The Declaration of Independence, written largely by Thomas Jefferson in Philadelphia in June 1776, was agreed to by Congress on 4th July that year. It comes in two parts: a list of particular grievances against the King of Great Britain, what it calls his "repeated injuries and usurpations," preceded by a general political philosophy, a theory of democratic government. The introduction is a rightly famous and significant piece of text.
When in the course of human events it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth the separate and equal station to which the laws of nature and of nature's god entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
The limpid clarity of this truly beautiful sentence shows Jefferson at his very best, characterised by what has been called "the distinctive Jeffersonian stamp of dignity, purpose, grace and lucidity." It is also a highly significant sentence for analysing the mathematical scientific underlay of this document.
Much effort has gone into investigating the phrase "the laws of nature and of nature's god," and tracing its antecedents. Where did Jefferson find so inspired a phrase? What does it mean? It has usually been thought that the whole document is an unfolding of the eighteenth-century doctrine of natural law, the part of law discoverable by reason, which for the Enlightenment was much the same thing as eternal law; and obviously there is that dimension to the document. But Bernard Cohen has cogently argued [in Cohen 1995, 108-134] that if that is what Jefferson had meant here he would have spoken of the law of nature, in the singular. Laws, in the plural, has to mean Newtonian laws, to judge from how Jefferson used these words throughout his life; what it has to mean at the least is "laws of nature" in much the sense in which Newton used it in Opticks (Query 31), and what it may mean is something even more specific, namely, the supreme examples of such laws, the three axioms or laws of motion from the beginning of Newton's Principia, a work which Jefferson had known and thought about for at least fifteen years. (As with everything he did, Jefferson's enthusiasm for Newton was very thorough, and extended to acquiring one of Newton's death-masks.)
In the Jefferson Memorial in Washington, DC the next sentence of the Declaration of Independence is written up on the wall: "We hold these truths to be self-evident: . . . " Why does he say that? You would only put it like that, you would only express your thoughts in those precise words, if you had studied Euclid at an impressionable age. Years later, Jefferson wrote to John Adams of his state of mind after he had stopped being President, saying that he was happy to have "given up newspapers in exchange for Tacitus and Thucydides, for Newton and Euclid."—a Roman historian, a Greek historian, and two mathematicians. His two favorite mathematical writers were Newton and Euclid, both men whose works he had read and studied from his days at William and Mary College. Awareness of the strength of an axiomatic system was firmly located in Jefferson's way of thinking, the use of unexamined, or unexaminable, or self-evident, principles as a solid foundation from which a complex superstructure could be logically deduced. Of course, Euclidean axioms and Newtonian axioms are rather different: Euclidean axioms are arguably 'self-evident' in a way that Newtonian axioms are most certainly not. Note too from the manuscript of the Declaration of Independence (see illustration above) that Jefferson only reached the phrase 'self-evident' truths after trying 'sacred and undeniable' truths. So there's a lot going on here.
In evaluating the role of mathematics in American political thought of the period we must bear in mind too that Jefferson's colleagues and co-signatories were educated in Newtonian science also. John Adams, who was to be the second president (the one in between Washington and Jefferson), had been a student at Harvard College under John Winthrop; he is the man who memorably remarked "I must study politics and war [in order that] my sons may have liberty to study mathematics and philosophy". No less than four signatories of the Declaration of Independence were educated at William and Mary College. Another signatory was the great scientist Benjamin Franklin. And of the younger generation James Madison, Jefferson's successor as fourth president of the United States, studied some mathematics and Newtonian science at Princeton. The whole group was, as politicians go, quite remarkably characterised by scientific awareness and a relatively deep imbibing of Newtonian thought-patterns. Jefferson was only the most prominent and most accomplished of a sophisticated and scientifically literate group of men, someone particularly alert to recent and current mathematical developments, and to the importance of promoting mathematics and mathematics education, which is something that Jefferson's public position enabled him to influence.