In this talk, I will briefly outline a combinatorial version of the proof of Hilbert's basis theorem using Dickson's lemma. This combinatorial proof, constructive in nature, is a modern restatement of the proof given by Paul Gordon- (in)famous for his quote "Das istnicht Mathematik, das ist Theologie". After adjusting the notion of noetherianity to equivariant noetherianity, we can think about (equivariant) noetherianity of a ring with infinitely many variables (spoiler: combinatorial ideas tells us many things). If time permits, as an application of equivariant noetherianity, I would talk about infinite dimensional algebraic varieties that are stable under large symmetric groups. Speaker(s): Kyu Jun (UM)