Higher-order partial differential equations (PDEs) with multiple independent variables can be classified, but the classification is complex and varies based on the order and number of variables involved. The Monge cone is a key concept for classifying second-order PDEs in n variables. However, there are equations that lack a clear classification, raising questions about the feasibility and utility of a general classification system. The discussion highlights the nuanced differences in classification approaches depending on whether the focus is on second-order equations or higher-order equations. Overall, the classification of higher-order PDEs remains a challenging area of study.