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This talk is about possible singularity formation for an evolving two-fluid interface such as the surface of an ocean wave, wherein the interface separates the water from the air. Using elementary ideas, I will show that this interface (commonly referred to as a vortex sheet) cannot self-intersect in finite time, whenever the interface remains locally smooth. In particular, this means that a locally smooth ocean wave cannot break. This is in sharp contrast to the one-fluid water waves model for which we known that the interface can self-intersect in finite time. I will show some videos to explain that the theorem does not contradict what we see in nature. The talk will not be technical and should be accessible to all graduate students. The theorem I will present is joint work with D. Coutand.