A 'normal' sequence of numbers is one in which no digit occurs more frequently than any other. The mathematical equivalent of White Noise.

'Normality' is usually considered to be one of the tests for randomnessplugin-autotooltip__plain plugin-autotooltip_bigRandom numbers

unknowable

"We can never decide for sure that a number is random, but what we can do is apply an increasing number of tests and treat our sequence of numbers as innocent until proved guilty."

Source : Prof. Colva Roney-Dougal, senior lecturer in Pure Mathematics at the University of St Andrews, speaking in.

The π sequence has now been computed to many trillions of digits, and appears to pass all tests for randomness, including 'normality'. But the conjecture that π is 'normal' has not yet been proved or disproved.

See: Are the digits of Pi random? US Berkeley Lab.

Notes :

1) No 'naturally occurring' mathematical constant has ever been proved to be 'normal' (or not normal) Examples include the square root of 2, and the natural logarithm of 2.

2) 2024. A group of researchers studying String Theory have accidentally discovered a new formula for calculating - or rather approximating - π. See Scientific American, Aug 2024