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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: 5, Interesting) by HiThere on Sunday June 11 2023, @04:51PM (4 children)
It's not really clear that you SHOULD believe in continuity, infinitesimals, infinities, etc. They follow from a certain set of assumptions, but I, personally, don't believe them. I believe that the universe is discontinuous at around the Planck length. This has certain problems in it's own right, but they are different problems than the ones that continuity entails. (And I think Cantor's red and blue number lines is just goofy. You can't assign colors to numbers, only to a more complex structure. What he really did was create two instances of the same [infinite] set, but then his reasoning isn't about the set, but rather about instances of the set. Either that, or he was creating a struct {int value; color bool;} and reasoning about that rather than about integers.)
Javascript is what you use to allow unknown third parties to run software you have no idea about on your computer.
(Score: 1) by shrewdsheep on Monday June 12 2023, @05:02PM (3 children)
Mathematics makes no claims about the universe. The deep point about calculus is about limits. Limits mean that you assign a single number to an infinite sequence of numbers. As a matter of fact most numbers are defined as sets of infinite sequences (equivalence classes). Mathematics is a game that allows you to manipulate sequences of symbols - no more, no less.
(Score: 1, Interesting) by Anonymous Coward on Monday June 12 2023, @08:02PM
> Mathematics is a game that allows you to manipulate sequences of symbols - no more, no less.
Interesting comment, thanks. If true, then my difficulty with math is common with my lack of interest in most games. I just don't get why most people like games.
(Score: 3, Interesting) by HiThere on Monday June 12 2023, @09:11PM (1 child)
Yes. And that's why I said "they follow from a certain set of assumptions". I'm not denying that they *do* follow from those assumptions, just that the assumptions properly describe the universe. (They do come pretty close, though.)
Javascript is what you use to allow unknown third parties to run software you have no idea about on your computer.
(Score: 4, Insightful) by hendrikboom on Tuesday June 13 2023, @01:48AM
And that's the difference between math and physics.
And that's why physicists still use math.