The keto (short for ketogenic) diet is a popular name for this. You only eat proteins and fats as your macronutrients (with room for 20g or less of net carbs per day). You have to consciously choose to avoid carbohydrates, which can be difficult. But the energy/mood stability and quick weight loss are undeniable positive results.
I keep hearing its adherents claim various benefits of "keto":
is there any credible sources (i.e. research) that back these claims up?
For instance, what about glucose for mental performance?
No offence, but my current (admittedly limited) understanding of the subject leads me to mentally file it under "dubious", along with "no-fap" and such.
If he/she is talking about added sugar its still not too meaningful. Drinking a glass of OJ has no added sugar but its still very similar to drinking soda.
