# Newton — forget the falling apple

(or Math on Renaissance, part 10)

Drums playing… Ladies and Gentleman, it's time to write about the great figure, Isaac Newton. Can you remember the first time you heard about him? I don't remember exactly, but I think it was in a cartoon mentioning the famous episode of the falling apple. But Newton's work is MUCH more than that.

The second clear memory that I have of many people screaming Newton's name was during High School, while we studies his Mechanic laws. "Damn Newton, why did you create this?" By that time, being a good student at Physics, the only thing I could think about was "How the hell did this guy realizes about all those facts?" I ended up reading some parts of Newton's biography, but it was only when I was twenty and something years old that I dedicated a considerable time reading deeply about his works.

Newton is very famous not only for his works on Physics, but for his giant contributions into differential and integral calculus, taking as much credit as Leibniz (which will be topic for a further post). However the first step for differential and integral calculus might have been made by the Greeks, with their exhaustion method (wanting or not, this is the main root for the definition of limit, which is the main root for differential and integral calculus), many other people gave their own contributions, such as Archimedes, Kepler (avid user of Cavalieri methods), Fermat and Descartes.

Isaac Newton (1642 – 1726) had a difficult birth in 1642. He was raised by his grandparents, since with the death of his father, his mother married again and spent some years far from her child. In his early years at school, he did not demonstrated any special talent. This started when Newton came into a discussion that ended up in a physical fight. History says that moment on, he decided to have an intelectual fight as well, becoming one of the best students in the class.

Newton spent some time creating his own clocks (this is interesting, since we mentioned Huygens in a previous post). However, he had to talent to manage the properties and lands of his mother. Due to his lack of skills to become a farmer, he went to Cambridge in 1661.

He also had a great lack of mathematical knowledge, since he studied in a simple school. Newton had to make some domestic services to raise some founds for his expenses during his time at University. He did not come from a total miserable family, however they could not support him financially. This scenario led him to be a really reserved person.

There was also few Mathematics being mad eon Cambridge. Isaac Barrow (who we talked about in this previous post) started more solid studies into the University few years before Newton's arrival. Barrow also stimulated the young Newton to dive into the area, and the professor became surprised about how fast his student could learn and absorb the content. Due to this fact, Newton won a scholarship in 1664, releasing him of the domestic work he had to do and giving him a precious extra time to study.

In 1665, Bubonic plague reached its critical point in Europe. Cambridge was closed and Newton came back to his home. It was during this time that "the story of apple" might have consolidated. Besides the episode itself, it was during this period that Newton (with 22 years old by that time) changed the perspective of his studies, reaching the maximum level of scientific production. Newton made works on Universal Gravitation, Binomial Theorem (general form of Pascal triangle; apply them to not only integer exponents, but also to fractional ones), Differential and Integral Calculus development (using John Wallis works as basis), colours theory, maximum and minimum of a function, trajectory of objects and many others.

Newton developed a solid idea that the inclination of a curve is a quantity of something. Measuring *how much it varies* gives us the derivative of this curve. This proceeding is described in Newt's work *Method of Fluxions*. On the other hand, studies on Binomial Theorem originated the Integral of a curve. Basically, the main reasoning was: "If I made a process to find the variation of inclination from a curve with area, the reverse process, get the variation and 're-wrap' it, will give me the area under the curve" That's brilliant. Since I read this, this analogy gave extra insights for Calculus lessons. Some years later, with Barrow, Newtown contributed to Fundamental Theorem of Calculus.

Newton made a giant progress to calculus, but some points remained unsolved during his living time, such as y = 1/x; x=0. What happens there? Some extra formal studies were necessary to deal with this kind of uncertainty.

Newton also worked to get the roots of many polynomial equations, which you might know as Newton's method for algebraic (and also transcendental) equations. Of course, as many mathematicians, he also found a precise value for π.

Many scientists studies the attraction forces between objects — Empedocles ( 490 BC — 430 BC), Nicole Oresme (~1320–1382), Robert Hooke (1635–1703). However none of them added mathematical formalities to their studies. Newton was the first one to establish qualitatively and quantitatively the gravity. He was able to synthesize the studies of Copernicus, Kepler and Galielo in a group of well formed formulas. What a unification! With his mathematical creation, he could solve questions related to Astronomy, Mechanics, Optics, tides, projectiles, equinoxes. See, the beauty of some equations, besides their mathematica poetry forms and meaning, is that they are so powerful that they can connect really different areas. ❤ His Physical laws remained incontestable until XX century.

Newton isolated himself to improve his techniques and dedicate his time to studies. When he returned to Cambridge, he was nominated Professor and some years later he went if Royal Socienty (more precisely in 1672). He had some disagreements with one person or another, such as Hooke, but given the reserved behaviour of Newton, disagreements did not last long (curious fact: Newton only published the results of the discussions with Hook after Hook's death, to avoid more and more disagreements).

Newton also studied Theology and Alchemy. With the aid of Edmond Halley, Newton published the famous *Philosophiæ Naturalis Principia Mathematica**.* In 1689 he becomes a member of Parliament of England. After that, he solved an old problem from Bernoulli's family, related to cycloid and brachistochrone.

Besides all the great work Newton made, he was not a wealth man. Lord Halifax, noticing such situation, worked to change this situation: he helped Newton (due to his lord influences) to became President of Royal Society (and consequently, achieve a way better salary). Newton passed away old and extremely recognized by European society (opposite from many other figures we have seen in previous posts).

Did you enjoy this post? Check some previous ones ☺

On the next post we will talk about Leibniz. See ya!