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How did summations evolve? For instance, is there an article, book, webpage, etc. that talks about how mathematicians came up with using $\sum_x{ f(x) }$? I'm very interested on how summations came to be used, and their history.

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  • $\begingroup$ In terms of infinite summation—do you know what the Ancient Greek horror infiniti was? Also, Bernoulli did quite a lot of sums (not sure which one—probably all of them). Euler's solution to the Basel problem is quite a huge moment in math history. $\endgroup$ – Akiva Weinberger Oct 5 '14 at 14:12
  • $\begingroup$ Viete's formula was an infinite product, but it was the first time anyone explicitly wrote out an infinite sum/product in math. It has been noted as the beginning of "the dawn of modern mathematics." $\endgroup$ – Akiva Weinberger Oct 5 '14 at 14:15
  • $\begingroup$ @columbus8myhw: I remember reading about the horror infiniti in a math history book. I'd like to hear more about this, though. Also, Viete's formula is very interesting. This is an excellent starting point. $\endgroup$ – Matt Groff Oct 5 '14 at 16:01
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    $\begingroup$ Could you provide some more hints which info you are expecting? Are you interested in the history of the symbol $\sum$ or the process of summing up or in the history of infinite sums? $\endgroup$ – Markus Scheuer Oct 9 '14 at 6:33
  • $\begingroup$ @MarkusScheuer Matt's comment above indicates to me that he's more interested in the history of summation rather than the history of its notation, but he also might have an interest in both to some extent. $\endgroup$ – David H Oct 9 '14 at 9:10

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