Zero based indexing came from early requirements to address things in arrays using offsets.
Subsequent languages don’t have this issue, and when you think about it, it causes a weird disconnect: 1-based indexing corresponds exactly with how you think about and see elements in a collection. 0 based indexing-despite how comfortable one gets with it requires additional arithmetic.
It’s a relic from the past, and unless you’re doing the very specific thing of indexing via offset instead of position, there’s no reason to hang onto this anachronism.
Most math books are written in a way where 1 is the first element. So if you take math examples and translate to code, it works more naturally.
Also this is how you talk normally. You don't talk about the zeroth-column or zeroth-row in daily speech. You talk about first column and first row.
Only reason 0 based indexing make sense to me is because I began programming as a teenagers and was forced to get accustomed to it. But I remember struggling with it. Yes when working with memory, pointers etc it is more elegant. But if you are not, then I think 1-based indexing looks better.
As a trivial example, if you want to get the sum of the first n numbers, that's `sum(range(n+1))` in Python. Or if you want to get all the prime numbers <= n, find the triangular numbers, etc. In general you end up with a lot of `n+1`s and it's easy to lose track or miss some, and end up with a silent, non-crashing error that produces the wrong result because you're accidentally leaving out the last element of your input.
Linear algebra is the most practically consequential one - and suffice it to say, it’s not a coincidence that BLAS, LINPACK, and LAPACK were all written in one-based languages. Matrix indexing is one-based, and beyond the issue of translating notation from equations, IIRC there is even a slight performance difference in some cases.
I believe what it really comes down to is that, just as zero-based really is more natural for offsets (zero offset means the first position, great for pointers), one based really is more natural for counting [and _sets_] (when your index is n that means you have counted n elements up until now).
