# Euler constant transcendality. [closed]

What attempts have been made to prove that $\gamma := \lim_{k\rightarrow \infty} \sum_{k=1}^{n} \frac{1}{k} -\log n$ is transcendental?

Any reference for stuff that has been proved on this constant?

We do not even now if $\gamma$ is irrational. The Wikipedia page has links to papers showing many formulas involving $\gamma$, and at least one paper (by Sondow) directly suggesting an approach to establish its irrationality. –  Andres Caicedo Mar 1 at 15:46