A huge study of 1.2 million men (including 260,000 sibling pairs, 3000 sets of twins, 1400 identical) born in Sweden between 1950 and 1976 when they entered their mandatory military service. Every measure of cognitive functioning increased with increasing aerobic fitness, but not with strength. This was true of twins as well, so they think it's causal rather than associative, i.e., getting fitter will make a person smarter. They assume it is because of blood circulation affecting brain plasticity.
If true, this has school policy implications for bringing back PE. Maybe we can sell exercise as a school readiness program.
And it makes me wonder how smart I would be if there were about 20% less of me, or if I ever got up from this stupid computer and walked around the block.