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"A Young Scholar" by
Jean-Honore Fragonard
Jean-Honore Fragonard
"The Vocation" by
William Bouguereau
William Bouguereau
Study of Euclid’s Elements had a tremendous influence on Galileo Galilei, Sir Isaac Newton, and Abraham Lincoln.
Lincoln’s study of geometry is mentioned at the National Park Service’s website, on the page devoted to the Lincoln Memorial. In discussing his early years,
they say:
But there is a great deal more detail on how mathematics, specifically Euclid’s Elements, sharpened Lincoln’s reasoning skills in “An ‘Old-Fashioned’
Nationalism: Lincoln, Jefferson, and the Classical Tradition” by Drew R. McCoy. Here is a good excerpt of this very interesting article:
And as Aristotle said in his Rhetoric: “it is absurd to hold that a man ought to be ashamed of being unable to defend himself with his limbs, but not of being
unable to defend himself with speech and reason, when the use of rational speech is more distinctive of a human being than the use of his limbs.”
Lincoln’s study of geometry is mentioned at the National Park Service’s website, on the page devoted to the Lincoln Memorial. In discussing his early years,
they say:
- Lincoln's mother provided his early education. She was a rarity on the frontier in that she could read and shared the skill with him at an early age. The
vast majority of his education was acquired by reading. He seldom was without a book and spent long hours studying Shakespeare, Byron, and even
Euclid's geometry. Despite having little formal education he triumphed with determination. Lincoln ultimately developed a talent for expression that could
have led to a very different career. His "Gettysburg Address" is considered one of the most succinct and eloquently written speeches delivered by an
American politician.
But there is a great deal more detail on how mathematics, specifically Euclid’s Elements, sharpened Lincoln’s reasoning skills in “An ‘Old-Fashioned’
Nationalism: Lincoln, Jefferson, and the Classical Tradition” by Drew R. McCoy. Here is a good excerpt of this very interesting article:
- As one historian of mathematics has observed, "no work, except the Bible, has been more widely used, edited, and studied, and probably no work has
exercised a greater influence on scientific thinking."… Specifically, Euclid's geometry had become, by Jefferson's time, a testament to the power of
human reason to deduce truth. On the basis of some formal definitions of terms and five postulates and five axioms whose truth was self-evident—such
as, "things that are equal to the same thing are also equal to one another," or "the whole is greater than the part"—Euclidean geometry "deduced an
elaborate system of propositions that seemed both to accurately describe physical reality and to compose a flawlessly logical system.” In this sense
Euclid did more than teach the principles and methods of correct reasoning in geometry; he could inspire readers of his Elements to apply reason to
philosophy, economics, political theory, art, and religion, and in so doing, to arrive at truths that were as valid as mathematical truth.
…
We do know that Lincoln was exposed to elementary mathematics during brief stints in the pioneer schools of Indiana, and that in his mid-twenties he
read up on geometry and trigonometry before trying his hand at surveying. The surveying texts he studied during the 1830's—Abel Flint's A System of
Geometry and Trigonometry, With a Treatise on Surveying, and Robert Gibson's The Theory and Practice of Surveying—drew heavily on Euclid, and
there is circumstantial evidence that Lincoln's study of Euclidean geometry was more or less continuous from this point on. As David Donald has recently
observed of the young Lincoln, he clearly liked "the logic and precision of mathematics." Indeed, by the late 1830s he was already well-known for the
logical precision of his political speeches, in which he characteristically stated propositions and proceeded to prove them, both by adducing documentary
or empirical evidence and by deducing them from axioms or self-evident truths. Lincoln then turned even more seriously to Euclid at some point during
the 1840s.
…
As his old rival Stephen Douglas rose to national prominence in Washington city, the scene of his own disappointment, Lincoln, now in his early forties,
may well have brooded on his personal failures and worked hard, as Burlingame would have it, on "healing the wounds of ego deflation." One thing
seemed certain: he needed more than ever to succeed in the law, which was now the sole source of his family's support. Sensing the deficiencies of his
education…and recognizing anew the importance of mental discipline and logical precision in the practice of law, Lincoln characteristically embarked on
a fresh course of self-education. While his fellow lawyers on the eighth circuit filled the room they shared for the night at country inns with what William
Herndon called "our interminable snoring," Lincoln pondered Euclid by candlelight into the wee hours of the morning.
…
As mental exercise, Lincoln's long hours with Euclid doubtless made him a better "close reasoner," to use Herndon's term, and hence a more effective
lawyer, which was surely his conscious purpose. But they also helped prepare him, in ways he could not have known, for the unexpected resumption of
his political career after 1854. Lincoln had always been noted for his ability to reduce his thought on any given subject to the simplest and plainest terms
possible; and during these critical years for the republic, his mastery of that skill allowed him to argue the case against both proslavery and popular
sovereignty with something close to "Euclidean coherence." Throughout his protracted debate with Douglas between 1858 and 1860, Lincoln "appealed
repeatedly to the nature of proof in Euclid" as the appropriate standard for evaluating the arguments of the two combatants. And in a larger sense, the
distinctive qualities of Lincoln's mature political thought, including its content as well as its form and precision, appears to have owed a great deal to his
immersion in Euclid.
Lincoln's ability to whittle down a complex issue to one key principle, or central axiom, directly informed his political message during the second half of
the 1850s, when we might say he took a vexingly complex issue, slavery, and whittled it down to a simple issue: the humanity of the slaves. Amid the
acrimonious wrangling over the complex details of the politics of slavery in the territories, Lincoln's simple message became unmistakable: If the Negro is
a man, then slavery is wrong, and must be disapproved of, and discouraged by all possible legal and constitutional means. In 1859, drawing an explicit
connection between Euclid and the Declaration of Independence, Lincoln identified "the principles of Jefferson"—including, of course, the eighteenth-
century Euclidean truth that "all men are created equal"—as "the definitions and axioms of free society."
And as Aristotle said in his Rhetoric: “it is absurd to hold that a man ought to be ashamed of being unable to defend himself with his limbs, but not of being
unable to defend himself with speech and reason, when the use of rational speech is more distinctive of a human being than the use of his limbs.”
| What are the benefits of a rational study of mathematics? |
© 2007 Michael Gold
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| Contact Michael Gold by phone at 281-770-2276 or by email at GoldMJ@aol.com. |