[jjtheblunt]

Apple definitely had an internal group doing mathematics research, which i know first hand. But yes there are, to your point, topics in science probably only done in academia etc, but, to my point, several are seriously funded in industry.

[whatshisface]

I couldn't say more without knowing the details, but industrial labs don't usually research mathematics, so much as ways to apply mathematics to their industry. These are called "mathematics research departments," because they hire mathematicians.