Wednesday, September 12, 2007

Wir müssen wissen, wir werden wissen!

With the above words (translation: we must know, we will know), Hilbert ended his 1930 address in Königsberg, at the Congress of the Association of German Natural Scientists and Medical Doctors. A four minute excerpt was broadcast by radio, and is available here. This I believe is one of the earliest audio files of a speech by a mathematician of note, available online.
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.

Later abstractions and the development of functional analysis on Hilbert space, by von Neumann and others, led to the theory of operator algebras which is of course one of the sources of NCG.

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):
`After reading your post and hearing Hilbert's voice (in the
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'


Doug said...

There may be a way of using Harsanyi techniques to deal with "Gödel's incompleteness theorems" from the perspective of energy economics?

"Professor John Harsanyi, the analysis of games with incomplete information is due to you, and it has been of great importance for the economics of information.

One may even be able to argue that Wolfgang Pauli used an Harsanyi like technique to hypothesize what became the neutrino.
Pauli essentially treated the conservation of energy as a zero sum game to deduce the emission of this neutral particle, "23 years before the experimental proof of the existence of the neutrino succeeded".

Nobel Prizes were awarded in 1988 and 2002 for indirect detection of the never directly observed neutrino.

Alejandro Rivero said...

I took this picture some years ago, if anybody wants to download it and use it anywhere, I grant my permission. Do not link directly, because the website will disappear in a few days.

Masoud Khalkhali said...

Dear Arivero,
Thanks for sharing the pic! I have updated the post by adding this picture. Do you remember the place?

Alejandro Rivero said...

Of course. It is a graveyard in Gottingen, I think that a parcel for the university. Hilbert's grave is in a corner, 10 or 20 meters left of Planck, who has the honour site in a small pond. Hahn and Laue have also central places there; I noticed it because I took the picture after my Erasmus work in the ILL at Grenoble, namer from Laue and Langevin. Also, in some other place in the graveyard, outside the academy parcel, you can find a black hole instead of a cross.

Anonymous said...

the Zeitgeist challenged by Hilbert in his address are briefly discussed here.

Apparently Godel was of opinion that that
Zeitgeist was in acccordance with the Hilbert's speech, and in fact was the motivation for the conjecture disproved by Goedel's incompleteness theorem.

I'd infer this from his essay on Zeitgeist and logic (roughly)

Masoud Khalkhali said...

I have just updated this post. Manfred Karbe has communicated some more information on Hilbert's radio address (see the update at the end).