What Links Abraham Lincoln to Euclid’s Elements?

Lincolnx400On February 27, 1860 Abraham Lincoln gave a speech at the Cooper Union Institute in New York City. The vast majority of the audience of approximately 1,300 were members of the Republican party. Lincoln, like many in the audience, was well aware that this speech was his one chance to show the party’s movers and shakers that the prairie lawyer from Illinois was cut from presidential timber. Lincoln’s physical appearance, poorly tailored suit, awkward gait, and frontier twang caused many in the audience to form the initial opinion that he would not be a suitable Republican candidate for President.

That evening, Lincoln’s speech was sensational, evaporating any doubts about his suitability as a Republican candidate for President. The audience was awed and dazzled by his command of historical facts and the airtight logic of his speech. Three months later Lincoln received the Republican nomination for President, and the Cooper Union speech effectively became the Republican Party platform for the 1860 presidential election.

In his book, Lincoln at Cooper Union, Harold Holzer brilliantly captures that magical evening and gives the reader a wonderful description of the events leading up to Cooper Union and the events afterward that made Lincoln President.

After reading and studying Holzer’s book several times, I realized that Lincoln’s Cooper Union speech was, astonishingly, modeled after a classic Euclidean geometric proof. This made sense. Both Lincoln and Thomas Jefferson admired and read Euclid’s Elements as a way to improve the mind and promote an individual’s ability to think and reason logically. For me, a former high school geometry teacher and Civil War buff, this was a thrilling realization, a moment of epiphany.


Lincoln organized his Cooper Union speech into three sections. The objective of the first section was to demonstrate or prove that Senator Steven Douglas’ principle of popular sovereignty was a false doctrine. The principle of popular sovereignty claimed that only the states had the power to decide whether or not to allow slavery into the territory of a new state, and the Federal government had no control over the spread of slavery. Lincoln believed that the Federal government had the right and duty to control the spread of slavery.

He began his Euclidian proof by stating a postulate that all parties in the popular sovereignty debate could agree with:  “Our fathers, when they framed the Government under which we live, understood this question just as well, and even better, than we do now.” “Question” refers, of course, to the spread of slavery, and the postulate was a direct quote from a speech given by Senator Douglas.

The manner in which Lincoln constructs and develops the statements in his proof is brilliant. It’s like watching a creative master teacher presenting a proof of a theorem to a class of geometry students. Each statement in his proof is a logical consequence of previous statements, all supported by facts in the historical record. During the course of his speech, Lincoln referred to the postulate no less than 15 times.

In section three, Lincoln’s goal is to rally the Republican Party around the principles that slavery is wrong and should not be allowed to spread beyond where it already exists. Republicans have a duty to publicly declare these principles and should not compromise them in order to appease Southern slaveholders. To prove his point, Lincoln used proof by contradiction, a sophisticated technique commonly used by mathematicians to prove a theorem.  The proof begins with the assumption that the negation of the statement is true. At Cooper Union, the negation of the statement Lincoln was attempting to prove was, “Slavery is right.” From the assumed statement, one draws logically correct conclusions that eventually lead to a statement that’s false. Therefore the negation of the statement must be false and the original statement must be true.

To fully appreciate and understand the Cooper Union speech, read Holzer’s book. Even if you normally don’t enjoy history books, I think you’ll find Lincoln at Cooper Union a great read. If Lincoln had failed at Cooper Union, he would not have become President, and the course of world history would have taken a far different path.

Have you read anything, or experienced anything in your life that prompted you to think about math concepts? What math epiphanies have your experienced?

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