[cohomologo]

Mathematica is actually 0-based - but with the zero index spot reserved. A list {1, 2, 3}=List[1, 2, 3] could be read as (List 1 2 3) in Lisp style; one can check if you have Mathematica that {1, 2, 3}[[0]] = List.

But I think that's neither here nor there. Whenever the index has more use than as a label, mathematics starts at zero. Modular arithmetic, polynomials, discrete fourier transformations - for that matter, any discrete approximation of continuous math - all naturally start at zero, and generate lots of -1s in one-based indexing.

[jasode]

In this subthread, the phrase "0-based / 1-based" is for the word "base" accessing the first element which is semantically equivalent to x[0] in C/C++/Python/etc or x[1] in R Language. Yes in Mathematica, putting "0" between "[" "]" will get you the reserved "head" but that's not how people are talking about "0-based" here.