I will present a proof of Lê’s conjecture, in its formulation that every holomorphic map germ $({\mathbb{C}}^2,0)\to ({\mathbb{C}}^3,0)$ admitting an injective representative has nonzero differential at the origin. The proof first reduces the possible counterexamples to map germs of order 2, 3 or 4. Separate arguments developed using AI exclude each of these three cases. The talk will focus on the first part: the reduction theorem, which combines plane curve singularities, explicit knot cobordisms, and bounds for the Seifert genus coming from the Υ invariant in knot Floer homology. I will conclude with an outline of the proof for the three remaining cases, based on a systematic study of holomorphic map germs of low order through their weighted initial forms.