Number theory concerns properties of whole numbers: can two perfect cubes (like 8 or 27) ever add up to a third perfect cube? Are there infinitely many pairs of primes who differ by 2 (like 29 and 31)? Problems in number theory are often simple to understand and state. However, the problems are often ferociously difficult to solve, and in modern times, a wide range of sophisticated mathematics, from hyperbolic geometry to calculus of complex numbers to ideas of quantum physics, have been applied to them. In fact, number theory has motivated many of the developments of modern mathematics.
This course will use number theory as a common thread in a historical overview of mathematics, and it will use number theory problems as motivation to introduce modern ideas in mathematics. Consequently, the course may be of interest, even if one is not particularly interested in the problems themselves.