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.

Definitions of sagacious
  1. adjective
    acutely insightful and wise
    “observant and thoughtful, he was given to asking sagacious questions”
    synonyms: perspicacious, sapient
    having or prompted by wisdom or discernment
  2. adjective
    skillful in statecraft or management
    “an astute and sagacious statesman”
    marked by artful prudence, expedience, and shrewdness
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