Jimmy Carter has been called the most  well educated president of the United States (it was in a documentary on climate change, not Al Gore's I don't think) of the current candidates, who most closely matches Mr Carter. Think about not just politics or law or business, but the sciences as well. My bet for most well educated candidate is  none of the above, they're all specialists who don't know much outside of their area of expertiese, they have advisors for that