If you think probability theory is bad... The old joke that "differential geometry is the study of properties that are invariant under change of notation" is f

If you think probability theory is bad... The old joke that "differential geometry is the study of properties that are invariant under change of notation" is funny primarily because it is alarmingly close to the truth. Every geometer has his or her favorite system of notation, and while the systems are all in some sense formally isomorphic, the transformations required to get from one to another are often not at all obvious to the student. —John M. Lee, "Introduction to Smooth Manifolds"