory of Pólya frequency functions.
- This work led Schoenberg to discover remarkable properties of polynomials all of whose zeros are negative and real.
- In 1966 Schoenberg moved from the University of Pennsylvania to the University of Wisconsin where he became a member of the Mathematics Research Center.
- During his time at Wisconsin, Schoenberg introduced another concept of major importance, namely cardinal splines.
- We noted above that retirement did not slow Schoenberg's productivity.

Born 21 April 1903, Galatz, Romania. Died 21 February 1990, Madison, Dane, Wisconsin, USA.

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Origin Romania

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive