Short Story of the Long S

October 28 or 29, 1675 – Gottfried Wilhelm von Leibniz (a German polymath who discovered the field of calculus independently) makes the first use of the long s (∫) as a symbol of the integral in calculus.

The long, medial, or descending s (ſ) is an archaic form of the lower case letter s. It replaced a single s, or the first in a double s, at the beginning or in the middle of a word (e.g. "ſucceſsſul" for "successful"), and in ligature form (e.g. "Tiſſick" for "Tissick"). The modern letter form is known as the short, terminal, or round s.

The medial 's' in Old Roman cursive

The long s was derived from the old Roman cursive medial s. When the distinction between majuscule (uppercase) and minuscule (lowercase) letter forms became established, toward the end of the eighth century, it developed a more vertical form. During this period, it was occasionally used at the end of a word, a practice that quickly died but that was occasionally revived in Italian printing between about 1465 and 1480. The double s in the middle of a word was also written with a long s and a short s, as in Miſsiſsippi.

Title page of John Milton's Paradise Lost, featuring an "ſt" ligature

The long s survives in elongated form, with an italic-styled curled descender, as the integral symbol ∫ used in calculus; Leibniz based the character on the Latin summa "sum", which he wrote ſumma. This use first appeared publicly in his paper De Geometria, published in Acta Eruditorum of June 1686, but he had been using it in private manuscripts at least since 28 October 1675.

Source - Wikipedia