Use the word sage for someone or something wise and judicious. Thanks to the sage advice of your friend, you didn't write your teacher an angry e-mail!
Although you might think of a wizard when you hear the word sage, really it means a wise man. Today you see it used to refer to someone who has insight in a particular field. If someone is a policy sage, he knows just what advice to give politicians to make them understand the issue and respond successfully to it. In a totally unrelated use, there is also a plant called sage that is useful in home remedies and cooking.
http://vocabulary-vocabulary.com/dictionary/sage.php
▸ noun: aromatic fresh or dried gray-green leaves used widely as seasoning for meats and fowl and game etc
▸ noun: a mentor in spiritual and philosophical topics who is renowned for profound wisdom
▸ noun: any of various plants of the genus Salvia; a cosmopolitan herb
▸ adjective: having wisdom that comes with age and experience
▸ adjective: of the gray-green color of sage leaves
http://en.wikipedia.org/wiki/Sage