So we've been using summations at least since the dawn of calculus. I'm wondering how the process of summing a function came to be known? Are there events that led to the invention of the summation operation? Can we attribute summations to a particular person, or persons?


How did mathematics evolve to include summation?


Less importantly, but still interesting, is how the summation symbol, $\sum$, came to be used.



How did the summation operation come into use?
according to this [source](http://jeff560.tripod.com/operation.html), the summation symbol $\Sigma$ was first used by Leonhard Euler in 1755:


*Quemadmodum ad differentiam denotandam usi sumus signo $\Delta$, ita summam indicabimus signo $\Sigma$.*


*In the same way that we use the symbol $\Delta$ to denote a difference, we will indicate a sum by the symbol $\Sigma$.*


[[Institutiones calculi differentialis](http://eulerarchive.maa.org/pages/E212.html) chapter I, paragraph 26.]


![](https://ilorentz.org/beenakker/MO/Euler_sum.png)


*in a similar way one has [...], so that, if for $\sum x^2$, $\sum x$ and $\sum 1$ we substitute the values obtained previously, one finds that [...].*


