Pi Day is upon us again and we still do not know if Pi is normal

The digits of pi have intrigued both the public and research mathematicians from the beginning of time. This article briefly reviews the history of this venerable constant, and then describes some recent research on the question of whether pi is normal, or, in other words, whether its digits are statistically random in a specific sense. 1 Pi and its day in modern popular culture The number pi, unique among the pantheon of mathematical constants, captures the fascination both of the public and of professional mathematicians. Algebraic constants such as 2 are easier to explain and to calculate to high accuracy (e.g., using a simple Newton iteration scheme). The constant e is pervasive in physics and chemistry, and even appears in financial mathematics. Logarithms are ubiquitous in the social sciences. But none of these other constants has ever gained much traction in the popular culture. In contrast, we see pi at every turn. In an early scene of Ang Lee’s 2012 movie adaptation of Yann Martel’s award-winning book The Life of Pi, the title character Piscine (“Pi”) Molitor writes hundreds of digits of the decimal expansion of pi on a blackboard to impress his teachers and schoolmates, who chant along with every digit.1 This has even led to humorous take-offs such as a 2013 Scott Hilburn cartoon entitled “Wife of Pi, ” which depicts a 4 figure seated next to a pi figure, telling their marriage counselor “He’s irrational and he goes on and on. ” [22]