I always thought engineering was simply applied math and science. You're not researching and testing new theory explaining the nature behind how phenomena work,

I always thought engineering was simply applied math and science. You're not researching and testing new theory explaining the nature behind how phenomena work, or developing new mathematical techniques, that's for scientists and mathematicians. Rather engineers take their work, and apply it to invent things and solve problems. As so, I'd consider software development can qualify as engineering. If you're taking the work of computer scientists and mathematicians (or any other science fields) and applying it to software, it fits the definition. If you're just laying code to a given spec without much more thought, then you're just a programmer/developer...