Who Discovered Calculus?

Newton's Claims

The debate over the invention of calculus has long been fueled by the claims of Isaac Newton's supporters. They argue that Gottfried Wilhelm Leibniz plagiarized Newton's work after a visit to England in 1673, where he interacted with Newton's associates 1. Despite these allegations, Leibniz's system of calculus, published in 1684, differed significantly in notation and usability, becoming the foundation for modern calculus 2. Gary Arndt notes, "If attribution in mathematics and science means anything, then it would mean something in the attribution in calculus."

If attribution in mathematics and science means anything, then it would mean something in the attribution in calculus.

--- Gary Arndt

Newton's failure to publish his findings until 1704 added complexity to the controversy, as his work remained largely unknown outside his circle 1.

   

Leibniz's Defense

Leibniz's defense against plagiarism accusations highlights the circumstantial nature of the evidence presented by Newton's supporters. Although he visited England and corresponded with Newton's colleagues, there is no concrete proof that he accessed Newton's unpublished work 1. Leibniz's calculus, with its distinct notation, was easier to use and eventually became the standard 1. Gary Arndt emphasizes that the accusations lack a "smoking gun," making it difficult to convict Leibniz of plagiarism in a court of law.

There really isn't a smoking gun. The letters which Leibniz received from his colleagues in England, which did mention parts of calculus, were mostly overviews and didn't go into any detail.

--- Gary Arndt

The Royal Society's investigation, led by Newton himself, concluded in favor of Newton, but modern perspectives suggest a more nuanced view 3.

   

Historian Consensus

Modern historians and mathematicians generally agree that both Newton and Leibniz independently developed calculus. However, the story doesn't end there, as evidence suggests that integral calculus might have been discovered much earlier by Archimedes 4. His work, found in the Archimedes Palimpsest, describes methods resembling integral calculus, laying a foundation centuries before Newton or Leibniz 4. Gary Arndt reflects on this lost history, stating, "If the work hadn't been lost for centuries, calculus and all the science which stems from it could have been discovered hundreds of years earlier."

If the work hadn't been lost for centuries, calculus and all the science which stems from it could have been discovered hundreds of years earlier.

--- Gary Arndt

This revelation underscores the complexity of attributing the invention of calculus to a single individual or era 4.