Sunday, January 25, 2009


Consilium simplex

One fine day in 1931, the learned and beloved Herr Doctor David Hilbert was reviewing his notes for the lecture he would give the next day at the assembly of mathematicians who had converged on Konigsberg to assist him in his endeavor to bring logical and axiomatic consistency to the theory of mathematics. He was also to receive a “major prize” from the City of Konigsberg recognizing his contributions to the field of Mathematics (and the tourist dollars being generated by the conference).

Due to expansions in the field of mathematics, such as non-Euclidian geometry and the specter of multiple infinities, Dr. Hilbert had been dissatisfied with the state of mathematics and determine to solve the 23 problems he had posed several years ago that needed to be solved in order to bring mathematics into logical and axiomatic consistency and prove-ability. Dr. Hilbert was doubtless in a good mood on that day and was preparing for a well-deserved triumph.

But, lurking in the wings, the unremitting and unforgiving gnome of chaos lurked in the unprepossessing form of Dr. Kurt Gödel. Even as Dr. Hilbert was reviewing his notes, the fiend Gödel perpetrated his Incompleteness Theorems upon the hapless audience of mathematicians, and other bon vivants, in attendance. What Gödel’s demonstrated showed that mathematical theorems, even those thought very probably true, could not be proven within the axiomatic framework of the theory of mathematics. The old “proof is not truth” dilemma. He converted the following statement into a mathematic framework to convey this:

“This statement is false.”

Logically, if this statement is inaccurate, it is true and thus not false. So it is inconsistent. Also if the statement is accurate, then it then it must be true, thus leading to yet another inconsistency.

Imagine Dr. Hilbert’s surprise the next day when, after his triumphant lecture he was told about Gödel’s theorems that suggested that his entire quest was in folly. It is not recorded whether or not he pulled out his hair, nor how he actually reacted. It is enough to know that he never published another article concerning this issue.

The moral to this story, boys and girls is there is always a Gödel waiting in the wings.