Number theory is quite the zoo of numerical specimens. It catalogs the properties of many different kinds of numbers. This field is also foundational for many of today’s computer systems: it’s used to tell computers how to store information and keep it safe.

Number theory is where we define what “number” means, work with different kinds of numbers, and discover relationships among numbers. One main focus of number theory is the set of positive integers: 1, 2, 3, and so on. Want to know why these numbers are such a hot topic in mathematics? Check out the page on prime numbers and learn about a puzzle that has stumped mathematicians for over 150 years. Want to wrap your head around something a little more exotic? Try exploring infinity by visiting a very bizarre hotel.