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Everyone is capable of, and can benefit from, mathematical thinking

(www.quantamagazine.org)
669 points sonabinu | 1 comments | 21 Nov 24 01:45 UTC | HN request time: 0.213s | source
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penguin_booze ◴[21 Nov 24 12:56 UTC] No.42203880[source]▶
To my mind, the premature formalization of the math is the principal contributor to gas lighting and alienation of people from maths. The reduction of concepts to symbols and manipulation thereof, is an afterthought. It's misguided for them to be introduced to people right at the outset.

People need to speak in plain English [0]. To some mathematicians' assertion that English is not precise enough, I say, take a hike. One need to walk before they can run.

Motivating examples need to precede mathematical methods; formulae and proofs ought to be reserved for the appendix, not page 1.

[0] I mean natural language

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1. Tainnor ◴[22 Nov 24 18:54 UTC] No.42216421[source]▶
This sentiment comes up all the time here. Mathematics uses formalism because it's easier.

It's easier to read "a(b+c+d) = ab+ac+ad" than

> If there be two straight lines, and one of them be cut into any number of segments whatever, the rectangle contained by the two straight lines is equal to the rectangles contained by the uncut straight line and each of the segments.

It's well known that good notation is exactly the one that elevates good intuition. For example, the Legendre symbol has the property that (a/p)*(b/p)=(a*b/p), an important visual cue that you wouldn't get from writing down (in way too many words) what the Legendre symbol actually means.

Also, most actually good mathematical textbooks aren't just dumps of formulae and proofs and they do contain motivation, examples, pictures, etc. You're attacking a strawman. But you can't just relegate the formalism and proofs to the appendices, that's crazy.