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.

# Deep Theorem

## See also

Theorem, Trivial## Explore with Wolfram|Alpha

## References

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.

## Referenced on Wolfram|Alpha

Deep Theorem## Cite this as:

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