For the original German text and an English translation click here. The above picture was kindly sent by A. Rivero. (See his interesting comments about the place the picture was taken). Many thanks to him!
Now that we are inaugurating a new section in the blog under the label `multimedia’ (see Matilde’s recent post for an example), I thought time is right to add something I always wanted to share with the readers of this blog. Hilbert’s address is not about NCG of course! Some of the relevant underlying philosophical and cultural aspects of the Zeitgeist challenged by Hilbert in his address are briefly discussed here. Notice, however, that Hilbert can be regarded as one of the great grandfathers of NCG and the subject owes a lot to him and his Göttingen school of functional analysis and spectral theory in the years 1900-1912 (Erhard Schmidt, Hermann Weyl, ….; as well as Otto Toeplitz who was not in Göttingen). Hilbert’s work was centered around the theory of integral equations and its allied spectral theory as it was mostly motivated by Fredholm’s 1900 papers. An immediate dramatic success was Weyl’s assymptotic law for the eigenvalues of the Dirichlet problem for Laplacian on bounded domains. This basic result of spectral geometry is one of the foundation stones of NCG as well.
It is interesting to note that Hilbert’s address was just one year before Gödel’s incompleteness theorems , which in a way showed that, at least globally, one can not be totally optimistic about the power of formalistic approach in mathematics!
Update (Sept 20, 2007): Manfred Karbe kindly wrote in to share the following interesting information (my sincere thanks to him):
unmistakable Low Prussian dialect) I luckily found the “Hilbert
Gedenkband” on one of my book shelves, edited by Reidemeister and
published by Springer in 1971……….Attached to this booklet (which is out of print now, no wonder at those times!) was a record which contains the four
minute excerpt that was broadcast by radio. See also
this public appeal to locate the original recording’