SDS 486: The History of Calculus — with Jon Krohn

Ancient Innovations

The history of calculus stretches back over 4000 years, with early records found in Egyptian and Greek civilizations. Jon Krohn highlights an Egyptian papyrus from around 1800 BCE, which contains area calculations related to integral calculus 1. The Greeks, notably Eudoxus and Archimedes, later developed the method of exhaustion, a technique for finding the area of curved shapes 1. This method was independently discovered by Chinese scholar Lui Hu, showcasing the global evolution of calculus techniques.

   

Medieval Contributions

During the medieval period, significant advancements in calculus emerged from Arab and Chinese scholars. Jon Krohn mentions that in the 11th century, Arab mathematician Al Haytham began using integrals to calculate volumes, marking a pivotal development in integral calculus 1. This era also saw the continued use of the method of exhaustion, bridging ancient techniques with more modern approaches.

   

Modern Evolution

The 17th century marked a revolutionary period in calculus with the contributions of Isaac Newton and Gottfried Leibniz. Jon Krohn explains that both mathematicians independently developed the foundations of modern differential calculus, including higher-order differentiation and integration 2. Newton applied calculus to physics, describing the laws of motion and gravity, while Leibniz devised the notation still used today 3. These advancements laid the groundwork for the calculus techniques we rely on in contemporary mathematics and science.