New research suggests it might:
[Neuroscientist Charles Hillman] rounded up 259 Illinois third and fifth graders, measured their body-mass index and put them through classic PE routines: the "sit-and-reach," a brisk run and timed push-ups and sit-ups. Then he checked their physical abilities against their math and reading scores on a statewide standardized test. Sure enough, on the whole, the kids with the fittest bodies were the ones with the fittest brains, even when factors such as socioeconomic status were taken into account.
The old explanation for the possible linkage between brawn and brains was that a stronger heart could pump more blood, better oxygenating brain cells and keeping jocks sharp. Turn out it's a bit more chemically complex than that:
The process starts in the muscles. Every time a bicep or quad contracts and releases, it sends out chemicals, including a protein called IGF-1 that travels through the bloodstream, across the blood-brain barrier and into the brain itself. There, IGF-1 takes on the role of foreman in the body's neurotransmitter factory. It issues orders to ramp up production of several chemicals, including one called brain-derived neurotrophic factor, or BDNF...It fuels almost all the activities that lead to higher thought.
With regular exercise, the body builds up its levels of BDNF, and the brain's nerve cells start to branch out, join together and communicate with each other in new ways. This is the process that underlies learning: every change in the junctions between brain cells signifies a new fact or skill that's been picked up and stowed away for future use. BDNF makes that process possible. Brains with more of it have a greater capacity for knowledge....In unlucky people with a faulty variant of the gene that makes BDNF, the brain has trouble both creating new memories and calling up old ones.
Exercise, it turns out, builds those cells, and those who make the greatest cardiovascular gains in studies also build the most neural capacity. The growth tends to happen in the sectors of the brain governing memory, and thus retards the earliest cognitive declines of aging. Sadly, though, this appears to be limited to cardiovascular fitness. Weight-lifting, stretching, and toning does little to nothing for the brain, unless by "brain" you mean "how cut your abs are."