The fact that the Hodge-to-de Rham spectral sequence degenerates for a smooth and proper algebraic variety over a field of characteristic 0 has numerous applications and two proofs. Firstly, it comes as a part of a general Hodge theory package, and secondly, there is a purely algebraic proof by reduction to positive characteristic given by Deligne and Illusie. It turns out that both the Degeneration Theorem and its positive characteristic proof admit a full non-commutative generalization. In fact, the proof becomes more transparent in the non-commutative setting, and reveals its essentially homotopical nature: the most direct way to the proof involves considering algebras over the sphere spectrum ("spectral algebras"). I am going to give an introduction to this circle of ideas, and exlain why homotopy theory helps.