I'll start by saying that I greatly prefer 0-based, and have used but 0- and 1-based indexing, but the choice is largely arbitrary.

0 makes sense as the '0-th offset' when thinking from a pointer perspective, but I often find when teaching, that 1-based comes more naturally for many students (the 'first' item).

You mention mathematical or scientific work...but I often/mainly see enumerations (such as weights x_1, x_2, ... x_n or SUM 1 to N) start with 1, so for these 1-based can be a more natural/direct translation of mathematical notation to code.