Open Questions
It is not known whether π + e or π − e is irrational or not. In fact, there is no pair of non-zero integers m and n for which it is known whether m π + n e is irrational or not. Moreover, it is not known whether the set {π, e} is algebraically independent over Q.
It is not known whether π e, π/e, 2e, ee, eee,πe, π√2, ln π, Catalan's constant, or the Euler–Mascheroni gamma constant γ are irrational. It is not known if nπ or ne is rational for any positive integer n.
Read more about this topic: Irrational Number
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