Number Theory

Number theory, which is sometime scaled "The Queens of Mathematics", is one of the branches of mathematics with longest history, which dates back at least to the ancient Greek. As the name of the subject suggests, it is intimately related to problems of numbers, in particular integers, as exemplified by the famous Fermat's last theorem. Throughout the history of number theory, those problems on numbers have attracted numerous mathematicians including many of the greatest geniuses in the history of mathematics.

Along the way through their endeavors to solve problems on numbers, however, mathematicians have also invented various new mathematical concepts, most of which are highly abstract, such as zeta function, modular form, automorphic representation, Galois representation, to name a few. As a result, contrary to the name of the subject, many (though not all) of researches in contemporary number theory are no longer on numbers but are focused on such abstract concepts which have their origins in problems on numbers, and number theorists study those abstract concepts through diverse techniques of modern mathematics including algebra, analysis and representation theory.