These terms were introduced in Mimi Swartz's Ticker about the artificial heart. The idea of divergent thinkers to "explore as many answers as possible when looking for solutions," like engineers building the robot heart. Physicians, by contrast, were convergent thinkers, looking for the "one right answer to the way the body worked and you'd better know it in a crisis" (p. 181). Of course, physicians thought they were smarter than engineers and visa versa.
Psychologist Joy P. Guilford first used the terms in the 1950's. Divergent thinkers want creative and more open-ended ideas by looking at multiple potential solutions, which could be considered non-linear. Information then is organized and structured in potentially useful ways (possibly by convergent thinking). Convergent thinking is related to the idea of a "correct answer" and little if any creativity--like the answers to standardized tests. [Note that convergent thinkers tend to have higher grades in school.] No ambiguity is expected. Extraversion and openness are associated with divergent thinking, including curiosity, originality and imagination.
What about how economists, politicians or entrepreneurs think? Start with accounting as convergent thinking, the right answer over creativity. (Creative accounting typically is discouraged.) Philip Tetlock used the hedgehog and fox analogy and convergent thinking seems to be a good fit for the hedgehog. Like accountants, economists are more likely to be convergent thinkers (although divergent thinking results in new, creative approaches). Entrepreneurs could fit either, although divergent thinking likely results in new and creative business ideas and practices. Lawyers likely favor convergent thinking, suggesting politicians would also (e.g., focusing on standard rules of law).