On the Horizontal Monotonicity of $|\Gamma(s)|$ Writing $s = \sigma + it$ for a complex variable, it is proved that the modulus of the gamma function, $|\Gamma(s)|$, is strictly monotone increasing with respect to $\sigma$ whenever $|t| > 5/4$. It is also shown that this result is false for $|t| \leq 1$. Keywords:Gamma function, modulus, monotonicityCategory:33B15