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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 mhajicek on Sunday June 11 2023, @04:49PM (4 children)
I had a very similar experience in high school geometry. Also, for me, I need to know an application in order to be motivated and really understand something. When I asked the teacher how this might be used in the professional world, she said "Trust me, you'll use it."
Then I went to tech school for machining, and I had applications for everything I learned. Vector math was a breeze, because I knew it was needed for polar coordinate programming on a live-tool lathe, for example.
The spacelike surfaces of time foliations can have a cusp at the surface of discontinuity. - P. Hajicek
(Score: 3, Interesting) by JoeMerchant on Sunday June 11 2023, @07:21PM (3 children)
I don't know that I have ever used high school geometry type of proofs. I know that I have never used path integrals around a singularity despite studying them for two semesters. I sort of forced diffeqs into service a couple of times but could easily have ignored them.
Integrals: yes, definitely, particularly discrete summations. Trigonometry: a lot. Discrete mathematics proofs by induction and similar... Not really.
🌻🌻🌻🌻✌️ [google.com]
(Score: 1, Funny) by Anonymous Coward on Sunday June 11 2023, @10:18PM
Q: Why did the mathematician name his dog Cauchy?
A: Because it would leave a residue at every pole.
(Score: 2) by aafcac on Sunday June 11 2023, @11:47PM
They are a complete and utter waste of effort at that point. It was mostly a matter of being able to refer to various proofs in the book and those mostly didn't have standardized names, so if you weren't working out of the same book, you probably wouldn't be able to understand the proofs. It's wonderful that there's been more focus on word problems, as those at least attempt to deal with a real problem people have. It's rare to be handed an equation to be solved, usually, you have to write and solve your own problem. The word problems in math tend to be rather artificial, but there's not much way around that if you're expecting to not require methods that haven't been taught.
(Score: 0) by Anonymous Coward on Monday June 12 2023, @12:39AM
Well it's all fucking irrelevant now we have rockstar CEO scientists that sell their visions to funding agencies and oversee a sweatshop of grad students on visas under threat of failing to meet the standards of a committee full of CEO mentors.