>> just as no human will ever train enough to beat computers at arithmetic.

Think of the amount of complex computation must be happening for an elite gymnast for example. Sure, they aren't solving the equations consciously but at some level computation is happening - or even something as simple as making sense of all of the individual photons arriving at the eye. The subconscious is what I am suggesting we try to exploit. Even then, it seems likely that a "special" brain would be needed - hence why large numbers would be required in order to find it.