There is much confusion in the world about education and intelligence. Education is knowledge acquired in formal learning environments, such as school. Intelligence is that actual ability to learn, to acquire, assimilate, and use new knowledge.
We are taught from the time we first enter school to judge someone's intelligence by their education and their performance in such formal environments, also known as "book smarts". This is taught by words, actions, and attitudes, from both teachers and, later on, other students. This concept that education equals intelligence is pushed on us so hard that few people ever get totally past it, even as they grow older.
You Can Be Highly Intelligent Without Being Highly Educated
Two of the most intelligent people I've ever met did very poorly in school. One graduated, but just barely, and the other never finished high school. When it comes to learning anything that they don't associate with school, they learn fast… much, much faster than normal.
People of well above average intelligence sometimes do poorly in school due to boredom. They sit there in classes designed for the lowest common denominator which don't provide enough stimulation for them, so they become bored and stop paying attention. They are distracted by the smallest things. People of less intelligence, on the other hand may have more of their mind occupied by the class, and thus be less prone to boredom. They are also more likely to be aware that they need to work hard and study in order to do well, where smart people may feel that it's easy and not study even when they DO need it.
You Can Be Highly Educated Without Being Highly Intelligent
On the other hand, I have met people with advanced degrees, including doctorates, who are of no more than average intelligence. This is not a bad thing… they have shown that they are willing to put in the time and effort to master something that does not come easy to them. It does also show, however, that higher education is not proof of higher intelligence.
There are also certainly professions which require extensive training (education), but not extremely high intelligence. Your average family practictioner, for example, can operate just fine without needing to have a genius IQ. He is following established procedures, prescribing standard medications for conditions diagnosed by standardized methods. He needs the education to teach him those standards, but he is not creating the standards, just following them… so having average intelligence is not a big deal at all.
Conclusion
Education is not equal to intelligence, though it is often used as an external measure of it. Certain types of education can give you a pretty good idea that someone is at least of certain minimum intelligence (you can't actually be dumb and have an advanced degree in mathematics), but they don't provide a measure of how far beyond that minimum they are, and a lack of education says absolutely nothing about their intelligence.
And, by the way, neither education nor intelligence prevent you from doing stupid things. As far as I know, nothing in the world stops that.
