The Decline and Fall of Reductionism in pure Mathematics

“The functional properties of materials and devices are critically determined by the electromagnetic field structures formed inside them, especially at nanointerface and surface regions, because such structures are strongly associated with the dynamics of electrons, holes and ions.”
“Hilbert’s idea is the culmination of two thousand years of mathematical tradition going back to Euclid’s axiomatic treatment of geometry, going back to Leibniz’s dream of a symbolic logic and Russell and Whitehead’s monumental Principia Mathematica. Hilbert’s dream was to once and for all clarify the methods of mathematical reasoning. Hilbert wanted to formulate a formal axiomatic system which would encompass all of mathematics.”

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