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What Honest Abe Learned from Geometry

In 1865, Rev. JP Gulliver asked Abraham Lincoln how he began to acquire his famous rhetorical skills. The president responded abnormally:

“In the process of reading the law, I have always come across the word” demonstrate. ” At first I thought I knew what it meant, but I couldn’t understand it right away …Finally I said, “Lincoln, if you don’t understand what you can never make a lawyer demonstration Means’; And I left my situation in Springfield, went back to my dad’s house, and stayed there until I could make a suggestion in six Euclid books. “

Geometry is the coriander of mathematics. Few people have a neutral feeling about it.

It’s geometry, not the constitution, not the scriptures. I went there when Lincoln needed to learn to persuade. Euclid was a Greek North African mathematician in the 4th century BC, and he gathered and systematized the geometric knowledge of the time. His “elements” are our own, not so much, in Lincoln’s time and are the standard model of mathematical proofs or “demonstrations”. Starting with an axiom that the reader can hardly doubt, Euclid carefully builds up a wealth of knowledge about angles, line segments, circles, and figures.

As any high school or former high school student knows, there is something special about geometry. Geometry is the coriander of mathematics. Few people have a neutral feeling about it. Some people hate it. Geometry says it was the moment when mathematics became meaningless to them.Others say it was only A part of mathematics that makes sense to them.

Illustration from the 1847 British version of Euclid’s “Elements”.


SSPL / Getty Images

The young Lincoln was one of those who couldn’t get enough. His legal partner William Herndon, who had to share a bed with Lincoln at a small country inn during his stay around Illinois, said the future president would wake up late at night and light a candle deep inside Euclidean. And I remembered that I had long legs hanging on the edge of the bed. Herndon once spent a full two days solving the old conundrum of the Squaring problem and discovered that Lincoln was in trouble. “Attempts to establish his proposal were unsuccessful,” Herndon recalls. “We thought in the office he was more or less sensitive to it and therefore cautious enough to avoid referencing it.”

Still, for most high school students, “Lincoln thought geometry was important” wasn’t a good reason to study it. Are teens today asked to square a circle somewhere on the boulevard of life (it doesn’t work because it proved impossible in 1882), or the outside angle of a polygon Are you asked to show that the sum of the is 360 degrees? Every time? I’m a math professor, but I’m waiting for it to happen to me.

Some say that the point of geometry is its beauty. That was the view of the poet Edna St. Vincent Millay. “Only Euclid saw the beauty exposed,” she wrote to Sonnet. Millet’s Euclid is an eerie person who has been struck by an axis of insight into “holy, terrible days.” If you’re lucky, Millet says, unlike our others, who might hear beauty footsteps rush down a distant corridor.

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Did you study geometry? What did you learn from that? Join the conversation below.

As a mathematician, I have benefited a lot from the fame of geometry. It feels good when people think that the work you are doing is mysterious, eternal, and higher than a common plane. “How was your day?” “Oh, sacred and terrible, as usual.” But the more you push that perspective, the more you tilt people to consider the study of geometry as a duty. It gets a slightly musty odor of something good for you.

Anyway, geometry isn’t just Euclid, and it hasn’t been for a long time. Even in Lincoln’s day, geometry began to go beyond its Euclidean baby clothes. Mathematicians like Bolyai, Lobachevsky, and Riemann have developed new concepts of distance, space, and curvature that their ancestors could not have imagined. By the beginning of the 20th century, it was more accurate to talk about geometry than it was.

Today, the subject is expanding faster than ever. Mathematicians study the geometry of social networks and analyze the spread of pandemics in terms of movement through those networks. Personality and political ideology can be modeled as points in higher dimensional space. The amazing new development of artificial intelligence is none other than the applied geometry that analyzes the paths of all possible algorithms in infinite dimensional space.

But Abraham Lincoln was neither an AI developer nor a pure mathematician breaking the paradigm. As he told Rev. Gulliver, he needed to know what the “evidence” was, which gave rise to his interest in Euclid. What made Lincoln stand out as a thinker was remembered by his friend and fellow lawyer Henry Clay Whitney, but it wasn’t his talent. Many people in public life are smart, some of whom have both good and bad sides. It was honesty that made Lincoln special. It’s his belief that you shouldn’t say anything unless you prove it’s right. Whitney writes: “It was morally impossible for Lincoln to argue fraudulently. He couldn’t do it more than he could steal. In essence, for him, theft, or illogical or false. It was the same thing to ruin a man of his property by reasoning. ”

In Euclid, Lincoln found a language that was very difficult to blame, cheat, or dodge questions. Geometry is a form of honesty.

The ultimate reason for young people to learn how to write proofs is that the world is full of bad logic, and we need to know the difference. Geometry teaches us to be skeptical when someone says “just logical.” If they’re talking about economic policy, the cultural figures they mourn, or the concessions they want you to make in a relationship, they’re just not logical. They want you to mistake a series of assertively expressed opinions for proof of the theorem.

Knowing geometry protects you: once you experience a sharp click of honest and good evidence, you will never fall into this trick again. Tell your “logical” opponent to draw a circle.

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What Honest Abe Learned from Geometry

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