It may be helpful to realize that the word “breakfast” can mean a great many different things and thus eating or skipping “breakfast” can have widely divergent impacts. For A breakfast may be a stack of pancakes with syrup, some toast with butter and jelly, a huge cup of fruit juice, and some coffee with heaps of sugar. For B breakfast may be a small espresso and a banana.
Furthermore, although most people are sedentary these days, if one is physically active as well as mentally active then having some calories before commencing may be necessary to fuel the physical and mental activity. Sure, you can get through an arduous two-hour workout followed by a course on advanced calculus on an empty stomach but your performance will undoubtedly be poorer than if you’d had some calories first.
As with all things, there’s no one-size-fits-all, especially when the definition of “breakfast” is unspecified.