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Concept
Otto Toeplitz
Summary
Otto Toeplitz (1 August 1881 – 15 February 1940) was a German mathematician working in functional analysis.
Toeplitz was born to a Jewish family of mathematicians. Both his father and grandfather were Gymnasium mathematics teachers and published papers in mathematics. Toeplitz grew up in Breslau and graduated from the Gymnasium there. He then studied mathematics at the University of Breslau and was awarded a doctorate in algebraic geometry in 1905. In 1906 Toeplitz arrived at Göttingen University, which was then the world's leading mathematical center, and he remained there for seven years. The mathematics faculty included David Hilbert, Felix Klein, and Hermann Minkowski. Toeplitz joined a group of young people working with Hilbert: Max Born, Richard Courant and Ernst Hellinger, with whom he collaborated for many years afterward. At that time Toeplitz began to rework the theory of linear functionals and quadratic forms on n-dimensional spaces for infinite dimensional spaces. He wrote five papers directly related to spectral theory of operators which Hilbert was developing. During this period he also published a paper on summation processes and discovered the basic ideas of what are now called the Toeplitz operators. In 1913 Toeplitz became an extraordinary professor at the University of Kiel. He was promoted to a professor in 1920.
In 1911, Toeplitz proposed the inscribed square problem:
Does every Jordan curve contain an inscribed square?
This has been established for convex curves and smooth curves, but the question remains open in general (2007).
Together with Hans Rademacher, he wrote a classic of popular mathematics Von Zahlen und Figuren, which was first published in 1930 and later translated into English as Enjoyment of Mathematics.
Toeplitz was deeply interested in the history of mathematics. In 1929, he cofounded "Quellen und Studien zur Geschichte der Mathematik" with Otto Neugebauer and Julius Stenzel. Beginning in the 1920s, Toeplitz advocated a "genetic method" in teaching of mathematics, which he applied in writing the book Entwicklung der Infinitesimalrechnung ("The Calculus: A Genetic Approach").
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