Tomorrow is the 350th birthdy of the symbol dy/dx! At the least, in the sense that it was first written down. And actually it was dx/dy, but still worthy of celebration.

Gottfried Leibniz was living in Paris at this time, studying quadratures, which is a kind of fancy term for areas, and writing them down in a manuscript that was eventually published. His use of dx and dy was a bit of a progression – he’d been starting to use similar notation – and the use of dx/dy at first literally meant a ratio. This means that it might be more accurate to say that the beginning of this notation was more of a time period than a single date, but, still, if you want to pick a moment, this is a reasonable one.

My favorite part of this story isn’t just the notation itself, which remains in use 350 years later, but *how *it was first used. He writes, essentially, “Let’s see whether dxdy is the same as d(xy), and whether dx/dy is the same as d(x/y).” In other words, he’s using the notation as he examines whether taking the derivative of a product or quotient is as straightforward as taking the derivative of a sum or difference. [Answer: No.]

So have a slice of cake and a slice of calculus in celebration of a pretty good notation!

Sources: A History of Mathematical Notations by Florian Cajori (Section 570 in Volume II), although I did also look at a 1920 translation of Leibniz’s manuscripts, which you can read here.

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