3Hilbert Spaces for Engineers

David Hilbert is considered to be one of the most influential mathematicians of the 20th Century. He was a German mathematician, educated at Konigsberg, where he completed his PhD thesis under the direction of Ferdinand Lindemann. At the same time, Hermann Minkowski was also a PhD student of Lindemann – they presented their PhD’s in the same year (1885) and thereafter became good friends. Hilbert was acquainted with some of the best mathematicians of his time and contributed significantly to important mathematical problems. He also supported the candidacy of Emmy Noether to teach at the University of Gottingen – at these times, this university was considered one of the best mathematical centers of the world and women had difficulty in finding academic positions. The history of mathematics teems with anecdotes and quotes of Hilbert. At the 2nd International Congress of Mathematics held in Paris, in 1900, Hilbert presented a speech where he evoked unsolved problems. His speech was transcribed in a long article, first published in German, but which was quickly translated into English [WIN 02] and is known globally as the 23 Hilbert problems or the Hilbert program – this text has widely influenced Mathematics along the 20th Century. The Hilbert program addressed fundamental difficulties of Mathematics – some of them remain unresolved to this day – and their study led to a large development of new ideas and methods. For instance, the research connected ...

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