Appalachian State University’s Dr. Jeff Hirst specializes in reverse mathematics, which combines proof theory and computability theory.
In 2011, Hirst received the John Templeton Foundation Grant. This grant enabled him to take a leave from teaching for 14 months. During his leave, he conducted research and attended workshops and conferences associated with his project, “Reverse Mathematics: Constructivism and Combinatorics.” Read more about Hirst’s research project here.
“This entire area of study stems from work of Kurt Godel and Alan Turing from the 1930s, so my whole research area didn’t exist 100 years ago,” Hirst said.
“Godel showed that any reasonable axiom system can only prove some of the theorems that are true. Here, an axiom system is reasonable if the axioms can be recognized by a Turing machine.”
Hirst has been teaching mathematics at Appalachian State University for over 20 years, since fall 1990. After finishing his Ph.D. at Pennsylvania State University in 1987, he had a three-year, post-doctoral appointment at Ohio State University. Appalachian was the next stop, he said.
Hirst chose to teach at Appalachian because he and his wife, Dr. Holly Hirst, were both looking for tenure-track positions in mathematics. Appalachian’s Department of Mathematical Sciences had two open positions.
“Appalachian offered the prospect of a career that balanced scholarship and teaching. At some larger research-oriented schools, successful faculty aren’t allowed to spend very much time or effort working with undergraduates. Here, effort in teaching is expected and rewarded,” Hirst said.
Hirst has taught all the courses in the calculus sequence, linear algebra and the Techniques of Proof course for freshmen and sophomores. For upper-level and graduate students, he has taught analysis, abstract algebra, advanced linear algebra and special topics courses in set theory and computability theory.
Hirst enjoys teaching a variety of courses. “I helped write the materials used in the Techniques of Proof course. That course starts with a nice dose of symbolic logic that I think is wildly fun. I also really enjoy teaching Calculus, especially Calculus I. The ideas in that course are simultaneously profound and remarkably accessible.”