I'm studying normal numbers for my university dissertation - in particular whether or not algebraic numbers are normal.
One thing I cannot find anywhere is why it matters. I'm not expecting a real world application, I just want to know, will it be of any significance, in any area of mathematics, if we can prove that all irrational algebraic numbers are normal. Or, for that matter, if we could prove that any number, say pi or e, was normal. Does it have any application?
Any ideas, however vague, would be appreciated. Thanks!