Obviously e is transcendental and π is transcendental, but it hasn't been proven one way or the other whether their sum is transcendental.
It is known that e + π doesn't satisfy any polynomial equation of degree ≤ 8 with integer coefficients of average size 10^9 (Bailey 1988, Borwein et al. 1989), but that doesn't exhaustively prove that e + π is or isn't transcendental.
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Obviously e is transcendental and π is transcendental, but it hasn't been proven one way or the other whether their sum is transcendental.
It is known that e + π doesn't satisfy any polynomial equation of degree ≤ 8 with integer coefficients of average size 10^9 (Bailey 1988, Borwein et al. 1989), but that doesn't exhaustively prove that e + π is or isn't transcendental.
e and pi are both transcendental, so their sum is probably transcendental too. But I can't prove it.
Herr Pi is transcendental.