The Grammarphobia Blog

Why is “m” a symbol for slope?

Q: This drives math teachers crazy, perhaps because it’s more of a language question: Why do we use the letter “m” for the slope of a line? If you don’t know, you’re in good company. Even people on the Math Forum aren’t sure.

A: We’re in good company, it seems, though we can clear up some of the nonsense found online about the use of “m” as a symbol for slope. Let’s begin with a bit of history.

The CRC Concise Encyclopedia of Mathematics (2nd ed.) by Eric W. Weisstein says the letter “m” was first used in print as a symbol for slope in the mid-19th century.

Weisstein traces the usage to an 1844 treatise on geometry by the British mathematician Matthew O’Brien.

That may be the earliest use of the symbol in an English work, but Sandro Caparrini, a scholar at the University of Torino in Italy, has traced the usage all the way back to a 1757 work by the Italian mathematician Vincenzo Riccati.

Why, you ask, did the letter “m” become the symbol for the slope of a line instead of, say, “s” or some other letter?

First, we ought to point out that the symbol is different in some other languages.

In Swedish, for example, it’s “k.” The mathematician Erland Gadde has speculated that the “k” stands for “koefficient,” which is part of a longer technical word for slope in Swedish.

But getting back to your question about the symbol “m,” one theory is that it comes from monter, which means to climb in French. Unfortunately, there’s no evidence to support this.

And the 17th-century French mathematician and philosopher René Descartes never used the symbol “m,” as many supporters of the monter theory have claimed.

Other unsubstantiated speculation is that the “m” refers to either mons, Latin for mountain, or montagne, French for mountain.

One common theory is that the “m” stands for the first word in “modulus of slope.”

Although the word “modulus” can refer to a number or function or parameter, we find no evidence that it was once commonly used with “slope.”

We have, however, found one explanation for—or rather comment about—this “m” business that makes sense to use.

In Mathematical Circles Revisited (2003), the math historian Howard W. Eves suggests that it doesn’t matter why “m” has come to represent slope.

“When lecturing before an analytic geometry class during the early part of the course,” he writes, “one may say: ‘We designate the slope of a line by m, because the word slope starts with the letter m; I know of no better reason.’ ”

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