It’s nice to see terms of art from mathematics being taken into the common

language. With the Iraq War last year we got “imbed,” long a favorite in

higher algebra and topology. (Though I’m not clear about whether “imbed” or

“embed” should be preferred. Mathematiicians seem to go for the former.)

It would be even nicer if one could feel that the writer or speaker actually

understands the mathematical meaning, though.

Recent case: “inflection point.” I caught James Pinkerton using it this

morning: “American politics is at an inflection point, where the

redistributionist force that corporate America fears most isn’t Big

Government, but rather Big Litigation.”

He means “turning point,” but feels that that’s too much of a cliche, so he

went with “inflection point,” which is in the air nowadays — I have seen or

heard it a couple of times in opinion columns or from TV talking heads.

Anyone who wants to use “inflection point” is welcome to use it, but you

might as well know what it actually means. Here is the definition from

Percival Frost’s 1872 classic AN ELEMENTARY TREATISE ON CURVE TRACING: “A

*point of inflexion* is a point at which the tangent to the curve cuts the

curve.”

The central point on a letter “S” is an inflection (or “inflexion”) point,

for instance.

In the case where the curve is the graph of a function, an inflection point

is one at which the second derivative vanishes. The function y = x^3 + x,

for example, has an inflection point at x = 0.