Leibniz vs. Newton – A Calculus Controversy

The Debate:  Who invented the concept of calculus? Newton (left) or Leibniz (right)?

Before we discuss the heated debate that spanned hundreds of years, it is important to introduce Gottfried Wilhelm von Leibniz’s opponent, Isaac Newton.  Sir Isaac Newton was born on January 4^th, 1643, in Woolsthorpe, Lincolnshire, England.  He is known for his contributions to physics and mathematics who played a significant role in the 17^th century Scientific Revolution.  Newtons discoveries include the laws of motion, the theory of gravity, and, of course, the discovery and development of calculus. 

Although Newton is remembered today as a great thinker of his time, he did not have such a reputation in his day.  He is noted to be “fiercely defensive” of his own discoveries and failed to view science as a cooperative and collaborative endeavor.  In 1703, he became the president of the Royal Society of London, where he ruled in a tyrannical manner and engaged in numerous conflicts among the other scholars.  With his power, he had the ability to manipulate and control the careers of the young and promising scientists.  Keep in mind that this was the same Royal Society of London that Gottfried Wilhelm von Leibniz joined in 1673. 

The “Calculus Controversy” begins two years into Newton’s autocratic power of the Royal Society of London.  In 1705, Gottfried Wilhelm von Leibniz accused Isaac Newton of plagiarizing his research in mathematics, particularly his work with infinitesimal calculus.  Although Leibniz published his work before Newton, it is almost certain that Leibniz had access to Newton’s early findings of calculus that were never published until the early 1690s (recall that Leibniz first published his work in 1684).  Leibniz’s theories are similar to the notes found in Newton’s personal journals, but there are some differences in their work on the matter. 

Most likely due to their separate background, (Newton in physics and Leibniz in philosophy) it is not surprising that Newton’s view of calculus was more focused on concrete reality, whereas Leibniz’s was more abstract, with a focus on infinities.  They each used a different notion – Newton’s clumsy and complicated and Leibniz’s thoughtful and straightforward.

Regardless, in 1712, the Royal Society of London formed a committee to further investigate the matter.  To simply state facts, the committee concluded that Newton should be credited for the discovery calculus and that Leibniz was guilty of plagiarism.  However, Newton’s role as president of the Royal Society of London, allowed him to oversee the appointment of the committee members, hence causing potential bias in the final consensus.  We may never know if Leibniz’s general idea of calculus was stolen from Newton or if he came about it entirely independently.

The controversial debate was not simply between the two great thinkers.  Both had players rooting for them who would plead cases against the other in public attacks.  It seems as though Team Newton had more solid evidence of Leibniz’s engagement with Newton’s findings, whereas Team Leibniz often attacked Newton’s character to weaken the argument.  Unfortunately, the drama surrounding this war between two brilliant mathematicians took place during the final decade of Wilhelm von Leibniz’s life, and when Gottfried died in 1716, it temporarily put an end to the controversy. 

Due to Newton’s English roots, and Leibniz’s German roots, the matter was bitterly debated as a matter of national pride.  Each country wanted the credit for discovering an entire new branch of mathematics.  Ultimately, England decided to divide itself from the rest of Continental Europe on the matter.  Unfortunately, this resulted in England falling behind in the advances in mathematics during the eighteenth century.  As we know, Leibniz’s notation was adopted and still triumphs today, but he died believing that the world would remember him as a fraudulent.  We can only hope that deep down Gottfried Wilhelm believed that the truth always comes to fruition. If only we could go back and tell him he would later be nicknamed the Father of Calculus.

References:

Mastin, Luke (2010).  17^th Century Mathematics -Leibniz.  Retrieved from: http://www.storyofmathematics.com/17th_leibniz.html

Rouse Ball, W. W. (1908) Gottfried Wilhelm von Leibniz.  A Short Account of the History of Mathematics’ 4^th edition.  Retrieved from: https://www.maths.tcd.ie/pub/HistMath/People/Leibniz/RouseBall/RB_Leibnitz.html

(2017).  Isaac Newton Biography. Retrieved from:  https://www.biography.com/people/isaac-newton-9422656