Someone almost hit the nail on the head above. Programming is mathematics.  More specifically, programming is a branch of mathematical logic called computability theory or recursion theory.

Other branches of math are involved directly, specifically formal language and automata theory. These help describe regular expressions, used in pattern matching, and formal grammars, used to describe and parse programming languages.

Anybody who says that programming is not mathematics either doesn't know what they're talking about, or has an ulterior motive, like a "Intellectual Property" maximalist, who hopes to profit by getting a patent on an algorithm or some other basic mathematical fact or discovery.

Some references for programming as math, and the corollary not knowing what you're talking about:

Program are Proofs: 19th Century Logic and 21st Century Computing

Programs are Proofs: Models and Types in Lambda Calculus

Wikipedia's Curry-Howard Correspondence article

On the Unusual Effectiveness of Logic in Computer Science

The Unreasonable Effectiveness of Logic

Yes, those are heavy on the "logic" part of mathematical logic, but mathematics is generally acknowledged to be a few axioms, and their logic consequences as developed via first order logic.

As far as saying otherwise and being an "IP" maximalist out for money:

How to patent an algorithm in the US.  Algorithms aren't patentable, but patents are granted on algorithms by not referring to them as algorithms. It's not hard to find a lot of material on the web that either points out, or attempts to explain, that contradiction.

What does mathematics have to do with programming?
I filed my federal taxes a couple of weeks ago, then realized I needed to amend them, so am going to file a 1040X in the next week or two. I have not yet filed my state (Oregon) taxes. I've been using TurboTax. I see two potential ways of doing this:


File federal amendment, file original Oregon Form 40, then file Oregon again with whatever the amendment form is.
File federal amendment and then file only the updated Oregon Form 40 attaching the updated 1040A.


Do I need to do the more complicated in option 1 or something like it, or is ok to just skip the original state filing as in option 2?
