The Life and Mathematics of Janos Bolyai

As an independent co-discoverer of hyperbolic non-Euclidean geometry, Janos Bolyai's impact on mathematics, science and humanity has been referred to as "Copernican" in nature. Yet, during his lifetime Bolyai was more reknowned for his swordsmanship and dancing than for his mathematics. He lived in relative obscurity as a mathematician, as his only published mathematical work appears as an appedix to his father's book; however, he left thousands of pages of manuscripts to posterity which reveal his mathematical genius. While best know for his work in geometry, he was also interested in number theory, algebra and the theory of complex numbers.

In this talk, I will present some of his mathematical accomplishments and their historical significance, as well as the life of this increasingly paranoid and troubled man.