Constructive Olympics?

I tend to have a recurring thought about this topic whenever the Olympics cycles around: whilst I am awed by the dedication that Olympic athletes exhibit in pushing themselves to the pinnacle human fitness and skill (in narrow disciplines), I don't consider the particular areas of focus to be all that interesting. Although there are no doubt useful derivatives of sports technology, in general Olympic athletes are not advancing humanity.

I wonder whether there are any people who engage in more intellectual disciplines that train as hard as and push themselves as hard as Olympic athletes? What happens if you take the most inherently mathematically gifted people in each country and then train them in the same way Olympic athletes are trained with: coaches; equipment; optimized diets; and (importantly for non-athletic endeavors), appropriate physical training?