A software product is a copy of runnable software installed on a computer. The vast, vast majority of such products are built the same way cars will be built in 2055: entirely automatically, with automatic testing and verification, with no human intervention whatsoever.
It's generally only when we are designing a new piece of software that has to handle a new set of requirements that we start building things by hand; but even then, we almost always use assemblies and sub-assemblies called "libraries" to get the bulk of the design. Then we run the design through a compiler and linker, which automatically manufactures a runnable copy of the software, and then we test it.
Mathematics builds new theorems the same way we build new software and the same way General Motors builds new car blueprints. This is likely to change somewhat as car manufacturing becomes more similar to writing software.
It's generally only when we are designing a new piece of software that has to handle a new set of requirements that we start building things by hand; but even then, we almost always use assemblies and sub-assemblies called "libraries" to get the bulk of the design. Then we run the design through a compiler and linker, which automatically manufactures a runnable copy of the software, and then we test it.
Mathematics builds new theorems the same way we build new software and the same way General Motors builds new car blueprints. This is likely to change somewhat as car manufacturing becomes more similar to writing software.