Who Invented Calculus? More to Know

Who invented calculus? The argument as to which is the correct answer is one that calculus experts have had for years. Was it Sir Isaac Newton or was it Gottfried Wilhelm Leibniz? In this article, you will be learning the origin of calculus and the people behind its invention. So, keep reading.

Who Invented Calculus Newton or Leibniz?

Experts usually credit ancient Greece as the city where calculus came to be. However, Sir Isaac Newton and Gottfried Wilhelm Leibniz are two men who contributed significantly to Calculus. Thus, it is a thing of argument when it comes to giving credit to who invented calculus first between the two. To conclude on who invented calculus first, it is important to give the background information of both men’s work individually.

Isaac Newton’s Contribution

For years, experts credited Isaac Newton as the first man who developed calculus. In the mid-1660, Isaac Newton developed the concept of calculus where he wrote a paper stating that he developed the basics of calculus. Between 1664 and 1676, he wrote about four papers on calculus but refused to publish them. What he did was circulate these papers among his friends because he was afraid that people would criticize his work. If he had not done this, it would have been hard to prove that he made any contribution to Calculus let alone invent the idea. However, Sir Isaac Newton’s papers were eventually published after his death.

Gottfried Wilhelm Leibniz’s Contribution

Other experts credit Gottfried Wilhelm Leibniz as the first guy who invented calculus. Just like Sir Isaac Newton, he invented calculus in the mid-1670s. He also wrote papers stating that he originated the idea of calculus. However, unlike Sir Isaac Newton, he was not afraid to publish his papers. In 1684, Gottfried Wilhelm Leibniz published the paper, “A New Method for Maxima and Minima, as Well Tangents, Which Is not Obstructed by Fractional or Irrational Quantities.” This is a pretty long name for a paper, yes? Similarly, this six-page paper was unclear and it was hard for people to understand the idea.

Who Invented Differential Calculus? Who Invented Multivariable Calculus? Who Invented Integral Calculus?

The credit for this goes to both Sir Isaac Newton and Gottfried Wilhelm Leibniz. However, differentiation existed even before these men were born. One can trace the history of differential calculus to ancient Greek where Archimedes used indivisibles to study areas and volumes. In 500 AD, Aryabhata, the Indian mathematician used infinitesimals in his study of the moon’s orbit. Bhaskara II, another Indian mathematician used infinitesimals to put together the rates of change. You will find this in his work, “Rolle’s theorem”.

Sharaf al-Din al-Tusi, the Islamic mathematician published the work “Treatise on Equations” where he stated conditions for cubic equations to have solutions. For example, he showed that the cubic ax2 – x3’s maximum happened when x was equal to 2a/3 (x = 2a/3). He then concluded that the equation ax2 minus x3 is equal to C (ax2 — x3 = c) has exactly one positive solution when c equals 4a3/27 (c = 4a3/27). Also, there were two positive solutions when 0 is greater than C and 4a3/27 (0 < c < 4a3/27).

Despite these great contributions to differentiation, it was Sir Isaac Newton and Gottfried Wilhelm Leibniz that gave an independent approached to differential calculus. What made them earn this was the theorem “the fundamental theorem of calculus”. James Gregory who lived between 1638–1675 first published the first state of this theorem. Isaac Barrow, Isaac Newton’s teacher, then gave a more defined generalization to this theorem while Isaac Newton concluded the development of this theorem. Gottfried Leibniz then systematized this theorem into calculus and then gave the notation which mathematicians use today.

What is Vector Calculus?

Vector calculus is an area of calculus that focuses on differentiation and experts credit J. Williard Gibbs and Oliver Heaviside for their invention. This has some geometric and physical quantities that are called scalars in calculus. In its graphics, points represent scalars on scales with numbers like a clock, for example. Vectors are also a type of quantities in vector calculus that require direction to be specified. In its graphics, a direct line segment and an arrow in the direction of the vector quantity represents the vector quantity.

Who Invented Precalculus?

The credit for this goes to Leonhard Euler. This man wrote the first book on precalculus in 1748 which contained methods and concepts used to study integral and differential calculus.

Newton vs Leibniz: the Story of the Great Controversy

As they both lived and formulated the idea for calculus at the same time, it was hard for the people of their time to tell who invented calculus first. Still, Gottfried Wilhelm Leibniz acknowledged Sir Isaac Newton’s work and released a statement where he said that Sir Isaac Newton had done a better job. Unfortunately, Sir Isaac Newton did not return the favor.

When he found out that Gottfried Wilhelm Leibniz had gotten the calculus idea first, he wrote him a letter. This letter showed where Sir Isaac Newton tried to establish the fact that it was he, and not Leibniz, who created calculus first. Such a letter led to the accusation of Leibniz that he stole Sir Isaac Newton’s ideas. However, because Gottfried Wilhelm Leibniz had published his ideas first, many people sided with him. They further accused Sir Isaac Newton as the one who stole Gottfried Wilhelm Leibniz’s ideas.

This led to a huge controversy in Britain for years as the friends of both men encouraged them to fight it out. Johann Bernoulli, who had used Gottfried Wilhelm Leibniz’s published work to increase the function of calculus, supported him. So did Sir Isaac Newton’s friends. During the long feud, Gottfried Wilhelm Leibniz called Sir Isaac Newton’s friends “enfants perdus” which is translated as “the lost children”. Sir Isaac Newton then accused Gottfried Wilhelm Leibniz of plagiarism. Unfortunately, despite the fact that Gottfried Wilhelm Leibniz published his paper first, Isaac Newton’s accusation was successful. Thus, he took the credit as the man who first invented calculus.

The Effects and the After

The establishment of the accusation of plagiarism affected Gottfried Wilhelm Leibniz’s life heavily. In those days, when someone accused you of something and most people believed your accusers, you were socially ostracized. And this is what happened to Gottfried Wilhelm Leibniz. When Sir Isaac Newton died, the state gave him a grand funeral, one that was complete with honor and glory. This was especially because of his work in calculus. Gottfried Wilhelm Leibniz, on the other hand, died, a poor man with no honor.

Still, people like Johann Bernoulli and Leonard Euler used Gottfried Wilhelm Leibniz’s calculus when they developed the field of applied analysis.

However, as the years went by, people who took up calculus to study saw the truth. They discovered that Gottfried Wilhelm Leibniz did not plagiarize Sir Isaac Newton’s work as he had not even read his manuscripts. Thus, calculus experts started to lift the accusation of plagiarism on Gottfried Wilhelm Leibniz. This is why teachers and students of calculus today give credit for an invention to both Gottfried Wilhelm Leibniz and Sir Isaac Newton.


Who invented calculus? Now you know that both Sir Isaac Newton and Gottfried Wilhelm Leibniz, among others, made great contributions to calculus. 

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