www.nytimes.com/2020/02/05/science/quadratic-equations-algebra.html

“Math is not about memorizing formulas without meaning, but rather about learning how to reason logically through precise statements,” Dr. Loh said.

(Kenneth Chang and Jonathan Corum, “This Professor’s ‘Amazing’ Trick Makes Quadratic Equations Easier,” NYTimes, 2-5-20)

Dr. Loh’s statement teases me, a non-adept at mathematics, in imprecise ways.

The saucy segments are: “formulas without meaning”; “reason logically”; and “through.”

There are no formulas “without meaning”; a formula “means” what it formulates. It abstracts and generalizes in a repeatable way, and it’s useful only to those who have it beyond memory. It’s the act of lazy head-stuffing that’s meant to be belittled.

To reason “logically” is the same as to drink “liquidly.” How else to do either?

“Through” is tricky. At first I read it as prepositioning the notion of advancement by means of penetrative navigation. Picture, if you will, a thicket of precise statements; then picture yourself reasoning your way “through” them. On second reading, however, I estimate Dr. Loh to imply instrumentality — “by means of.” Picture yourself engaged in a reasoning process, and doing so by making a series of precise statements — reasoning “through” them.

Much stuff is about the likes of “through,” which is why computers are better at arithmetic than at translating.

(c) 2020 JMN