No, many did not, especially some of the earlier presidents, including George Washington and Abraham Lincoln; a few of the later presidents like Grover Cleveland and Harry Truman also did not complete a college degree. I enclose a link to which schools were attended by which presidents.
No.
For one, Abraham Lincoln.
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Woodrow Wilson was the only U.S. President who had a doctorate.
The electoral college
There are no constitutional requirement concerning the education of a president. You question is obviously a matter of opinion. In general a college degree is most helpful in getting a first job. It is no guarantee that the person will be a good employee-- what really matters is what the person does once he is on the job. Being President requires many skills that can not be taught.
Yes. He got a degree at Kenyon College, and he also graduated from Harvard Law School. Kenyon College was in Gambier, Ohio. Hayes received a BA degree there. He was admitted to the Ohio Bar and began to practice law.
Richard Nixon earned a BA Degree from Whittier College in 1934 and a LLB Degree from Duke University Law School in 1937. As President, he was given many honorary degrees from US Universities.
The first U.S. President to graduate from a college was George Washington, who graduated with a surveyor's license. This is not considered a college graduation in terms of today's standard since this school was indeed a trade school. The next president to graduate from an institution was John Adams, our second president. He graduated from Harvard College (now called Harvard University) in 1755.
No, there are no educational requirements to be president. Eleven presidents either did not attend college or dropped out. These presidents are George Washington, Andrew Jackson, Martin Van Buren, William Henry Harrison, Zachary Taylor, Millard Fillmore, Abraham Lincoln, Andrew Johnson, Grover Cleveland, William McKInley, and Harry Truman.
The US President is chosen by the Electoral College
Henry Dunster was the first college president in what became the US. He became president of Harvard in 1640.
The last U.S. President to hold office with no college degree was Harry S. Truman. He was our 33rd President. Just because he did not have one does not mean he never tried. He applied for the United States Millitary Academy in West Point but was rejected due to his poor eyesight. He also studied for a while at the Kansas City Law School but never achieved his degree.