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
Famous quotes containing the words open and/or questions:
“We were young, we were merry, we were very very wise,
And the door stood open at our feast,
When there passed us a woman with the West in her eyes,
And a man with his back to the East.”
—Mary Elizabeth Coleridge (1861–1907)
“I loved reading, and had a great desire of attaining knowledge; but whenever I asked questions of any kind whatsoever, I was always told, “such things were not proper for girls of my age to know.”... For “Miss must not enquire too far into things, it would turn her brain; she had better mind her needlework, and such things as were useful for women; reading and poring on books would never get me a husband.””
—Sarah Fielding (1710–1768)