30
$\begingroup$

A little reading suggests:

It is known that either $\pi + e$ or $\pi \times e$ is transcendental (or possibly both), but no proof is known that one of those two numbers in particular is transcendental.

If we just want irrationality rather than transcendence, is a proof known?

Can we prove $\pi+e$ is irrational? Can we prove $\pi \times e$ is irrational?

  • 1
    And this: http://mathforum.org/library/drmath/view/51617.html2011-03-21

1 Answers 1

22

It is not known whether $\pi + e$ is irrational, nor whether $\pi \times e$ is irrational. See $\# 22$ here.

  • 0
    The link does not work anymore. [Here](https://docs.google.com/open?id=1h1YKOImdD9cB3_r26W2h6JMcoubjt1v15HhMTVapZkrBDhUUH_nqO6gpaNsY) is the version from Google cache.2012-06-17