As ambiguous as the exact membership in the set may be, taken as a whole, the group clearly evinces certain properties, among which are education and intelligence. It is worth noting the distinction between the two: intelligence is the native ability to learn; education is the state of having learned.
If one would compare the Founders to leaders of the United States in the last quarter of the twentieth century and the first decade of the twenty-first century, the Founders represent themselves well. While there are certainly some intelligent, and even very intelligent, people in the latter group, the educational level among the them lags behind that of the Founding Fathers. Among the former group, there are many intelligent and very intelligent people, and a handful of sheer geniuses; the education among the Founders is astounding.
As concrete examples, one might note the Benjamin Franklin not only pioneered the printing and publishing industry in North America, and carried out groundbreaking research into the nature of electricity, but also invented a new and unique musical instrument: the glass harmonica. Franklin spent time in Europe, and his invention, which he preferred to call 'the glass armonica' (dropping the 'h' in a nod to the Italian language), soon caught the attention of composers like Wolfgang Mozart, Ludwig van Beethoven, and George Handel. They composed pieces for it. Thus some of the leading musical artists of Europe were directly influenced by an American Founding Father. In addition, he developed an odometer for wheeled vehicles, the lightening rod, a refined version of the wood-burning stove known as the 'Franklin Stove' or the 'pot-bellied stove', and the bifocal lens. The lattermost invention combined advanced mathematics, for calculating curves precisely, and more advanced techniques in lens grinding.
Jefferson, in addition to his political leadership and his authorship of first rough working draft of the Declaration of Independence, was an architect - designing his home, Monticello, which remains a building closely-studied architects to this day.
The educational excellence of the Founders is clearly seen in the field of languages. One might visualize them, gathered as the First Continental Congress, the Second Continental Congress, or the Constitutional Convention: a room full of people. Realize that in this room, it was taken as a minimum that each of them present could, at a minimum, read Latin, Greek, and French. Those who were considered especially well-versed could read perhaps German or Italian as well. In addition to reading those languages, most of them could write, and - in the case of modern languages - speak them as well.
By contrast, imagine being in the halls of Congress in 1975 or 1985 or 1995 or 2005 or 2015, and asking the members of the House or of the Senate how many of them can read or write Greek! Needless to say, the number of affirmative responses would be low.
One might question the value of reading Greek and Latin for a Senator or a Representative in the early twenty-first century. Yet this value remains largely uncontested, and indeed manifold: such particular skills sharpen one's general language skills - one's ability to express one's self, and one's ability to analytically read complex documents. Such an education invariably includes encounters with the documents from the era of classical Greece and classical Rome, documents which pose the enduring questions about justice and about forms of government.
As a boy, barely a teenager, Thomas Jefferson had read the works of Thucydides in the original Greek, a task which is daunting even for a graduate student at a good university. This type of reading, and the concepts gleaned from such texts, are detectable in the documents which Jefferson and others crafted: The Declaration of Independence, The Constitution, and The Bill of Rights.
Knowledge of modern languages likewise sharpens linguistic skills and includes encounters with texts, texts which touch upon crucial questions of governance. In addition, modern languages sharpen one's sensibilities in terms of international relations. As many discussions in Congress will touch upon diplomacy in one form or another, such global sensibilities bring insight to the task of analyzing bills and motions brought to the floor for debate.
Consider one of the Founding Fathers who was considered to possess only minimal education: Patrick Henry of Virginia. The following description of his learning was written by Colonel Samuel Meredith, Patrick Henry's brother-in-law. This primary text has been quoted both by historian Richard Beeman and by historian George Morgan:
He was sent to a common English school until about the age of ten years, where he learned to read and write, and acquired some little knowledge of arithmetic. He never went to any other school, public or private, but remained with his father, who was his only tutor. With him he acquired a knowledge of the Latin language and a smattering of Greek. He became well-acquainted with Mathematics, of which he was very fond. At the age of 15 he was well versed in both ancient and modern history.
The text deals with his education up to the ages of 15. After trying his hand at the retail business and at farming, he later resumed his education by studying law and being admitted to the bar. After that point in time, he became involved in the American Independence movement.
We see, then, that a man who knew both Latin and Greek, who was "well-versed in both ancient and modern history," and who was recognized as a man with superior knowledge of both law and of legal procedure, was considered to be one of the less-well-educated men among the Founding Fathers. Such a man, who in any other setting, would be obviously one of the more intelligent and better-educated individuals, was among the Founders considered a bit common.
If we understand the high levels of intelligence and education present among the Founders, it is no surprise that they had brilliant insights about the centrality of freedom and liberty in political culture, and brilliant creativity in crafting the documents which, during the last quarter of the eighteenth centuries, created and structured our nation.