Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the theorem itself (Shanks 1993). Shanks (1993) cites the quadratic reciprocity theorem as an example of a deep theorem.

Shanks, D. "Is the Quadratic Reciprocity Law a Deep Theorem?" §2.25 in Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 64-66, 1993.

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Weisstein, Eric W. "Deep Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DeepTheorem.html

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