Dan has a Ph.D. in Pure Mathematics from Tel Aviv University, where he also completed his B.Sc and M.Sc. in Pure Mathematics. His main topic of research was number theory, mostly dealing in function field analogues. He has more than 10 years of experience in research of mathematical algorithms.

As a student, Dan participated and won bronze, silver and gold medals in international math and informatics olympiads for both high school and university students. He has since been involved in the training of Israeli students for the International Mathematical Olympiad, and in recent years acted as leader of the Israeli delegations to the International Mathematical Olympiad and other competitions for high school and university students.