Lesson 7

David Hilbert was also one of those who wanted to provide secure foundations for all mathematics. The goal of Hilbert's program was to set up a finite system of axioms with the following three properties.

• Completeness:  a proof that all true mathematical statements can be proved.


• Consistency:  a proof that no contradiction can be obtained.


• Decidability:  there should be an algorithm (not necessarily efficient) for deciding the truth or falsity of any mathematical statement.

Hilbert was an optimist in mathematics and believed that this should be possible.

(The Latin maxim ignoramus et ignorabimus, meaning “we do not know and will not know”, represents the idea that scientific knowledge is limited.)