Viro's quantization of Arnold invariant. Mathematical background, 1920s -- Topological invariant of know projections, 1930s -- Classification of knot projections under RI and RII, 1990s -- Classification by RI and strong or weak RIII, 1996-2015 -- Techniques for counting sub-chord diagrams, 2015-future -- Hagge-Yazinski theorem, necessity of RIII -- Further result of strong (1, 3) homotopy -- Half-twisted splice operations, reductivities, unavoidable sets, triple chords, and strong (1, 2) homotopy -- Weak (1, 2, 3) homotopy -- Viro's quantization of Arnold invariant.
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