There is an interesting proof of Wigner's unitary-antiunitary theorem by Kai Johannes Keller which is based on the fundamental theorem of projective geometry. (On the realization of symmetries in quantum mechanics ). The conclusion of this paper is the following.
But the highlighted statement is false since we know that besides the identity and the complex conjugation, there are also so-called "wild" automorphisms of $\mathbb C$. Does this mean that Keller's proof isn't complete (since it doesn't prove that the transformation can be linear or anti-linear), or Wigner's theorem isn't true (because there are some symmetries that cannot be obtained from unitary or anti-unitary transformation, only from some wild semi-linear transformation?