1. Nunn (UK)

2. Murdzia (Poland)

3. Pfannkuche

TEAMS:
1. Poland 2. Russia 3. Germany

Just a snippet her, on the topic:

"The mathematical concept of a <Hilbert space>, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. In addition, Hilbert spaces are required to be complete, a property that stipulates the existence of enough limits in the space to allow the techniques of calculus to be used.

Hilbert spaces arise naturally and frequently in mathematics, physics, and engineering, typically as infinite-dimensional function spaces. The earliest Hilbert spaces were studied from this point of view in the first decade of the 20th century by David Hilbert, Erhard Schmidt, and Frigyes Riesz. They are indispensable tools in the theories of partial differential equations, quantum mechanics, Fourier analysis (which includes applications to signal processing and heat transfer) and ergodic theory which forms the mathematical underpinning of the study of thermodynamics. <John von Neumann> coined the term "Hilbert space" for the abstract concept underlying many of these diverse applications. The success of Hilbert space methods ushered in a very fruitful era for functional analysis. Apart from the classical Euclidean spaces, examples of Hilbert spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized functions, and Hardy spaces of holomorphic functions."

championSPIEGEL: How that?

"I am constantly astonished at how often tournament organisers invite noted draw specialists to their event, and then throw up their hands in horror at the number of quick draws that ensue." - John Nunn

But, he has 211 draws in 20 moves or less in the database. That's over 13% of his games.

http://www.chessgames.com/perl/ches...

I'll bet Reshevsky would have, though-victories over the very strongest players appeared to be a chief criterion in his selection of games.

< Chess is to a considerable extent about <pattern recognition>. The more patterns you have firmly fixed in your memory, the more effective you are likely to be at the chessboard.>

-- Nunn