The pilot episode calls the Professor a "Research Scientist and well known Scout master" [even gives him a name as Roy Hinkly!]... but it never really spoke about his field of study.
The Professor showed an unbelievably wide range of knowledge from various fields, covering everything from basic physics to chemistry to agriculture and languages. This was cleverly done to give plausible reasons for some of the various creations and misadventures that happened on the show.... but realistically, he must have specialized in one field. Even as a Scout Master, with a wide breadth of knowledge, he couldn't have covered everything we see him do in the series.
So what exactly were his one, two, or possibly three fields of expertise?
I'm open to educated guesses, but canon answers would be preferred.