How would you define 'intellectual prowess'?

An intellectual prowess is a display of exceptionally high intelligence and knowledge. To be highly skilled, knowledgeable at/of something.
Prowess often has a negative connotation though. A person who is self-centered or a braggart may be said to be speaking of their prowess in something, to include intellect. When others speak of prowess it is often satirically said.
A more positive statement might be intellectual capability, capacity and so forth.