Does exercise change your brain?

After yesterday's post suggesting no effects of common dietary supplements on cognitive changes with aging, I thought I would note work regarding exercise and brain health. mentioned by Reynolds, in particular a study by Burzynska et al. that monitored the daily activities of non-athletes:

...the most physically active elderly volunteers, according to their activity tracker data, had better oxygenation and healthier patterns of brain activity than the more sedentary volunteers — especially in parts of the brain, including the hippocampus, that are known to be involved in improved memory and cognition, and in connecting different brain areas to one another. Earlier brain scan experiments by Dr. Burzynska and her colleagues had established that similar brain activity in elderly people is associated with higher scores on cognitive tests.

Again, there is the caveat that a correlation does not prove a cause.