Professor Paul Tran-Hoang's research research focuses on logic, philosophy of logic, and philosophy of mathematics. He's also interested in the history of science and 19th and 20th century philosophy. In particular, he is interested in questions concerning the nature of mathematical truth and mathematical knowledge. Mathematics is philosophically puzzling for a variety of reasons: the truths of mathematics seem to be such that they couldn’t be otherwise, mathematical truths are knowable without appealing to sense experience, and mathematical objects, such as numbers, don’t seem like the kind of things we can encounter in physical reality. His work seeks to make sense of these puzzling features of mathematics by incorporating insights from formal logic and by considering how mathematics has developed historically.