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In the recent years, there has been much interest in the Robinson-Schensted-Knuth correspondence (RSK), due to the various emerging applications. While studied for decades, the classical RSK remains difficult to describe, which can be explained by its heavy combinatorial definition. In the talk, I will present a continuous generalization of the RSK, based on a completely different, rather geometric approach. Basically, we define RSK as a piecewise linear map between two convex polytopes, which will be explicitly defined. The exposition will be self-contained, and no combinatorial background is assumed. Further, lack of familiarity with RSK is a plus.