intellect

• book smarts

  Intellectual ability and knowledge acquired through studying, formal education, and academic pursuits, often contrasted with practical experience.

• A stroke of genius

  An extremely clever and original idea or action that solves a problem or achieves a goal effectively.

• A brainwave

  A sudden, brilliant idea or moment of inspiration.

• To have one's wits about one

  To be mentally alert and able to think clearly and respond quickly, especially when faced with an unexpected challenge.

• To be sagacious

  To possess or display keen mental discernment, good judgment, and practical wisdom.

• A bright spark

  An intelligent, clever, and often lively person, especially one who comes up with good ideas.

• a font of wisdom

  Someone or something that is a rich and inexhaustible source of profound knowledge, sound judgment, or valuable advice.

• Beyond my ken

  Too difficult or impossible for someone to understand or know.

• Pedantic display

  An ostentatious show of minor details or academic knowledge, often made to correct others or assert intellectual superiority.

• Clever clogs

  Someone who is ostentatiously intelligent or academically inclined, often used with mild annoyance or teasing.