. 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). In 1927, Toeplitz and Hellinger completed an article on integral equations for Felix Klein's
Encyclopedia of Mathematical Sciences. 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"). The book introduces the subject by giving an idealized historical narrative to motivate the concepts, showing how they developed from classical problems of
Greek mathematics. It was left unfinished, edited by
Gottfried Köthe and posthumously published in German in 1946 (English translation: 1963). In 1928 Toeplitz succeeded
Eduard Study at
Bonn University. In 1933, the
Civil Service Law came into effect and professors of
Jewish origin were removed from teaching. Initially, Toeplitz was able to retain his position due to an exception for those who had been appointed before 1914, but he was nonetheless dismissed in 1935. In 1939 he emigrated to
Mandatory Palestine, where he was scientific advisor to the rector of the
Hebrew University of Jerusalem. He died in
Jerusalem from
tuberculosis a year later. Toeplitz's son, (1913-2006), was a co-founder of the
Israel Philharmonic Orchestra. == Quotes ==