Mathematics is the study of patterns, any kind of pattern, in anything. "Difficulty" of maths problems is a kind of measure of how well you know the patterns i

Mathematics is the study of patterns, any kind of pattern, in anything. "Difficulty" of maths problems is a kind of measure of how well you know the patterns involved (which is related to how good our notation, terminology, and visualisations for them are). That means research developing brand new maths or applying it to new problems is often difficult, because no one knows the patterns yet, or has good ways of describing them.