Waxahachie — In science and mathematics, an open problem is a known problem which is assumed to have an objective and verifiable solution that remains unsolved. Examples in mathematics would include Fermat's Last Theorem and the Four Colors Theorem in the 20th century, and the Poincaré conjecture in the 21st century.
Few people choose to tackle math problems requiring more than a moment to complete. Yet, SAGU Professor in Mathematics, Dr. Tom Ferguson, spent two years addressing a known Lie superalgebra problem: bounded highest weight modules of osp(1,2nk). Mathematics of this variety often underlie complex science such as string theory and particle theory.
Why does someone choose to spend two years on a single problem? According to Dr. Ferguson, the allure is the "challenge of addressing a question that no one has ever answered." He describes the process as a 1,000-piece puzzle. "Pieces on the edges are placed first. Then, you work toward the middle."
In the instance of his open problem, Dr. Ferguson began from each end and worked toward the center. Unlike a puzzle where the creator knows instantaneously that the last piece has been put into place, Dr. Ferguson was not immediately aware that his journey was complete. That revelation came when his lead professor in his doctoral program said, "Well, I guess that's it. You're done." Dr. Ferguson paused and realized, "Oh, yeah."
What followed was an 80-page dissertation explaining how the problem was solved.
An abbreviated paper was published in "Proceedings of Symposia in Pure Mathematics: Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics," coauthored with Dr. Dimitar Grantcharov and Dr. Maria Gorelik. The volume is available for purchase online.