"theorize on" is correct and can be used in written English.
You can use it to describe the act of creating or developing theories about something. For example, "The scientist has been asked to theorize on the possible causes of climate change."
They sat in front of television sets and watched experts analyze the contest and theorize on first one candidate, then another.
While one can only theorize on the hidden message in a confluence of racing games, the message of Sega's Super Monkey Ball is crystal clear: eat Dole bananas.
Charles Darwin was one of the first scientists to theorize on the function of the appendix, which in his day had been identified only in humans and other great apes.
They neither want to theorize on the possible source of the anthrax, nor give too much detail about operations in Afghanistan.
It would have to be a lot stickier — that is, people would have to use it much more regularly than they do now — and be around longer for us to even begin to theorize on psychological impact.
Based on these findings, we theorize on the interplay of different dimensions of social capital in university-industry collaborations over time.
And though it is too soon to say conclusively, experts theorized on Friday that ice, one of aviation's most common problems, could indeed have brought the plane down.
We believe that the script theory of guidance in CSCL has the potential to establish a closer link between cognitive theorizing on collaborative learning in psychology, on one side, and organizational and institutional research on collaboration in other social sciences, on the other.
"There's a piece in the World Tribune today — one of the papers in the United Kingdom — exactly as theorized on this program early on," he said on his radio show.
This is obviously another core question in the theory of collective intentionality, one where philosophical analysis on the one hand and the interests of social science and normative theorizing on the other meet.
Archimedes theorized on the displacement of water in the bathroom.
