History Of Calculus | Who Invented Calculus and How?

The discovery of calculus is often attributed to the greatest scientist of all time none other than Sir Issac Newton but at the same time when he was exploring the wonders of variables changing with time there was another scientist who was doing the same but with the different understanding, he was Gottfried Wilhelm von Leibniz. 

Discovery of Calculus:

Although Newton and Leibniz never crossed paths in real life their discoveries in the respective domain eventually came across and transformed mankind for the best. Calculus is basically used to measure the rate of change associated with any object over a period of time but that’s not all, it has fundamental usage in various fields of technology and is quintessential for almost all types of space voyages. The word calculus is derived from the word ‘pebble’ this is because in ancient Rome nearly all the things were measured in terms of pebbles such as distance, tallying votes, etc, and hence calculus was thought of as a means of computation.

As mentioned earlier calculus in its present form was developed in the 1600s but the inception of this concept predates even the Great Roman and Greek empires. The Babylonians introduced this idea of measuring the rate of change although in a very premature way but it sufficed the purpose from there the concept of the calculus was matured further by many great scientists and mathematicians such as Archimedes, Bhaskara II, Madhava, etc. 

The notion for calculating the rate of change was conceived when the Babylonians were trying to calculate the movements of Jupiter during the first 60 days it appeared above the horizon by plotting the planet’s irregular motion away from the regular path of the Sun. The Babylonian scholars were people with sensitive scientific and mathematical temperaments their mathematics was so advanced that the sexagesimal number in which they represented all natural numbers using the 60 symbols system they introduced is still in effect, albeit with some tweaks. They also introduced a unique form of writing known as Cuneiform which was distinct from alphabets it used 600-1000 symbols inscribed on a clay tablet to pronounce different syllables.

Cuneiform Code Chart:

So far there wasn’t any proof of Babylonians using the concepts of calculus but recently in Ancient cuneiform texts etched into clay tablets in British Museum it was found that Babylonians were successful in tracking the movement of Jupiter by plotting a graph between the apparent velocity and time taken which resulted in a decreasing slope and formed a trapezoid which was referred to as ‘Ox-head’ by them. In this way, they calculated the area under the graph and were able to track the movement of Jupiter which was no ordinary feat in 1800 BC. 

What the Babylonians did can be called Calculus in its nascent stages after the great Babylonian Empire fell most of their scientific works were deleted from the annals of history which if kept intact might have resulted in a faster pace of development. In the late 5^th century BC a great Greek astronomer and mathematician Eudoxus of Cnidus gave the method of exhaustion for calculating the areas of various polygons by breaking them into simpler shapes such as triangles and rectangles but this method was deemed useless in the case of circles because even if we try to break a circle half of circle will still be a semi-circle. 

The solution to this problem was given by Eudoxus he said, the area of a circle will be equal to the polygon inside the circle which occupies the whole of the circle for doing this the polygon must have ‘n’ number of sides and in this case, the value of n shall be infinity. Hence, the area of a circle is equal to a polygon with an infinite number of sides enclosed in it since drawing such a polygon was impossible hence the concept of limits was first used.

Indian Astronomers Bhaskara II and Madhava too have their fair share in discovering this concept before it was recognized by the world but most of their works were lost. Bhaskara II in his book ‘Siddhant Shiromani’ meaning the crown of treatises mentioned various concepts which were alien to the world before their discoveries by western scientists for example he gave a very simple method for determining the Earth’s circumference and diameter, the values he calculated then are astonishingly close to the present values of earth’s circumference and diameter. Madhava in his book ‘Ganit Yukti-Bhasa’ gave the proof for derivation and the proof for infinite power series of an inverse tangent. In his book ‘Mahajyanayanaprakar’ he also gave the expansion of pi/4 which was later re-discovered by Leibniz. 

After all these facts the obvious question that comes to one’s mind is if this was the case then why were Newton and Leibniz given all the credit for the discovery of calculus, the answer is very simple before Newton or Leibniz used these principles and they were all scattered here and there they were the ones who tied all this together and brought them in one place although they never worked together and their use case and definition of the calculus was different but they were the ones who laid the foundation of calculus which was then modified with time to its current version, It is only fair to say that we cannot even dream about living in a world without calculus almost every major scientific breakthrough makes use of calculus, it is a major part of every discipline right from Biology to Economics. Calculus finds its usage in every walk of life and if not for these great minds we would not have had a chance to advance as a society and explore what lies beyond us.