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Newton Or Leibniz: Who is The Inventor of Calculus?

Calculus is the mathematical study of continuous change, much like how geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

Its two primary subfields are integral calculus and differential calculus; the former works with the accumulation of items and areas under or between curves, while the latter deals with curve slopes and instantaneous rates of change.

Both of these disciplines use the fundamental concepts of infinite sequences and infinite series convergent to a well-defined limit, which are connected by the calculus fundamental theorem.

Prior to Newton and Leibniz, the name “calculus” applied to any body of mathematics, but as a result of their discoveries, the term “calculus” later came to denote a particular branch of mathematics. Building on this work, in the late 17th century, Newton and Leibniz independently created the associated theory of infinitesimal calculus.

Leibniz also put a lot of effort into creating clear and practical notation and notions. Some of the most significant applications of integral calculus to physics were given by Newton.

Newton 

Sir Isaac Newton by Sir Godfrey Kneller, Bt.jpg , Public domain, via Wikimedia Commons

Sir Isaac Newton was an English mathematician, physicist, astronomer, alchemist, theologian, and author who was known in his day as a natural philosopher. He lived from 25 December 1642 to 20 March 1726/27. He had a significant role in the Scientific Revolution and the ensuing Enlightenment.

Many earlier findings were gathered in his groundbreaking book Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), which was first published in 1687 and established classical mechanics. 

It has been noted that Newton’s contributions “distinctly advanced every branch of mathematics then studied.” A manuscript from October 1666 including his work on the topic—often referred to as fluxions or calculus—is now included in a collection of Newton’s mathematical writings. Isaac Barrow referred to John Collins’s June 1669 submission of De analysis per aequationes numero terminorum infinitas as the product “of an extraordinary genius and proficiency in these things” in a letter to Collins he wrote in August.

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Leibniz

Gottfried Wilhelm (von) Leibniz. jpg , Public domain, via Wikimedia Commons

German polymath Gottfried Wilhelm (von) Leibniz, who was active as a mathematician, philosopher, scientist, and diplomat, was born on 1 July 1646 and died on 14 November 1716. He is a well-known character in both the philosophical and mathematical histories.

He wrote books on philology, politics, theology, ethics, law, and history. Leibniz made important contributions to physics and technology as well as foresaw ideas in fields like probability theory, biology, medicine, geology, psychology, linguistics, and computer science that would emerge much later.

Who is The Inventor of Calculus?

C05c The arc length of the graph of f.png , CC0, via Wikimedia Commons

Prior to Newton and Leibniz, the name “calculus” applied to any body of mathematics, but as a result of their discoveries, the term “calculus” later came to denote a particular branch of mathematics. Building on this work, in the late 17th century, Newton and Leibniz independently created the associated theory of infinitesimal calculus. Leibniz also put a lot of effort into creating clear and practical notation and notions. Some of the most significant applications of integral calculus to physics were given by Newton.

The main knowledge base of European mathematics had shifted by the middle of the 17th century. As opposed to the previous century, which continued to use Hellenistic mathematics as the foundation for inquiry, Newton, Leibniz, and his colleagues began to turn more and more to the ideas of more contemporary thinkers.

As a result of his studies in geometry and physics, Newton became interested in calculus. Calculus, in his opinion, is a scientific theory that describes how motion and magnitudes are produced.

Leibniz, in contrast, concentrated on the tangent problem and came to see calculus as a metaphysical theory of change. The formalization of the inverse characteristics between the integral and the differential of a function was an important aspect of their breakthrough. They were the first to conceptualize calculus as a system in which new rhetorical and descriptive concepts were formed, even if their forebears had anticipated this understanding.

In contrast, many of Newton’s mathematical discoveries were communicated via letters, shorter works, or as embedded elements in his other final compilations, such the Principia and Opticks. Newton never finished a definitive book formalizing his fluxional calculus. As Isaac Barrow’s designated heir, Newton would start his mathematical education in Cambridge.

After countless experiments, Newton finally understood the fundamental characteristic of inversion. By taking into account a brief increase at a point, he had developed an expression for the area beneath a curve. In essence, his calculations contained the calculus fundamental theorem.

Although his new formulation had great potential, Newton was already aware of its logical flaws. He acknowledges that his accomplishments were “shortly explained rather than accurately demonstrated” and that “errors are not to be disregarded in mathematics, no matter how small.” Newton developed his fluxional calculus in an attempt to evade the informal use of infinitesimals in his calculations.

While Newton started working on his fluxional calculus in 1665–1666, his discoveries were not widely disseminated until much later. Leibniz also worked to develop his calculus in the interim years. Leibniz began his intensive math studies with a developed intellect, in contrast to Newton, who started studying math at a young age. His intellectual interests and accomplishments included metaphysics, law, economics, politics, logic, and mathematics. He was a polymath.

Modern mathematics still uses Leibniz’s notation, although his logical foundation was different from ours. Leibniz accepted infinitesimals and wrote extensively in order “not to make of the infinitely small a mystery, as had Pascal.” Leibniz’ zeroes, according to Gilles Deleuze, “are nothings, but they are not absolute nothings.

Newton co-developed the concept of infinitesimal calculus with German mathematician Gottfried Wilhelm Leibniz, and he made important contributions to optics as well. However, Newton is often credited as the primary inventor of calculus, while Leibniz is credited with independently developing a similar but distinct notation system.

Calculus was developed by both Isaac Newton and Gottfried Wilhelm Leibniz, but Newton is generally regarded as the principal inventor. Newton had a priority advantage because he published his calculus techniques in 1687. He established the basis for differential calculus by creating the idea of “fluxions” and concentrating on limits and infinitesimals.

Calculus was developed and accepted as a result of the mathematical community being greatly influenced by Newton’s theories. His standing as an accomplished scientist and mathematician further cemented his connection to the development of calculus. Newton’s efforts and publication precedence helped him to be recognized as the primary inventor, even though Leibniz independently created a unique notation system.

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