# Is there an intentional correlation between Latin letter esh and various summation syntax?

So when browsing Unicode characters, I stumbled upon one mysterious case, esh.

The upper case Ʃ looks very similar to sigma Σ which is used for summation notation ∑.

The lower case ʃ is also suspiciously similar in appearance to the integral ∫ which is also used for sum-related things.

I am fairly confident that, since it is a latin character, the connection to sigma is not a coincidence, but did the person who first devised the integral syntax know of the existence of this character, and decide to use a tall s or is it a coincidence because both just happen to be tall s's; one as a lowercase letter the other as a symbol intended to allude to the first letter of the word which brings to mind the symbol which represents it infinitely recursively forever? which it represents?

• I think these characters go back way before Unicode. – Gerry Myerson Apr 14 at 5:01

For the summation symbol $$\Sigma$$, the use of the capital Greek letter for "s" is due to the use of Latin in Early Modern Europe as universal language; see summa : (mathematics) sum, summary, total.

The first usage is due to Leonhard Euler in 1755; see Institutiones calculi differentialis, page 23 :

Quemadmodum ad differentiam denotandam vsi sumus signo Δ, ita summam indicabimus signo $$Σ$$.

Similarly for the long $$s$$ :

Leibniz favored the name calculus summatorius and the long letter $$\int$$ as the symbol. Bernoulli favored the name calculus integralis and the capital letter $$I$$ as the sign of integration. [...] Leibniz and Johann Bernoulli finally reached a happy compromise, adopting Bernoulli's name "integral calculus," and Leibniz' symbol of integration.

• Yea I already knew the first one but the second ones interesting thanks for sharing I guess since summation notation and integration both came before Esh the question would be whether the person who invented Esh was aware of the former two symbols. yeah. supposedly he didnt have much knowledge of mathematics but then again maybe he did. Just maybe. Not sure why he didnt make the upper case and lower case look more like eachother though, come to think of it. Maybe he was creating a secret easter egg after all. Maybe Im the first to find it—and ask about it on stack exchange sites—thx – cmarangu Apr 16 at 3:44
• @cmarangu - who knows ? Isaac Pitman was not a mathematician, but obviously he knowed Greek alphabet (as every "learned man" of his time). – Mauro ALLEGRANZA Apr 16 at 7:10
• mauro-allegranza interesting point – cmarangu Apr 18 at 1:25

The letter esh was introduced by Isaac Pitman in 1847, whereas the integration sign waa introduced already by Leibniz in 1675. (Cf. https://en.wikipedia.org/wiki/Esh_(letter) and https://en.wikipedia.org/wiki/Integral_symbol )

• oh‮‭​​‮‭​​‮‭​  ​‮‭ – cmarangu Apr 14 at 4:04
• so then I guess Isaac Pitman did he know about the integral symbol and decide to base te letter off of summation syntax for fun? – cmarangu Apr 14 at 4:06
• The Wikipedia article on Pitman offers no hint that he had any connection to or knowledge of mathematics. I think esh is derived from long s. – Robert Israel Apr 14 at 5:33

yea so for the sigma one thats obvious but the integral one is probably because both the integral sign and miniscule esh are based off of the long s, as it was the first letter of Summa and a lower case form of some sigma—or s-related character at some point hope this answeres your question thx

• hey man great answer if u can fix ur spellin and grammar i might appreciate ur answer more u know stack exchange sites u know how it is – cmarangu Apr 22 at 4:57