en.wikipedia.org/wiki/Kolmogorov_complexity

The date here is off.

A standard survey by Zvonkin and Levin states: "In 1964 Kolmogorov introduced the concept of the complexity of a finite object". That same survey treats Kolmogorov's complexity work as a mid-1960s development, not a 1963 publication.

Math-Net's bibliographic record for Kolmogorov's foundational paper "Three approaches to the definition of the concept 'quantity of information'" shows it was published in 1965. By contrast, the 1963 paper listed in the references is "On tables of random numbers", which is a different publication.

So the article is right that the notion is named after Kolmogorov, but "first published on the subject in 1963" is not consistent with the cited historical record; the key dates are 1964 for introducing the concept and 1965 for the first dedicated publication.

As written, this formula is mathematically wrong.

The standard chain rule / symmetry-of-information statement is that the joint complexity equals the sum of the marginal and conditional complexities up to an additive logarithmic error. Modern statements write this as

• K(x,y) = K(x) + K(y|x) ± O(log K(x,y)), or equivalently
• K(x,y) ≤ K(x) + K(y|x) + O(log n) and K(x,y) ≥ K(x) + K(y|x) - O(log n).

That is very different from an exact equality with a specific positive term + c*max(1, log(K(X,Y))). The latter fixes the sign and size of the error instead of allowing a bounded additive discrepancy. So the article should use an O(log ...) / ± O(log ...) formulation, not the displayed exact equality.