Newton vs. Leibniz (The Calculus Controversy)
After “Batman vs. Superman” it’s time to learn about another great rivalry of our world — “Newton vs. Leibniz”!
As always, I will not dive deep into mathematics, keeping my context approachable to everyone.
Who Cares About Dinosaurs? (A pre-introduction for those who are not into history)
Some people like reading about history and some don’t. I think that the point of view makes all the difference. It’s all about what you are studying (the interest of the topic itself, that is subjective after all), but more importantly why are you studying? Is it because you “have to”, or some other, inner force drives you to do so. This can be just wanting to read for fun, curiosity and much more… it doesn’t matter.
I personally find it more than interesting to learn about remarkable events of the past that have survived all these ages. Except for the fun part, you can always reach out to some new perspectives you never thought of by yourself that can lead even to a tiny personal growth. Above all, studying history can and should be inspiring. Learning about the lives and deeds of the great old ones we admire, we can just taste a scent of their brilliance that can inspire us to try to follow their lead.
As history and past knowledge is the steam we are the steamboats that use the energy of that primordial force to push ourselves forward, making the best out of the present.
Introduction
Calculus is one the most fundamental branches of mathematics that studies how things change. The tools that provide us are critical in almost every aspect of modern science. Physics, engineering, economics, biology and computer science are only some of the fields that are using calculus. Even in Data Science and Machine Learning (my personal field of interest) calculus has a crucial role, especially in algorithms and optimization.
The development of calculus as a process started since Babylonian times as a concept and continued evolving slowly on through the ages. The Ancient Greeks with their geometry and their approach to the concept of infinity who are so ahead of their time, the Arabs who were pioneers in algebra, and Indians, great contributors to mathematical science with specified interest in astronomy, all of them, were vital parts of what we call the evolution of calculus and mathematics.
But, it was until the late 17th century when both Newton and Leibniz with their works transformed calculus to a separate branch of mathematics, taking the form we know today. Although both Newton and Leibniz are considered the fathers of calculus there is a great controversy about who was the first one, the one who holds the reins. This rivalry became one of the most famous debates in the history of science.
Issac Newton
Issac Newton (1643–1728) was an English physicist, mathematician and astronomer. Chosen by Issac Barrow, Newton began his mathematical training at the Trinity University in Cambridge. Barrow was another English mathematician and theologian (who will appear later again in the story) and he is also considered one the pioneers in Calculus development. He is most known for his proof of the fundamental theorem of calculus (which, in fact, was based upon Newton’s calculations).
In Cambridge, Newton studied earlier mathematical works on pre-calculus and early calculus ideas and pretty fast came up with brand new findings that changed the whole scientifical landscape. These findings, among other works of his, were so extraordinary that made him become the leader of the scientific revolution.
In 1666 (at the age of 23) he developed the method of fluxions in order to find solutions to real-world problems, especially those that had to do with gravitation (and its change over time), as well as with the planetary motion. He used his mathematical findings not for the sake of mathematics themselves but to solve physical and astronomical problems. His interest was all about the physical world and how it works.
In 1687 he published Principia Mathematica, one the most important works of his, demonstrating how calculus can be used with great efficiency to explain several celestial mechanics.
Gottfried Wilhelm Leibniz
Born in Germany, Leibniz (1646–1716) was also a polymath as he was a mathematician, logician, philosopher and more. He had been convinced to study mathematics in a greater depth by another key figure in the Scientific Revolution, Christian Huygens.
Leibniz developed differential and integral calculus in the late 1670s and published his findings in 1684 (3 years before Newton). He also provided us with the very helpful Leibniz’s notation, which mostly derives from his manuscripts of 1675, where he recorded some of his discoveries.
His notation system was clearer than Newton’s notation and it is still used today. This, along with his social personality and his traveling activity, led to broader spread of his ideas all through Europe.
The Core of the Controversy
The main question and the core of the rivalry is if Leibniz plagiarized Newton’s unpublished work or if both men developed calculus independently.
Despite developing calculus in the mid 1660s, Newton kept his work private and only started to release it after seeing Leibniz’s publications in the 1680s.
The story began when Newton’s students and friends accused Leibniz, who’s supporters also fought back and this rivalry came to life. Years later, the two great scientists involved personally started accusing each other. Also, as the two men came up from different backgrounds, and importantly, from different countries (England and Germany), so this personal rivalry got some national extensions as well.
Newton supported that Leibniz saw some of his papers on the subject before 1675 and obtained the fundamental ideas of calculus from those papers. Leibniz denied everything and as there was no evidence, none could have made him wrong.
That Leibniz saw some of Newton’s manuscripts had always been likely. Before any publication of Leibniz, Newton gave some copies of his manuscripts to Issac Barrow and he passed them to another English mathematician, John Collins. In general, a broad sharing of ideas was taking place back then through manuscripts, so it’s possible that Newton’s precious papers could have ended up to Henry Oldenburg. He was a German philosopher, who was working with Leibniz at the time. Newton came in contact with Oldenburg accusing Leibniz of stealing his ideas while discussing some concepts of infinity with both Oldenburng and Collins. Leibniz fired back, mentioning that this letter exchange could have been beneficial for both sides.
Years later, the tension increased when Newton’s supporters brought up the accusation once again, but this time in a more formal way. In more detail, in 1699, the English Royal Society (of which Newton was a leading member) openly accused Leibniz of stealing Newton’s ideas. The accusation came up in written form, as a report, part of which probably written by Newton himself, who was the president of the Royal Society at the time. This fact had an enormous effect on Leibniz’s fame and status. The Royal Society never asked Leibniz his version of the story.
Many mathematicians and important personalities of the time took part in this controversy joining the one side and accusing the other. Johann Bernoulli (Swiss mathematician), Nicolas Fatio de Duillier (Swiss polymath) and Guillaume de L’ Hopital (French mathematician) are only some of those. L’ Hospital published his book about calculus in 1696. His calculus had a Leibnizian point of view and he also preferred Leibniz’s notation. Johann Bernoulli entered the “battle”, joining initially the Leibniz Party. Later on, after communication with both men, he tried to organize a calculus competition, but Newton denied.
Eventually, both the British and the Leibniz side published their points of view but they achieved nothing.
The End of the Controversy and Conclusion
While the rivalry was still in full force, in 1716 Leibniz died, putting an end to the whole story. Centuries later and we still can’t be sure about what really happened. Since then, no further enlightening evidence came to light.
Despite their inevitable similarities, the two approaches also have significant differences which don’t allow us to conclude that the one derives from the other. The acceptable conclusion from most people is that both men developed calculus independently and… simultaneously! The sure thing is, regardless who was the first, both Newton and Leibniz contributed the most to calculus, to science and to the progress of humanity in general.
What do you think? What side will you join?
Thank you for reading!
