Why is $m$ used to denote slope?

What is the reason, historically, that the letter $m$ is used to denote the slope of a line?

• In elementary school (later years) in Sweden, $m$ usually denotes the intercept, as you can see here: sv.wikipedia.org/wiki/Linjär_ekvation – Henrik Jan 31 '12 at 18:49
• ‘We designate the slope of a line by m because the word slope starts with the letter m; I know of no better reason.' – DSM Jan 31 '12 at 20:05
• I believe it comes from the phrase modulus of slope. – Karl Jan 21 '17 at 17:18
• For purposes of cross-reference, this question is also asked on math ed SE. There are a number of very good answers there. – Xander Henderson Jan 7 '18 at 2:33

According to Wolfram MathWorld, there's no consensus. Some think it may have come from French monter meaning to climb, but this is just speculation $-$ it's likely just a trend that caught on. The article I linked to contains a greater elaboration and some examples of where it's not used.

• See Also: jeff560.tripod.com/geometry.html. There is a huge section on slope, and seems to agree that the reason $m$ was chosen is not clear. – Aryabhata Jan 31 '12 at 19:09
• Thank you Clive. I saw the MathWorld page, I was hoping someone knew more than what was written there. – Jim Jan 31 '12 at 19:25
• @Jim: I think that, short of undertaking some hardcore historical analysis, we'll have to make do with the answer that no-one knows the answer. – Clive Newstead Feb 1 '12 at 12:58

Not a reason, but a lovely coincidence is that the higher dimensional analogue of a slope is a matrix.

$$\vec{y} = M(\vec{x})$$

would be the higher dimensional analogue of

$$y = mx$$

where $\vec{y} \in \mathbb{R}^m$, $\vec{x} \in \mathbb{R}^n$, and $M$ is a $n \times m$ matrix.

So I like to think of the "m" as standing for "matrix".

It is not known why the letter m was chosen for slope; the choice may have been arbitrary. John Conway has suggested m could stand for "modulus of slope." One high school algebra textbook says the reason for m is unknown, but remarks that it is interesting that the French word for "to climb" is monter. However, there is no evidence to make any such connection. Descartes, who was French, did not use m. In Mathematical Circles Revisited (1971) mathematics historian Howard W. Eves suggests "it just happened."

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