Yes this is in fact true. As one author already said, a healthy outside starts from the inside. As we grow old it is necessary to keep our fitness level up!
According to the medical college of Pennsylvania, long term aerobics keeps you mentally sharp! Especially this is affected to an age group of people above 60 years old. During the study, people who exercised 5 and more years did much better in the intelligence test, as well as performing more complicated tasks.