The construction of higher dimensional cubature formulas remains an art, even for very standard measures. A new approach towards constructing cubatures for given measures was advocated in the last decade by Curto and Fialkow, see for instance R. E. Curto and L. A. Fialkow [Trans. Am. Math. Soc. 352, 2825–2855 (2000; Zbl 0955.47011)], and their older works cited there. The present note by Monique Laurent brings a welcome simplification to the Curto-Fialkow scheme. Although the main idea is the same (to analyze the flat extensions of certain moment matrices), her use of the real Nullstellensatz makes the proofs shorter and more accessible to the beginner. No doubt, this will be the textbook proof of Curto and Fialkow’s main result.