Fax App for Android?

Today, one of my fellow devs at Dark Horse received a random call on his mobile phone from a fax machine. After the obligatory "faxes are so old" jokes, he mentioned, "yeah, my mobile can't accept faxes, sorry".

But then! We all got the same idea. Why not? Why isn't there an app that would let you answer the phone, and if you hear the telltale beeping you tap an icon on your screen and the fax app takes over, answering the fax on the other end, receive the transmission then save it as a PDF?

A spotty connections would be an issue of course, but other than that I don't see many hurdles.