We construct maximal real algebraic curves of any degree d ≥ 3 in the projective plane with the maximal number of real inflection points, answering to a question posed by Arnol'd. To construct these curves, we follow a tropical approach. Namely, we study tropical limits of inflection points of classical plane algebraic curves. The main tropical tool we use to understand these tropical inflection points are tropical modifications. Theorem 1.1 (Klein [Kle76], see also [Ron98], [Sch04], and

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... ). A non-singular real algebraic curve in RP 2 of degree d ≥ 3 cannot have more than d(d − 2) real inflection points. Klein also proved that this upper bound is sharp, by constructing in any degree d ≥ 3 a nonsingular real algebraic curve in RP 2 with d(d − 2) distinct real inflection points. However, the Date: February 15, 2011.