Home STEM How Do You Invent Math? The Origin of Calculus

How Do You Invent Math? The Origin of Calculus

by Angela Xu

How does one create math out of nowhere? The calculus we know and love (or hate) was invented during the Scientific Revolution, but to this day, we still aren’t sure who the first person to invent it was. 

Math Before Calculus:

Before the Scientific Revolution, math was based on Algebra and Geometry which had existed since ancient Greece. For example, you may have heard of the famous Pythagorean Theorem (a^2 + b^2 = c^2) which was created by ancient Greek mathematician Pythagoras around 500 BC. A few centuries later, Archimedes found a way to calculate the area of a circle and the volume of a sphere, using a value that we know today as Pi. Math remained roughly the same for the next one thousand years.

Why Calculus?

So what changed from 500 BC to 1500 AD? Astronomy. The scientific revolution began with the life-altering discovery that the universe did not look like this:

Here's a diagram of the solar system from the Middle Ages
It was known as the geocentric model - or with Earth at the center of the universe.

Copernicus, a Polish monk, was credited for this discovery, which he detailed in his book On the Revolution of Heavenly Spheres in 1543. Then, in the early 1600s German astronomer Johannes Kepler developed three new theories on the planets and the solar system:

  1.  planets orbit around the sun in an ellipse (oval) rather than a perfect circle
  2. planets speed up and slow down during their orbits
  3. the time a planet takes to make its complete orbit is precisely related to its distance from the sun.

The universe that Europeans had studied for over a thousand years was a complete lie – at least for scholars and astronomers (this type of knowledge was unknown to the typical lower class citizen). Astronomers soon realized it was impossible to calculate to calculate why orbits were an ellipse with algebra and geometry.

The Great Sulk (Epic Math Battle!)

Let’s meet the players!

Sir Isaac Newton (1643-1727)
Gottfried Wilhelm Leibniz (1646-1716)

Newton is arguably one of the most famous physicists in the world, however he was also a talented mathematician and astronomer. Newton is known for his discovery of gravity and laws of motion. While studying Newton, he realized that the speed of a falling object couldn’t be calculated using algebra and geometry. Therefore, as the story goes, he created calculus (which he referred to as the “method of flexions”) as a mathematical explanation for gravitational force. This was the same force that made the Earth attracted to the sun and other planets—which created elliptical orbits.

Probably the lesser known of the two, Leibniz was a German polymath: talented in mathematics, philosophy, science, and diplomacy. In 1617, he invented a version of the digital calculator: a machine that could add, subtract, multiple, divide, and extract roots. By 1674, Leibniz had created the foundations of calculus as well, and created a system of notations for it.

Fun fact: Leibniz is actually credited with creating the “=” sign!

The Debate: Newton vs Leibniz

Newton invented calculus first in 1655, however didn’t publish it until 1705.  Leibniz invented his similar version of the math later on in 1674, but published his findings first, and was able to create a set of notations for it. Both Newton and Leibniz claimed that the other party had plagiarized from themselves. In 1712, England’s Royal Society investigated both men’s claims and wrote the report Commercium epistolicum, which sided with Newton. However, this proves nothing, as Newton was the president of the committee and head author of the paper himself. (not cool Newton)

This controversy, often called “The Great Sulk” actually hurt a lot of future mathematical discoveries. The British sided with Newton’s method of calculus while the rest of Europe used Leibniz’s version.  This caused England to be isolated from mainstream scientific thought during the Scientific Revolution 

Today, modern scholars and mathematicians reached the consensus that both men discovered calculus independently. 

Bonus Fun Fact!

“If I have seen further it is by standing on the shoulders of Giants”

This was one of Newton’s most famous quotes, and people often use it to refer to our progress in science. Many believe Newton said this to credit all of the great mathematicians, physicists, and astronomers before him that helped him reach his discoveries. However, some historians actually believe this was meant to poke fun at Leibniz’s height (who was only around 5 feet tall), hence Newton was a “giant” compared to Leibniz!






Leibniz, Gottfried Wilhelm

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