Use the formal adjective, sagacious, to describe someone who is wise and insightful like an advisor to the president or a Supreme Court justice.
Someone like an inspirational leader or an expert in a field who seeks knowledge and has foresight can be described as sagacious. If you comment on something at a deeper level, you are making a sagacious observation. The word is a descendent of Latin sagus "prophetic" and is related to the Old English word seek. Synonyms include discerning, insightful and another formal word perspicacious.
