And a lot of the time it makes the syntax more compact than it would be with 0-indexing.

  for i=1,#arr do
    foo(arr[i])
  end

I don't feel that strongly for or against either way of indexing though, they both have their pros and cons.

Perl is usually used with the first element being zero and the same loop would be

    for (0..$#arr) {
        foo(arr[$_])
    }

Whatever you're feeling is not in starting at one.

You are correct that 1-based indexing is the norm among mathematicians, but none of the creators of Lua is a mathematician, AFAIK. You can read about the early history of Lua here:

https://www.lua.org/history.html

> The 1 indexes are only a difference from what you're used to

The left handed scissors are only a difference from what you're used to.

> Lua was made by mathematicians

The default value is nil and using nil as an index on a table returns nil. Yet nil + number is not valid and results in a runtime error.

> it's pretty much just a leftover habit from C devs

It's reflective of the fact that these languages are either intended to work with C APIs or are implemented in C itself. This makes writing FFI and extensions _far_ easier than it would be otherwise.