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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 ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

The reciprocity theorem for x^8=q (mod p).

The star polygon {10/3}.

The star polygon {12/5}.

The star polygon {8/3}.

The number q in a star polygon {p/q}.

For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G=Gal(K/F) correspond with the subfields ...

There are so many theorems due to Fermat that the term "Fermat's theorem" is best avoided unless augmented by a description of which theorem of Fermat is under discussion. ...

R^n is homeomorphic to R^m iff n=m. This theorem was first proved by Brouwer.