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To: Gib Bogle who wrote (13009)	6/9/2006 4:28:07 PM
From: E. Charters	Read Replies (2) \| Respond to of 78419

Computer programs that detect viruses were predicted by Godel as having to work outside the operating system. I think Godel is a tad more important than credit you give. Kurt Godel (1906 - 1978) was a logician who discovered some of the most fundamental and amazing facts of modern mathematics. In fact, Godel's discoveries placed fundamental limits on mathematics. Godel's Undecidability Theorem proves that there are statements in mathematics that are true but cannot be proven. This amazing fact was quite a shock to the mathematical world. Before Godel's Undecidability Theorem, mathematicians were attempting to establish a complete set of axioms from which all results of mathematics can be deduced. Godel proved that you cannot have such a set of axioms -- sets of axioms must always be incomplete. Godel's ideas were later applied by Alan Turing to point out that computers have their limitations as well -- that some things simply cannot be decided by a computer. This undergraduate research project will examine the life and mathematics of Kurt Godel.