Is the Euler–Mascheroni constant ([tex]\gamma[/tex]) an algebraic number?

Hmm. Is 1. [tex]\gamma = \frac{\sqrt{z^{2} - 1}}{2}[/tex]?

Remark: We tentatively assume [tex]z[/tex] is an algebraic number where [tex]1.5 < z < 1.6[/tex].

We can apply Newton's Method to equation one and study its convergence with regards to [tex]\gamma[/tex].

Warning: This a difficult problem! We suspect there's much more to the true nature of the beast ([tex]z[/tex])... It may have deep secrets that are not easily discovered.

Dave.

Relevant Reference Links:

https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant;

https://en.wikipedia.org/wiki/Newton%27s_method.