Bringing the lofty ideals of pure mathematics down to earth


The film-length course distributed by MasterClass starts well enough. Tao represents calmness and self-confidence. Mathematical thinking, he says, makes the “complex world a little more manageable.” He suggested that his class might be “more suitable for people without formal mathematics education”. But soon, the futility of this attempt to break through the mysteries of mathematics becomes inevitable.

For most of the session, Tao sat in a white chair; No blackboards, no pens, no paper. “Mathematics is a real language of communication,” says Tao, and here he doesn’t have the most powerful tools to achieve that. Although he tried to approach, he talked about how he was weak in an exam and struggled to fit the window curtains, I have no connection to the world of mathematics. After a 90-minute session, I was left unable to distinguish the ways in which PT was taken from what I was learning about Mindfulness: “Everything is the same” and “Embrace failure.”

I’m not the only one who has tried to break into the church of math and failed. Recently, New York writer and longtime believer in self-improvement Alec Wilkinson took on a year-long project to conquer some of the basic math classes he missed in his youth: algebra, geometry, and calculus. In the book of 2022 Divine languageAfter confronting high school math, he describes his journey as a quest for redemption. He wrote: “I was abused, and I was very upset. Armed with half a century of wisdom, I was returning to knock the smile off Math’s face.

Wilkinson has a better plan than mine: he starts with standard textbooks. He also has help. His niece, a mathematics professor, agreed to take his hand in this trip. But even the first steps in algebra go back. An adult’s doubt gets in the way; He doesn’t seem to grasp the rules—how to add and multiply variables, how fractions and exponents work—as easily as children. What’s more, he found the textbooks horrible.

Wilkinson says that revisiting algebra as an adult is “like meeting someone you haven’t seen in years and remembering why you don’t like him or her.”

“Math is not only fun, but there is a quality to prose! But it’s also the duty of a vaguely patriotic, adolescent citizen who cares,” he wrote. “Besides omitting things, they were indifferent to language, their sentences were disorderly, their thinking often sloppy, and their voices excited and irrationally impatient.” Although he tackled algebra determinedly, six hours a day, six to seven days a week, and worried about it the rest of the time, his simple aptitude eluded him. Revisiting algebra as an adult, he says, is “like meeting someone you haven’t seen in years and remembering why you don’t like him or her.”

When Wilkinson isn’t bogged down by textbooks, he marvels at the mystique surrounding math. The mathematicians he talks to talk about their profession with a religious fervor and think of themselves as mere mountaineers. When Wilkinson complains that his niece won’t give him math, he says, “For a moment, think of it as monasticism. Take what I tell you by faith. When his niece and others see patterns and order, he perceives only “inconsistency, obfuscation and chaos.” A monk feels that he sees lesser angels than all those around him. Now he has become abusive towards his education and his younger self: Why didn’t he learn all this better when he had the feelings of a child?

A year later, Wilkinson was able to solve some calculus problems, but the journey was difficult, the terrain difficult and often undesirable. Mathematics is often referred to as the logic of language as grammar. But when you learn a language like Spanish, you can take certain words for granted and immediately open up to a new culture. Promotional measures toward formal accounting, on the other hand, require a commitment to rigor and abstraction while denying any benefits. Among mathematicians, as Wilkinson discovered, there is general derision, even of those seeking useful applications. In the year GH Hardy famously said in 1940, “Isn’t the position of the ordinary practical mathematician a little sad in some ways?” Or John Baez’s recent comment: “If you don’t like abstraction, why bother with mathematics?” You should probably be in finance, where all the numbers have dollar signs in front of them. In return for unwavering thinking, the mathematical covenant is as lofty a plan as a cult. Wilkinson hangs in the Arctic Ocean, exhausted and exhausted as a shipwrecked victim.

My frustration and Wilkinson’s highlight the inadequacy of the media often employed in mathematics education. Textbooks are not always written with accessibility in mind. They pass between walking and hand-waving farewells, and the exercises they offer can seem like a series of pointless exercises. At the same time, overview attempts can feel frustratingly empty. What Wilkinson and I wanted was a sympathetic voice—the testimony of someone who had risen to the heights of a draft bill but had the patience to guide a newcomer.


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