A recent study of twins indicates leg strength directly relates to better long-term cognition.
It has been widely assumed that exercise helps keep the brain healthy and fight off age-related declines in memory. This month the research journal, Gerontology, published a paper showing leg strength predicting cognitive function as far as ten years out. The study was done with female twins to help eliminate genetic differences.
"A striking protective relationship was found between muscle fitness (leg power) and both 10-year cognitive change"
It is unclear if the legs are somehow special in their predictive power. The legs, particularly the thighs, are considered good indicators of overall physical activity.
The legs are often referred to as the "second heart" due to their ability to help pump blood back up the leg. I cannot help but wonder if this increase in circulation contributes to the cognitive findings published.
Regardless of the cause it is good news. Go out there and walk, run, bike, yoga, ski, or climb. Either way both your legs... and brain will thank you!
[Further reading: New York Times]