How an Ancient Mathematician Shaped American Politics
December 24, 2020
Ashbrook Scholars share a passion for politics and the history of government. But not all are history and political science majors. A math major, Donnie Dottei, just defended his Ashbrook Statemanship thesis showing how the methods of an ancient mathematician shaped our founding document and the history that followed.
To write his thesis, “Self-Evident Government: The Impact of Euclid on Jefferson and Lincoln’s Political Thought,” Dottei examined the methods of a Greek thinker from the third century BC. Euclid established basic principles of geometry, using an air-tight logic that mathematicians prior to him had not yet achieved. “Euclid showed how to demonstrate with certainty” that certain geometric principles are true, Dottei explains.
Mathematicians before Euclid had discovered such facts as that the three angles of a triangle add up to 180 degrees. But Euclid proved these discoveries, using a powerful method. Before offering a proposition, he defined what each word in it means—what is a point, what is a line, and so on—“in a clear and concise manner.” He also outlined five axioms or “common notions” —ideas whose truth is self-evident—to establish the ground rules for the propositions he would prove.
Because it demonstrated a logical process, Euclid’s Elements is still widely studied two millennia later. Dottei argues that Jefferson would have mastered Euclid’s proofs when he studied at the College of William and Mary. Speaking later about the formation of his political and ethical ideas, Jefferson would credit his math professor, William Small, for guiding his thinking. Small “combined ethics, philosophy, and other branches of science into mathematics so that every aspect of life could be described with the logic of math,” Dottei argues in his thesis.
Dottei goes on to show how this training caused Jefferson to structure the Declaration of Independence as one would a Euclidean proof, using its six-point structure of enunciation, exposition, specification, construction, demonstration, and conclusion.
Lincoln, who had to teach himself what Jefferson learned from tutors and professors, studied Euclid’s work while riding circuit as a lawyer. After others he traveled with had gone to bed, Lincoln studied by candlelight, learning how to prove all of Euclid’s theorems. Lincoln recognized that Jefferson had used Euclidean language in the Declaration, identifying the principles that give rise to American independence as “self-evident” truths.
Dottei argues that Lincoln used a Euclidean strategy when he worked out his ideas about whether the Constitution admitted or supported the persistence of slavery in the nation. He would admit his frustration that ideas considered “axioms of free society” in Jefferson’s time had ceased to hold this status in the public mind. Hence Lincoln’s task, Dottei said, was “to enlighten listeners to the self-evidence of what was now considered a ‘proposition’ (an unproven statement): that all men are created equal.”
The idea that Lincoln’s thinking was influenced by Euclid is not a new one, but it was a new idea to Dottei when, as he cast about for a thesis topic, Professor Peter Schramm suggested he take a look at a recent study, Abraham Lincoln and the Structure of Reason. The authors, David Hirsch and Dan Van Haften, are not professional historians; one of them, like Dottei, comes from the field of math. Ashbrook thesis projects are designed not for students to break new scholarly ground but rather to help them broaden their own understanding. What was important for Dottei about his thesis is that it helped him see that mathematical precision is a skill important to political persuasion— which, while not Dottei’s major, something he cares about as a citizen.
Dottei came to AU from Toledo, Ohio, planning to study math education. He became aware of the Ashbrook program during his sophomore year at AU. “I’ve always had an interest in politics, and I wanted to participate in the classes and listen to the speakers who came to campus.” So he asked to be admitted to the program. Because he would stay a fifth year on campus to play football, he would have time to take courses he missed as a freshman and sophomore.
Defending his thesis, Dottei was asked about a scene in the new Lincoln movie which mentions Euclid. At the time Lincoln is trying to decide whether a delegation from the Confederacy, on its way toward Washington with the intent of suing for peace, should be invited to meet with him. Lincoln goes down into the telegraph room, from which he would have to send the message about whether the delegation should be given safe passage into the city. There he talks at first with the young telegraph operators about his beloved geometer. “Euclid’s first common notion is this: things which are equal to the same thing are equal to each other. That’s a rule of mathematical reasoning. It’s true because it works. Has done and always will do. In his book, Euclid says this is ‘self-evident.’ You see, there it is, even in that 2,000-year-old book of mechanical law. It is a self-evident truth that things that are equal to the same thing are equal to each other.”
Dottei sees Lincoln musing here over the issue of equality on which the war turns. Lincoln is reminding himself, the movie suggests, that the “same thing” that both white and black people are equal to is their common humanity. Immediately after this, Lincoln dictates a message instructing that the delegation not be admitted into Union territory. The war will continue until the truth of human equality is upheld by the Union victory.
Dottei looks forward to teaching as a career that will allow him to “structure young minds with the logic of mathematics, so that they can make reasonable decisions in their future.” Since opportunities for new teachers are not abundant in Ohio at present, Dottei worked with the AU education department to arrange student teaching assignments in two southeastern states. For two months this term, he is living in Beaufort, SC with three Ashland University graduates who hold jobs in the local school district and helped arrange his assignment to Bluffton High School. A strong school with a science-technology emphasis, it serves 1000 students from a socio-economically diverse community on the coast just off Hilton Head Island. Later, Dottei will take another two-month assignment in Florida.
Dottei has only a four or five year age advantage on the students he is now meeting, and he knows he will “have to work to earn their respect.” He can be confident that when students toss him one age-old question—“What use is this math stuff, anyway?” he can draw an answer straight out of politics.