History of Calculus - Animated

Key Takeaways

calculus the mathematical study of how things change it includes differential calculus rate of change using slope as a function and integral calculus determining quantities like areas and volumes under changing conditions two people are responsible for calculus Isaac Newton the guy behind the laws of cartoons the guy who had publicized light is made up of particles called Karpis gills which allow us to see color when they enter our eyes or just the Apple guy and Gottfried Leibnitz boat Newton and Leibnitz are independently responsible for the foundations of calculus that we see today now did calculus start with them of course it didn't let's go back in time to far Babylonia was an ancient Mesopotamian state comprising of modern Iraq Syria and Egypt the capital city Babylon was about 60 miles from modern Baghdad babylonians offered an early intuition on the infinite process they could determine the square root of a rational number to any number of decimal places a contributing factor was their sexagesimal number system that allow for a compact notation sexagesimal number system has a base 60 that means they represent all real numbers using sixty symbols this is different from the base ten or the decimal number system that we use today the ten symbols being the digits 0 through 9 Babylonian mathematics recorded their research and observations on clay tablets called cuneiforms this is a famous cuneiform that shows that the diagonal of a square is root 2 times its side they were also able to define other numbers with potentially infinite precision like the length of a year or even represent the value of pi fast forward to 300 BC Babylonian astronomers thought everything that happens in this world from changes in the weather to rise and fall of tides was associated with the motion of planets so the Babylonians used geometry to study the motion of planets specifically Jupiter since their God Marduk was associated with Jupiter recording velocities at instantaneous times they could determine how far the planet travels in an interval of time this was similar to finding the area under a curve with the trapezoid rule which forms the basis of integral calculus that we see today did they do everything of course not around the same time in ancient Greece were the prominent figures Eudoxus of knidos and Archimedes they were able to prove areas of shapes through the method of exhaustion for normal polygons say an octagon we split it up into a number of triangles and find the area of each triangle then add it up to get the area of the polygon circles are a special case since they can't directly be split into triangles half a circle is just half a circle so they inscribed a polygon and gradually increase the number of sides so the area of the circle would approximately be equal to the area of the polygon but the area of the circle would only be the same as the inscribed polygon with infinite sides from this we got the concept of limits and it also incorporated the idea of the infinite process onto the medieval era India had their share of contributions - in the 12th century mathematician and astronomer Bhaskar - wrote the Siddhanta shadow money which contained texts in astronomy with proofs using calculus he proved the added size point the instantaneous speed of a planet is zero actually I don't know what that means but that's what it literally says in this paragraph of a news article in a language you don't care about and this paragraph talks about how some English mathematicians called Newton and Leibniz are known for this discovery even though Basquiat said it a few centuries earlier one of the greatest mathematicians and astronomers in the 14th century India madhava linked the idea of infinite series with geometry and trigonometry he was able to formulate infinite series expansions for sine cosine arctan and even pi so you see these expansions here you know the one that we call the power series expansions but nope they're actually called them out of a series this is the mod of a sine series is the model of a cosine series and this is them although arc tangent series but if he did find this then why didn't mother but get the credit himself we can't find his work the only sources were the mathematicians who reference him Newton and Leibnitz and other Western mathematicians were 300 years too late the history of calculus and mathematics isn't straightforward different countries came up with their own methods around the same time using this knowledge we attribute its flourishing as a promising field to the people who tied it all together Newton was a physics buff his calculus was defined out of necessity to lay the foundations of gravitation and the laws of motion so it's no surprise that he thought of calculus in terms of motion and called his calculus the method of fluxions a variable of interest was called the fluent and it's velocity was called the flexin while Newton thought of his calculus in terms of motion Leibnitz had a more mathematical interpretation to him calculus was more sums of infinitesimal distances the same meaning behind the notation we use today and so most of the notation we use is actually from Leibnitz so who took the credit for calculus Newton conceived his ideas in the 1660s while Leibnitz came to similar conclusions a decade later but Lena's published his findings nearly a decade before Newton well initially it was Newton but after their deaths both were attributed the title inventors of calculus regardless as we've seen calculus wasn't invented overnight it's a branch in mathematics that has multiple roots from thousands of years ago and it continues to power newer fields like machine learning and AI if not for all these people some of us would be doing different things hope you guys like this little tension from the hardcore math videos I've been dishing out lately subscribe for more content on data Sciences and I will see you in the next one