But, if you need a bit... it works for me. When I am hiking or skiing 3-4 times a week, I get a lot more done.
I don't know how to make my diet better.
Here's one better. It's a type 2 diabetes study that compared exercise against metformin against a placebo. The conclusions were so overwhelmingly in favor of exercise that the study was stopped early.
Two of four subtasks that reflect complex cognitive speed (Stroop color/word interference and Concept Shifting Test) showed main and interaction effects with age of aerobic capacity in a hierarchical regression analysis, accounting for up to 5% of variance in parameter score after correction for age, sex, and intelligence main effects.
Still, that study is rather weak evidence. The benefits could be relegated to preventing decline in older people. Anecdotally, I do feel duller on days when I don't run; even if I didn't, I'd still exercise. It helps me relieve stress.
In terms of general benefits, most people would be better off if they exercised more, not less. I mean it's not like fit people wake up one day, look at a mirror and see a firm, toned body with six-pack abs then scream at the sky, "Nooooo! Why me?!"