How do we prove Pauli's exclusion principle? My professor makes a Slater determinant and then merrily shows how it disappears when two columns or rows are same. That is not Pauli's principle, is it? It is based on an assumption that certain particles are described by certain states. So my question translates to why fermions (half integral spin particles) are described by antisymmetric states while bosons (integral spins) are described by symmetric states?