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from the how-to-learn-mathematical-thinking dept.
Technology Review is running an unusual book review -- books about learning math, pure math, not applied math, https://www.technologyreview.com/2023/04/24/1071371/book-reviews-math-education/
The author admits to being adrift,
As a graduate student in physics, I have seen the work that goes into conducting delicate experiments, but the daily grind of mathematical discovery is a ritual altogether foreign to me. And this feeling is only reinforced by popular books on math, which often take the tone of a pastor dispensing sermons to the faithful.
An initial attempt led to a MasterClass by a "living legend of contemporary math", but the master is seated in a white armchair with no blackboards, pens or paper and does not enlighten.
A side story covers a writer for the New Yorker who plans a year to go back and learn the high school algebra/geometry/calculus that escaped him, but mostly fails. For backup he has a niece who is a math professor...but after months without getting it, he complains. Her answer?
"For a moment, think of it as a monastic discipline. You have to take on faith what I tell you." Where his niece and others see patterns and order, he perceives only "incoherence, obfuscation, and chaos"; he feels like a monk who sees lesser angels than everybody around him.
I won't spoil the end, but the author does make some progress with books by mathematician and concert pianist Eugenia Cheng, starting with "Cakes, Custard and Category Theory", where each chapter starts with an analogy to baking.
Unfortunately, for the SN audience, the article does not include any car analogies...
(Score: 3, Interesting) by AlwaysNever on Sunday June 11 2023, @10:05PM (1 child)
I was good at math in school, as in I aced the exams where you applied learned theorems or techniques to solving math problems.
I, however, never understood math as in what it means and how it relates to things. I was just good at doing math exams after dedicating hours to drill example math problems.
Math remains an impenetrable mystery to me.
(Score: 2) by JoeMerchant on Sunday June 11 2023, @10:44PM
In grad school I took an analog filters design class ~12 students, 10 who basically copied the verbal lecture presentation into notes and hoped to interpret them later, and two of us who actually kept up with the prof and could really follow along with his presentation.
One day the prof stopped and asked: "So what's the gain at the center frequency in this case?" and it was some godawful complex design with multiple stages and I just kind of estimated the stages and came to "5" which I said out loud. My counterpart was more methodical, cranking out the exact answers doing the integrals on the fly with pencil on paper, prof waited for him about 30 seconds as he scratched away and finally said: 4.98... yeah, five.
I always figured there would be computers and calculators for that stuff, better to be able to judge when the computer is wrong (meaning: somebody screwed up something in the inputs.) My physics prof in 1985 had been teaching this for years: when you solve a physics problem, don't solve the problem using numbers, derive the equation and put the numbers in at the end. That way, you can play with the inputs: if I double the mass does the result react like I expect? How about cutting the distance in half? etc. It's way too easy to drop a negative sign somewhere, regardless of which method you use, but combining the numbers along the way to the answer erases your ability to check the result near the end.
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