The fermionic Fock space is the semi-infinite wedge of a countably infinite dimensional vector space, with a basis indexed by pairs of a partition and an integer. We explain how the 𝔤𝔩(∞)-action decomposes the Fock space into irreps, using a basis of 𝔤𝔩(∞) built from composing exterior multiplication with contraction. We then introduce operators as infinite sums of the 𝔤𝔩(∞) operators, whose action on each irrep can be used to identify it with the ring of symmetric functions. Along the way, we reprove the skew Jacobi-Trudi identity. No physics background assumed.