Arithmetic operations in Bitcoin (OP_ADD, etc)
Short answer: arithmetic on large numbers will cause the script to fail.

Long answer:

Script arithmetic is limited to 32-bit arithmetic.

You can find the code for arithmetic operations in script.cpp, in the function EvalScript, where the opcodes are evaluated using CScriptNum in [script.h](https://github.com/bitcoin/bitcoin/blob/master/src/script.h].

The numeric limit is enforced through the constant nMaxNumSize.

The CScriptNum constructor shows that numbers larger than 32 bits throw an exception, resulting in failure of the script.