Janos Bolyai, Hungarian Mathematician (December 15, 1802 - January 27, 1860) was a Hungarian mathematician, known for his work in non-Euclidean geometry, a geometry that differs from Euclidean geometry in its definition of parallel lines. The discovery of a consistent alternative geometry that might correspond to the structure of the universe helped to free mathematicians to study abstract concepts irrespective of any possible connection with the physical world. By the age of 13, he had mastered calculus and other forms of analytical mechanics, receiving instruction from his father. He became so obsessed with Euclid's parallel postulate and came to the conclusion that the postulate is independent of the other axioms of geometry and that different consistent geometries can be constructed on its negation. In addition to his work in geometry, Bolyai developed a rigorous geometric concept of complex numbers as ordered pairs of real numbers. He was an accomplished polyglot speaking nine foreign languages. No original portrait of Bolyai survives.