As other posters noted, in mathematics both 0 based and 1 based indexing is used. When dealing with matrices and vectors (including data tables and data column

As other posters noted, in mathematics both 0 based and 1 based indexing is used. When dealing with matrices and vectors (including data tables and data columns), there is a strong preference for 1 based indexing: first row, first column, first entry, etc. Most matrix and vector based algorithms in literature use 1 based indexing. Programming these in a language with 0 based indexing is a mess, and a common source or errors. When dealing with sequences, especially recursively defined ones, there is usually an initial value (indexed with 0) and then the n-th value is obtained by n applications of the recursive step, so 0 based indexing makes more sense, but in literature there is no fixed convention, and you can find examples with 0 based and with 1-based indexing. Another example of 0 based indexing in math are polynomials (and in extension, power series) where the index is the degree of the term, or in general any functional series where the 0-th term is the constant term. There are also negative indices.