I don't know what your current industry is, but Google publishes their research and collaborates with academic institutions is one that immediately comes to mind. The government (NASA, NSA for one), tech companies (IBM, Microsoft, etc.), medical companies, aerospace/defense (JPL), just to name a few. I am sure there are way more than I could think of and I am sure others will care to fill in as well.
Research is not exclusive to academia.
Yeah, but this is specifically about pure mathematics. Do Google and medical companies publish pure math research?