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In many fields, it's common for $\Delta$ (the Greek letter delta) to represent a change or difference. Math uses it, physics uses it, engineering uses it, etc.

Why was $\Delta$ chosen for this?


I realize that "difference" starts with "d", but I'm wary to assume that just because I can think of a word starting with "d", that that's why the notation $\Delta$ was introduced.

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    $\begingroup$ Probably from the use of that letter in the calculus of finite $\Delta$ifferences and in calculus. $\endgroup$ – KCd Apr 30 '15 at 1:57
  • $\begingroup$ @KCd, that's another example of the same thing I'm wondering about; I'll edit the question to make that clear. $\endgroup$ – Joe Apr 30 '15 at 2:58
  • $\begingroup$ I think KCd just meant that it was used since "difference" starts with d, hence delta. $\endgroup$ – Jair Taylor Apr 30 '15 at 5:06
  • $\begingroup$ See this post and Cajori, page 265. $\endgroup$ – Mauro ALLEGRANZA Apr 30 '15 at 7:39
  • $\begingroup$ Some things are just simple. I believe Conifold's answer is as good as it gets. $\endgroup$ – hjhjhj57 May 4 '15 at 5:58
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There was a related question on Math.SE, which Mauro Allegranza answered with reference to Cajori's classic History of Mathematical Notations (v.II, p.205). It is a great source and is freely available online.

Surprisingly, it was not Leibniz, the notational lion of calculus, who introduced it. "A provisional, temporary notation $\Delta$ for differential coefficient or différences des fonctions was used in 1706 by Johann Bernoulli. Previously he had used the corresponding Latin letter D". The Math.SE thread also claims about Leibniz that "in developing his calculus for infinitesimal differences he was inspired by his previous work on finite differences". But I was unable to confirm that, in the famous 1684 paper he manipulates infinitesimals from the get go. The foundational Treatise on Finite Differences by George Boole, the inventor of Boolean algebra, first appeared in print in 1860.

The choice of $\Delta$ was natural since Latin $d$ was already taken for differentials, and the Greek word for "difference", which both Leibniz and Bernoulli were likely familiar with, is διαφορά. Its transliterated negation, adiaphora ("indifference"), is in modern use, mostly by philosophers and theologians, referring to morally neutral actions, neither good nor bad.

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  • $\begingroup$ +1 for "notational lion" $\endgroup$ – Danu May 1 '15 at 8:49
  • $\begingroup$ @Danu Yep. Apparently lion is not always recognized by his claws. $\endgroup$ – Conifold May 1 '15 at 22:04
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I actually made this question a couple of months ago and deleted it after a comment by Alexandre Eremenko, if I recall correctly, which, in my opinion, made it perfectly clear. I'll try to expand it a little:

It's used because of the word difference, whose latin etymology happens to start with a "d" also.

Differ comes from the latin word differre, derived from the word ferre which can often be translated by "carry". Pretty much every word which contains the word "differ" is derived from this.${}^*$ In here you can find a similar explanation of the etymology of the word.

From this it's clear that $\Delta$, $\delta$, $d$, and even $D$, are all associated with the change of a given quantity (except when talking about a river delta, in which case it has to do with how the greek uppercase symbol looks).

Even though this is most likely the reason, asking who was the first one to use it, or to set a bound would be very interesting. In that sense this isn't a complete answer.

$(*)$ I'm translating this from an etymological dictionary in spanish and assuming the roots can't be that different, given the overwhelming influence french had in it.

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  • $\begingroup$ It sounds like you're giving an answer to "What's the etymology of difference?", which isn't what's being asked. $\endgroup$ – Joe Apr 30 '15 at 5:29
  • $\begingroup$ @Joe I agree, but given the extended use of latin in science this would answer at least why Leibniz invented his notation for the derivative, for example. I've edited the answer. $\endgroup$ – hjhjhj57 Apr 30 '15 at 6:12
  • $\begingroup$ @Joe Now it explicitly answers the question. $\endgroup$ – hjhjhj57 Apr 30 '15 at 6:19

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