Perhaps my understanding of APIs is different because I'm an engineer and not a lawyer, but how is this not an open and shut case?
The cookbook analogy is not applicable for the same reason one could not apply it in Baker, accounting methods are not of themselves copyrightable creative works. (They may be patentable, but I believe patentability is NOT at issue here.)
Selecting and arranging recipes requires creativity. I do not believe API code of a math library is in any way the same level, having designed hundreds of APIs and several SDKs myself. Perhaps creating a specification upon which the API design based upon is, but that leads right back to Baker. What am I missing here?
[1] https://en.wikipedia.org/wiki/Baker_v._Selden
Edit: And if you think about it, an API code is really just a set of templated forms for conveyance of data between systems. In this sense it is really no different from the accounting ledger templates in Baker.
Second edit: It would be worthwhile to enlighten the judges on the early history of computer programs and their ties to recipes which should make the cookbook analogy and its potential misapplication here even more obvious.
Third edit: Another line of enquiry would be to discuss differences between API contracts and APIs. They are not the same, though often confused, even by practicing software engineers.