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?!"
I agree that regular exercise, a healthy diet, proper sleep, and a good schedule is a great solution most of the time.
It really is habit forming, though once you fall out it's hard to get back in. After all, being lazy is habit forming too, and once you've stopped accounting for gym time in your day it can be hard to start squeezing it back in.
.. certainly not easy to kick sugar/bread/milk habit.