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Zbl 0817.01030
Pietsch, Albrecht
(Kufner, A.)
Hilbert \& Schmidt or A milestone in the history of mathematics. (Czech)
[J] Pokroky Mat. Fyz. Astron. 39, No.2, 65-94 (1994). ISSN 0032-2423

This is a Czech translation (by Alois Kufner) of an afterword to a collection of reprinted papers by D. Hilbert and E. Schmidt [{\it D. Hilbert} and {\it E. Schmidt}, Integralgleichungen und Gleichungen mit unendlich vielen Unbekannten (on integral equations and equations with infinitely many unknowns), Hrsgg. und mit einem Nachwort versehen von A. Pietsch, Teubner-Archiv zur Mathematik 11 (1989; Zbl 0689.01012)]. The translator, in his very short preface, stresses that these works by Hilbert and Schmidt represented a milestone in the history of linear functional analysis. He also notes that the afterword by Pietsch extends the framework of an ordinary afterword by putting these works in a substantially broader context and showing the influence of classical ideas and methods on the development of modern theory, i.e., showing ``what happened next''. The afterword emphasizes Hilbert's motto: ``Wir müssen wissen. Wir werden wissen.'' It describes not only the work by Hilbert and Schmidt, but also later relevant work, including work in related areas. It includes a list of the dissertations written on integral equations by members of the Hilbert school (including such well- known mathematicians as Hermann Weyl, Hugo Steinhaus and others), short biographies of Hilbert and Schmidt, and a bibliography of more than 150 historical and mathematical items (from Poincaré 1886 to Barnes/Murphy/Smyth/West 1982).
[H.Kilov (Millington)]

MSC 2000:: *01A75 Collected or selected works
46-03 Historical (functional analysis)
01A60 Mathematics in the 20th century

Keywords: integral equations

Citations: Zbl 0689.01012

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