More on Hilbert

[Richard Romeo]

Just some tidbits:

two important years

In 1904, Hilbert published his theory of eigenfunctions and eigenvalues, and 
he began for the first time in its history to frame the foundations of 
mathematics, proof itself being made an object of mathematical inquiry, 
which later included the problem of the solvability in principle of every 
mathermatical question; the problem of finding a standard of simplicity for 
mathematical proof; the problem of the relation of content and formalism in 
mathematics; and the problem of the decidiability of a mathematical question 
by a finite procedure.

In 1922, Hilbert came to the defense of mathematics against those (called 
Intuitionists--neither language nor logic was a presupposition for math, its 
only source being intuition which makes concepts and inferences clear)) who 
beleived that a statement that an object exists having a given property 
means that, and is only proved when, a method is known which in principle at 
least will enable such an object to be found or constructed, thus refuting 
Hilbert's pure existence proofs of his younger days, such as the existence 
of a finite basis of the invariant system and many others.
Hilbert felt that if the Intuitionists program was adopted the general 
concept of of the irrational number, the function, and the logical principle 
of the excluded middle.
Hilbert felt that the Intuitionists were saving math by throwing overboard 
what they felt was troublesome, mangling it in the process, reducing it if 
you will by dispensing with its more subtle beauty.

more to come


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