Please define what you mean by a simple diet.
In any case, while I do believe that there are many diet-related conditions that can impair brain function, actually improving on baseline is probably harder.
While you're growing, it's imperative to have a nutritious diet with little toxins. For example, see how wheat impacts IQ in children.
When you're grown, you can get "brain fog" from toxins created by pathogenic gut bacteria, fungi or even brain infections. If you have an unhealthy gut flora, eating the wrong foods (e.g. lots of grains or fructose or too much protein) will feed the gut flora, which release toxins and impair brain function.
I'm not sure about the influence of blood glucose levels on brain function. Certainly too little is problematic, and some eating patterns (e.g. lots of simple sugars) can give you reactive hypoglycemia. I would (and do) eat starches instead of sugars and eat those starches with fats or acids to lower the GI.
Finally, to maintain your brain tissue you need a good Omega-3 and Omega-6 balance, meaning you should avoid all grain/seed oils as well as foods containing them and eat fatty fish once or twice a week. Cholesterol is also important, eat mussels etc and egg yolks.
Basically, if you follow a healthy diet (like Perfect Health Diet) you'll be doing everything you can to optimally use your brain.