Gottfried Wilhelm Leibniz's introduction of the long s (∫) as a symbol for the integral marked a pivotal moment in the history of mathematics. This notation stemmed from his exploration of calculus during the late 17th century, a period characterized by significant advancements in mathematical theory and practice. Before Leibniz, mathematical expressions for areas and volumes were often cumbersome, lacking a unified symbolic representation. Leibniz's choice of the long s was inspired by the Latin word 'summa', which means 'sum', highlighting the integral's relationship with summation processes over continuous intervals.

Leibniz developed this notation while collaborating with fellow mathematicians and independently pursuing his interest in calculus's fundamental principles. His innovations were documented in a series of papers and letters exchanged with contemporaries, wherein he outlined the principles of differentiation and integration, establishing a notation that would be adopted widely. The introduction of the integral symbol facilitated more advanced discussions in mathematics, allowing for clearer and more effective communication among mathematicians.

As Leibniz's notation spread throughout Europe, it galvanized further exploration and development in the field of calculus, inspiring legends such as Newton and later mathematicians to refine and expand the theory. This adoption laid the groundwork for modern calculus and mathematical analysis as we know them today. The aesthetic clarity and usability of Leibniz's notation contributed significantly to its success over alternative notations, cementing its place in mathematical literature.