Math (usually) uses 1-based indexes because those parts of math started before the concept of zero as a number, and then the convention persisted, even down to

Math (usually) uses 1-based indexes because those parts of math started before the concept of zero as a number, and then the convention persisted, even down to Matlab. There are many similar path-dependent conventions in human culture. E.g. percentages originated before the concept of decimal fractions, base-sixty time units come from ancient Mesopotamia, and conventions about multi-dimensional array memory layout are based on the convention for drawing matrices on paper. Most common mathematical sequences and series work better (more naturally/clearly) when zero indexing is used instead, and off-by-1 errors are a problem in mathematics just like computing (but less of a problem, because notation errors get silently corrected in readers’ heads, and don’t actually have to be interpreted strictly).