In the mid 1960s American mathematician Stephen Schanuel devised a complex mathematical conjecture regarding the 'transcendence degree' of certain 'field extensions' of the rational numbers.
Formally stated :
Given any n complex numbers z1, …, zn that are linearly independent over the rational numbers Q, the field extension Q (z1, …, zn, ez1 , …, ezn) has transcendence degree at least n over Q
Source :Wikipedia
At present, the conjecture has neither been proved or disproved.
If it is eventually proved, it could have profound implications for exploring the nature of Irrational numbersplugin-autotooltip__plain plugin-autotooltip_bigIrrational numbers
unknowable
An irrational number is a real number that can't be expressed as a ratio of integers, i.e. as a fraction.
Put another way, it can never be specified with absolute accuracy.
Well known examples are π and √2
For many irrational numbers, relatively simple mathematical proofs exist which show that it's impossible to ever arrive at a finite solution. For example, such as π and the natural logarithm e.