All squares are (but not all rectangles are squares); therefore the square is a special case of the rectangle.

that aⁿ + bⁿ = cⁿ has no solutions in positive integers with n > 2, is a special case of Beal's conjecture, that a^x + b^y = c^z has no primitive solutions in positive integers with x, y, and z all greater than 2, specifically, the case of x = y = z.

The unproven is a special case of the generalized Riemann hypothesis, in the case that χ(n) = 1 for all n.

which states "if p is a prime number, then for any integer a, then ${\displaystyle a^{p}\equiv a{\pmod {p}}}$" is a special case of Euler's theorem, which states "if n and a are coprime positive integers, and ${\displaystyle \phi (n)}$ is Euler's totient function, then ${\displaystyle a^{\varphi (n)}\equiv 1{\pmod {n}}}$", in the case that n is a prime number.

${\displaystyle e^{i\pi }=-1}$ is a special case of Euler's formula which states "for any real number x: ${\displaystyle e^{ix}=\cos x+i\sin x}$", in the case that x = ${\displaystyle \pi }$.