A real number $x$ is normal in base $b$ if every block of digits $B$ occurs in the $b$-ary expansion of $x$ with relative frequency $b^{-|B|}$. In 1909 E. Borel proved that almost every real is normal in every base, but no computable examples were given until many years later. We will discuss the historical development of normal numbers as well as connections to ergodic theory, fractal geometry, number theory, probability theory, descriptive set theory, computability theory, and algebraic geometry. We will also discuss some open problems.

# Thinking about UNT?

It's easy to apply online. Join us and discover why we're the choice of over **37,000** students.