Does a president need a minimum level of scientific understanding about the world and, if so, what is the minimum?
Law, neuroscience, sociology.
John Meakin commented
Basic physics and essence of quantum theory.
This makes no sense. So you're going to ask the president what he thinks the next presidents level of science should be instead of asking his opinion on pressing scientific matters?
The future of our nation is becoming clear - that of a diminishing power. Our pinnacle was when the pursuit of discovery and unleashing those discoveries in ways that changed and advanced humanity. The greatest example was the pursuit of the moon. A president without a vision for the future will continue to lead us into stagnation and irrelevance - bad for the US and bad for the world. Leadership in green energy has already been ceded. Will we go to Mars? Not if we have a president that is only interested in personal "legacy", who is short-sighted, and who is scientifically disinterested and undereducated.
Gee, Phil, why don't you vent a little?
Yes, few American presidents have had a primarily technical background, but many were scientifically literate and the best consulted advisers who were better informed. Carter holds an engineering degree and is a very bright man, but was not an adroit politician. By contrast, the self-termed "CEO president" was quite proud of trusting his gut over scientific literacy (and numeracy) turned a historic current-account budget surplus into searing deficits, excessive debt, and an economic collapse.
We don't need a PhD president, but we do need a President who understands what science is, how it works, and what value it adds to our country in an increasingly technology-driven world.
Phil, dude, Jimmy Carter the worst? Short memory, man. Tricky ****? Ronnie Rayguns? But you raise the problem, which is that you've got to know who to ask and you've got to know how to evaluate what they tell you. See the aforesaid Ronnie R. That's why some level of science literacy is needed. E.g., someone told Ronnie that Star Wars would work and he believed them.
A requirement of running for the presidency should be taking a first-year university course in basic ecology (covering populations, communities, ecosystems) and passing with at least a C+. Our planet's health is too important to trust to politicians whose knowledge of ecology is either outdated or nonexistent.