Crises In Mathematics (Part 2): A Raging Tempest

Beyond non-Euclidean geometries, one of the earliest encounters with completeness was that of the works of Georg Cantor (1845-1918). This was especially so in reference to the axiomatizing of set theory. Various of the questions there raised were to identify the most disturbing and turbulent of fundamental mathematical matters, not only concerning decidability but consistency itself.

Though Cantor's work was not fully appreciated at the time, many mathematicians of stature were to echo his setiments about mathematical completeness and decidability. Such concerns further occupied the unwavering attention of twentieth-century researchers. Among those pursuing and resolving certain of these deeper questions was a Czechoslovakian mathematician named Kurt Godel.

Table of Contents:

NOTABLE UNDECIDABLES

A SUPERFICIAL CALAMITY IN MATHEMATICS

REFERENCES