public static int MaxNum (int x, int y, int z)

This is not a mathematical formula. It is a declaration of intent to name some code that takes three ints and returns an int 'MaxNum'. It says nothing about what the code can, should or must do.

Now, if you've come up with some novel way to perform some computation on three integers and produce an integer:

- you might be able to patent that procedure.

- you might write some code that performs that procedure, and you would hold a copyright over that specific set of code

- you might, I suppose, name your algorithm 'MaxNum' and declare a trademark over it

But I don't think any of those could prevent someone from writing

public static int MaxNum (int x, int y, int z)

in another codebase.

- your patent protection might limit their ability to make a substantially similar implementation of such a function

- your copyright protection might prevent them from literally copying your implementation word for word

- your trademark protection might prevent them from passing off their implementation of MaxNum as if it were yours

But in no way does this have anything to do with the uncopyrightability of mathematics.

When you get down to it, copyright is a whole bunch of contradictory rules. Courts decide every time there is a new kind of work, whether it is copyrightable or not. Trying to divine whether something is copyrightable by analogy to other kinds of works is a hopeless endeavour.

That was the case with computer software when it first became interesting to copyright. After all, it's just a series of instructions which are often not considered copyrightable. But, in general, copyright has carried over fairly naturally from the printed word to new types of media as technology advanced.

That literally is not a mathematical formula.

This is not a persuasive argument because, by your logic, function implementations are also mathematical formulas and everyone agrees that they are copyrightable.

The copyrightable part of them is the creative decision making used to organize the workings of the function itself, not the formulas. Two functions could have identical algorithmic performance, but be stylistically and semantically different, have been written independently, and neither would infringe on the copyright of the other.

An API design is also a creative and highly stylistic work. Anyone who has ever designed a large API, or suffered a poorly designed one, can attest to that. A bad design can work just as well as a good design.

Also, you are distorting the argument by making it about one method signature instead of thousands of interconnected types and methods that work together to present an ergonomic interface for the developer.

Arguably API design is the most creative aspect of programming. The space of possible interfaces is infinite, whereas function implementations are heavily constrained by the interface and often there is only a handful of ways to write an implementation for a given interface.

Two equally good programmers may come up with radically different interfaces. Whereas if given an interface and instructed to implement it, they are likely to converge to a similar implementation.

The quality of good/bad or ergonomic is insufficient to meet the threshold for copyright protection.

A table of baseball batting averages or telephone numbers is not copyrightable, no matter how good or bad it is organized.

An API design is plenty creative. The bar for what is creative enough to get copyright protection is extremely low, basically zero. An alphabetized phone book is literally the example people have to use for something that isn't.

There's a reason the Supreme Court didn't adopt the argument you are pushing and instead ruled on fair use grounds: It's a bad argument because a large API is clearly a creative work.

Function implementations are definitely not mathematical formulas. To see what I mean, check out any HN discussions on TLA+ syntax.

It’s when you see an actual mathematical syntax that you realize how different programming really is.

Not try to be tedious here, just pointing out that actually programming is different than math, even for a language like Haskell.

Consider the following:

gcd(X, Y) = X if X == Y or gcd(X - Y, Y) if Y < X or gcd(X, Y - X) otherwhise.

Is this a formula? Should this be copyright-able?

Of course not, this is math; it is not copyrightable.

It would have made perfect sense to Euclid.

Some computers can understand this and execute it as if it were computer code. That's amazing! Kudos to those compute language designers and compiler authors. But their ingenuity does not suddenly grant copyright protection to anything their clever compilers can now understand.

The law says nothing about computability (nice straw man) but it does say ideas and math are not protected whereas code is. My point is the API declarations at the heart of this case are not protected by law because they are examples of the former. Like a formula, they are ideas that describe what to do, but not exactly how to do it.

If you code GCD in a low-level computer programming language then of course you can claim a copyright on that code, but nobody owns the idea of the Euclidean algorithm.

Exactly. That argument would never fly in a court. I’m always amused when software people think they have some legal checkmate like “any digital work is somewhere in the infinite digits of pi therefore cannot be copyrighted.” That’s not how law works.

Yes, but neither is an API signature a formula. I was assuming the logic of the person I was responding to, to show that it could not be right.