Think of the fighter as an army. Think of the ring as the terrain upon which that army gets deployed. And any successful army must be trained and prepared, fortified with the provisions of excellent physical conditioning and heavily-drilled technique.
Beyond that, no army can go to war without a strategy and still hope to win. A fighter in a world championship-caliber fight needs to enter the ring with a Plan A, and be ready to follow up with Plans B through E as the changing situation requires.
A boxing trainer is very much like a military general, preparing and deploying his one-man army. To excel at this requires a highly analytical mind.
I have left active boxers off this list. I can see obvious arguments for fighters such as Bernard Hopkins, Floyd Mayweather Jr. and Guillermo Rigondeaux, but I have chosen to focus exclusively upon trainers.