**Schmidt** is best remembered for the Gram-Schmidt orthogonalisation process, which takes a basis of a space and constructs an orthogonal one from it.

- Erhard's university career followed a pattern which was common in Germany at this time, namely that students studied at several different universities as their course progressed.
- The main ideas of this thesis appeared in Schmidt's 1907 paper which we describe below.
- After leaving Bonn, Schmidt held positions in Zürich, Erlangen and Breslau before he was appointed to a professorship at the University of Berlin in 1917.
- Schmidt arrived at the University of Berlin shortly after the death of Frobenius, who had jointly led the department with Schwarz.
- Carathéodory was appointed in 1918 to fill Frobenius's chair and to jointly head mathematics in Berlin with Schmidt.
- Schmidt now had the main responsibility for filling the vacant chair.
- Schmidt drew up an impressive list of candidates: Brouwer, Weyl, and Herglotz in that order.
- When Schmidt arrived in Berlin there was no applied mathematics there, the subject being considered more suitable for technical colleges.
- However Schmidt was the main person who pushed for the founding of an Institute of Applied Mathematics in Berlin.
- After the Institute was set up Schmidt had to fill the new chair of applied mathematics and the post of Director of the Institute of Applied Mathematics.
- Credit for bringing Berlin to this leading role in applied mathematics must chiefly go to Schmidt.
- The 1930s were difficult years for Schmidt.
- With the Nazi rise to power in 1933 life became increasingly difficult for Schmidt's Jewish colleagues and Schur, von Mises and several others were forced out of their posts.
- In 1951 a meeting was held in Berlin to celebrate Schmidt's 75th birthday.
- In 1936, when the problems were very difficult, Schmidt was made head of the German delegation to the International Congress of Mathematicians at Oslo.
- Schmidt held positions of authority at the University of Berlin through these difficult years of Nazi rule.
- Schmidt's main interest was in integral equations and Hilbert space.
- Schmidt published a two part paper on integral equations in 1907 in which he reproved Hilbert's results in a simpler fashion, and also with less restrictions.
- In this paper he gave what is now called the Gram-Schmidt orthonormalisation process for constructing an orthonormal set of functions from a linearly independent set.
- We should note, however, that Laplace presented the Gram-Schmidt process before either Gram or Schmidt.
- In 1908 Schmidt published an important paper on infinitely many equations in infinitely many unknowns, introducing various geometric notations and terms which are still in use for describing spaces of functions and also in inner product spaces.
- Schmidt's ideas were to lead to the geometry of Hilbert spaces and he must certainly be considered as a founder of modern abstract functional analysis.
- Schmidt defined a space HHH whose elements are square summable sequences of complex numbers.
- Again he gave the Gram-Schmidt orthonormalisation process in this setting.
- What are today called Hilbert-Schmidt operators also appear in this 1908 paper.
- After Schmidt moved to Berlin his interests turned towards topology.
- Schmidt's interest in topology influenced Hopf and, in 1929, he was an examiner of Hopf's doctoral thesis.
- Later still Schmidt became interested in isoperimetric inequalities, publishing an important paper on this topic in 1949.

Born 13 January 1876, Dorpat, Russian Empire (now Tartu, Estonia). Died 16 December 1959, Berlin, Germany.

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Algebra, Origin Estonia, Topology

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