Who Invented Calculus?: The Math Scandal Involving Isaac Newton and Gottfried Leibniz

In this article:

• The history of calculus is marred by a centuries-old controversy about who has the rightful claim to the title, “father of calculus.”
• The controversy stems from the fact that both Isaac Newton and Wilhelm Gottfried Leibniz seem to have invented a version of calculus independently of each other.
• When Leibniz’s far simpler notation started gaining traction, Newton loyalists started accusing Leibniz of plagiarism.
• The accusations weren’t just part of a sober, academic debate about who invented calculus. They ballooned into a heated rivalry between two mathematicians with a penchant for pettiness that rivals that of even the most unhinged reality show stars.
• At its core, the controversy is just one of many examples of multiple discovery theory, the theory that most ideas and inventions are simultaneously discovered by multiple people.

It’s hard not to equate the great men and women behind key discoveries, theories, and inventions with their work. Our textbooks call people the “father of…” — or, as the case may be, “mother of…” — when talking about the biggest intellectual breakthroughs of the last few centuries.

Strangely, though, this isn’t the case for calculus.

Now, unless you’re a history or math buff, you probably haven’t noticed that the history of calculus is marred with a controversy involving two of the most influential thinkers of the 17th century: Isaac Newton and Wilhelm Gottfried Leibniz.

Not only did the two mathematicians somehow invent calculus independently of each other (though they probably won’t agree), but they also had completely different approaches to thinking about and writing the subject.

Who Invented Calculus?

If you’ve taken calculus in high school or college, you might remember it as one of the math subjects where you calculate with letters instead of numbers — kind of like algebra except it comes from an even deeper circle of hell. Those letters are called notation.

But what does this have to do with who invented calculus? Well, it’s the fact that Wilhelm Gottfried Leibniz‘s method of notation is one of the two popular types of calculus notation in use today.

Leibniz’s notation uses dy and dx to denote small increments of x and y, our archnemeses from high school math classes.

The popularity of Leibniz’s notation was driven mainly by how simple it was to learn and understand. Since doing calculus before the advent of modern calculators was hard enough on its own, the last thing old-timey mathematicians needed was a convoluted way of conveying ideas.

Except that’s exactly what Isaac Newton did when he started writing about calculus. Newton — of the “discovering gravity after being bonked on the head by an apple” fame — used a more convoluted notation called dot notation.

While dot notation made sense, it was created primarily for Newton’s personal use, unlike Leibniz’s notation which appeared to have been created by someone with a better grasp on presenting information to other people in an efficient way.

Because of this, Leibniz’s notation became the more popular method of writing calculus. Its adoption made studying everything from probability to creating space telescopes easier to do.

But when fans of Newton’s work saw Leibniz gain traction, they suspected Leibniz of plagiarizing Newton’s work.

Here’s the thing, though: the work they claimed Leibniz copied wasn’t even published until the 18th century. Leibniz? He published his ideas in 1684.

Isaac Newton and Gottfried Wilhelm Leibniz Had Beef

It was on.

Neither Leibniz nor Newton were the type of men to back down from a fight. Of course, there’s little we directly know about their personalities but their writings give us a glimpse into their character and their temper.

Isaac Newton had a prideful streak. While he might look like a gentle guy in his portraits, this is the same person who ranked at the top of his class because he wanted to one-up a bully. Now, what the bully actually thought of that isn’t known but he may have considered chucking an apple at Newton’s head.

Meanwhile, Gottfried Wilhelm Leibniz, or Gottfried von Leibniz, as he liked to be called, was a lawyer in addition to being a mathematician. It wasn’t exactly out of the question that he wouldn’t let attacks on his character and intellect slide so easily.

The public argument over who invented calculus broke out in the 1710s — an argument that probably wouldn’t have started if Nicolas Fatio de Duillier, a Swiss mathematician and fan of Newton’s, hadn’t accused Leibniz of plagiarizing Newton’s work in 1699.

At the time, neither Newton nor Leibniz seem to have paid attention to it though Newton’s temper suggests he may have been aware of Duillier’s accusation. Heck, maybe he even felt smug about it.

It wasn’t until someone wrote a bad review of a paper Newton wrote that he went ballistic. The anonymous review pointed out that Newton was the one plagiarizing Leibniz, whose work had been, as mentioned earlier, published at an earlier date.

Newton was pissed. This is a man who, in his youth, had threatened to burn his mother and stepfather’s house down with them inside it because he hated his mother for remarrying. Petty wouldn’t even begin to describe his next steps.

Capitalizing on his greater fame, Newton plotted the creation of the Commercium Epistolicum, a document that contained all the allegations of plagiarism against Leibniz. Note that at the time, Newton was the president of the Royal Society which never asked Leibniz to join them and talk about the odd similarities in his and Newton’s work.

So what does Leibniz do? You’d think he would sue Newton for defamation, but he decided to just chill and stay unbothered. In a letter written on April 9, 1716, Leibniz wrote:

“In order to respond point by point to all the work published against me, I would have to go into much minutiae that occurred thirty, forty years ago, of which I remember little: I would have to search my old letters, of which many are lost. Moreover, in most cases, I did not keep a copy, and when I did, the copy is buried in a great heap of papers, which I could sort through only with time and patience. I have enjoyed little leisure, being so weighted down of late with occupations of a totally different nature.“

TLDR: Leibniz thought it was tedious drama and that he had better things to do than beef with Isaac Newton.

That said, Leibniz never conceded that Newton was the inventor of calculus. When Leibniz finally kicked the bucket, Newton seemed to stop talking about it. Whether he thought he already had the upper hand, we’ll never know. But we are still using Leibniz’s notation.

The Leibniz-Newton Calculus Controversy Is a Classic Example of Multiple Discovery

Niche mathematician drama aside, the dispute between Newton and Leibniz regarding who invented calculus is a classic example of what’s called multiple discovery.

Multiple discovery, also known as simultaneous invention, is a theory that posits that there really isn’t a single “great man or woman” who comes up with inventions entirely on their own.

While people do make their discoveries independent of each other, multiple discovery shakes off the idea that only one person can think of a single thing.

After all, all ideas are informed by the same sensory world around the person who has that idea. When everyone is receiving more or less the same information, it’s only natural that they’ll come to similar, if not the exact same, conclusions.

The odds of coming to the same conclusions go up when you can safely assume that two people are of comparable intellect, as in the case of the two men who invented calculus.

Oddly enough, we see this principle at work in nature as well. If you’ve attended an anatomy and physiology class, you may have heard of convergent evolution. This concept in evolutionary biology refers to the process where different animals develop the same traits and characteristics despite not being genetically related to each other for no other reason than being in environments that demand they develop a specific adaptation.

And speaking of evolution, that brings us to another case of multiple discovery that’s a lot more mature than the controversy over who invented calculus.

It’s Not the Only Case of Multiple Discovery in History

The man you see in the photo above is the man who discovered natural selection and ideated the theory of evolution. If you’re wondering why that doesn’t look like Charles Darwin, that’s because he isn’t Darwin. He’s Alfred Russel Wallace, a lesser-known discoverer of natural selection.

Wallace’s legacy is more obscure than Darwin’s, but he was an equally brilliant biologist who came up with the theory of evolution around the same time Darwin was doing his work on the subject. Having heard that they were working on the same subject, Wallance reached out to Darwin to talk about their ideas on evolution while he was recovering from malaria in Indonesia.

Indonesia was Wallance’s Galapagos Islands. There, he studied the biodiversity of the Malay archipelago and began writing to Charles Lyell, another biologist and friend of Darwin’s, who still didn’t believe that species could change the way Darwin told him they could. At first, Darwin thought Wallace also believed in creationism.

But then he received Wallace’s letter.

Darwin replied and began to keep a long correspondence with the much younger Wallace. Their independent works were presented to the Linnean Society in 1858 and the two biologists went on to publish multiple papers and books on the subject and would defend each others’ theories and reputations against critics.

While Wallace’s name is far less remembered today, the pair are an example of what could have become of Newton and Leibniz if they’d chosen friendship over petty rivalry.