The work of the mathematician Kurt Gödel changed the face of mathematics forever. His famous incompleteness theorem proved that any formalized system of mathematics would always contain statements that were undecidable, showing that there are certain inherent limitations to the way many mathematicians studies mathematics. This paper provides a history of the mathematical developments that laid the foundation for Gödel's work, describes the unique method used by Gödel to prove his famous incompleteness theorem, and discusses the far-reaching mathematical implications thereof.

Author Bio

Tyson Lipscomb is currently finishing his undergraduate work in Computer Science and Applied Mathematics at Marshall University and plans on attending Wake Forest University for graduate studies in Computer Science in the Fall of 2010. He is currently living in Barboursville, WV, where he enjoys playing music, fishing and working with The Vine, a local peer-led Bible study and community service group. Tyson chose the topic of Gödel's incompleteness theorems for his mathematics capstone research because of the unique method that was used to prove them and the insight that they provide into the philosophy of human understanding in relation to formalized mathematical systems.