As a Math Professor, I think you would best fit in a Machine learning/Data scientist role in any tech company.

It's where Most people of your demographic (I can think) of are.

Its also one of the most difficult fields in tech, so your "deep thinking" is an obvious advantage.

How to promote/sell your ability?

I advise you to may be get into the industry (also learn some python) http://www.deeplearningbook.org/

Write some papers on your orginal thoughts/ideas and publish them on the http://arxiv.org