Optimal upper bound for degrees of canonical Fano threefolds of Picard number one

We show that for a $\mathbb{Q}$-factorial canonical Fano $3$-fold $X$ of Picard number $1$, $(-K_X{)}^3\le 72$. The main tool is a Kawamata–Miyaoka type inequality which relates $(-K_X{)}^3$ with ${\widehat{c}}_2(X)\cdot c_1(X)$, where ${\widehat{c}}_2(X)$ is the generalized second Chern class.