[Ancapistani]

> However, we still don't know if pi, e or square root 2 are normal.

The math is somewhat beyond me - at least, without digging into the formal proof - but my understanding is that we can prove that pi cannot be represented as a ratio of two integers, and therefore cannot have a finite decimal representation.

[kosievdmerwe]

We know all these numbers are irrational. That's been known for a long while. Normal numbers are something different, however.

You can look at the wikipedia definition[1], but that involves a few levels of definitions that I don't know, like density, but the gist is that every sequence of N digits occurs with equal frequency to every other sequence of N digits in the expansion of the number.

The definition is complicated due to dealing with infinity and multiple bases.

But that said even with this superficial understanding we can see two things: * Rational numbers can never be normal, since the digits repeat after some period. (Just choose a sequence of numbers longer than the period and you can easily construct a sequence that doesn't appear) * Normal numbers contain every sequence of N digits in their decimal expansion. So if we prove pi is normal (like we believe it is) then we know somewhere in its decimal expansion we can find any sequence of digits we want. Which is the property this comment[2] was referring to.

[1]: https://en.wikipedia.org/wiki/Normal_number [2]: https://news.ycombinator.com/item?id=25282609