Bibliography

Bibliography

Hatch, Robert A., Dr. "Isaac Newton Biography." Isaac Newton Biography. N.p., 30 Nov. 1999. Web. 30 Apr. 2014.
             (Dr. Robert A. Hatch is a professor at the University of Florida and I highly recommend reading this biography he wrote).

"The Thirty Greatest Mathematicians." The Thirty Greatest Mathematicians. N.p., n.d. Web. 30 Apr. 2014.

"Isaac Newton Biography." Bio.com. A&E Networks Television, n.d. Web. 30 Apr. 2014.

"The Apple, the Moon, and the Inverse Square Law." The Apple, the Moon, and the Inverse Square Law. N.p., n.d. Web. 30 Apr. 2014.

"The Inverse Square Law." YouTube. Google, 02 Sept. 2009. Web. 30 Apr. 2014.

"Symptoms of the Plague." Symptoms of the Plague. N.p., n.d. Web. 30 Apr. 2014.

All images were borrowed from google images.

Newton's Later Years and Conclusion

In 1684, Edmund Halley, Robert Hooke, and Christopher Wren all were pondering a solution to the problem of planetary motion, but to no avail. Halley visited Newton in Cambridge that year. His motive for the visit was to answer the question: "What type of path does a planet make in its orbit around the sun if you assume that the inverse square law holds true?" Without hesitation, Newton answered, “an ellipse.” Halley was surprised that Newton already had the answer to the problem that the three other men had been pondering for so long. Halley asked Newton how he knew. Isaac replied saying that he had already calculated it.

 Newton had just answered one of the most difficult riddles of the universe before everyone else, but he lost the paper containing the calculations. He alone possessed the ability to derive such a calculation and Halley knew this. After talking for awhile, Newton agreed to repeat the calculation and show it to Halley. During the fulfillment of his agreement, Newton produced his work entitled, “De Motu,” in 1684.

This book led to what may be the most important book anyone ever wrote about science and physics, Newton’s “Principia.” Newton used the “De Motu” as a stepping stone to create what is widely considered his greatest publication. The “Principia” was funded by Edmund Halley. The book was very well received; although, it was cast into doubt by none other than Robert Hooke starting the controversy. Hooke claimed that he played a large role in Newton’s discovery of the theories contained in his book. This time, Hooke actually had some justification, being that he wrote Newton letters (as previously mentioned) in 1679 and 1680 containing his ideas and also his theory that the inverse square law was somehow involved. Newton was absolutely furious that Hooke would dare try to steal the spotlight for the work that he created. Isaac Newton actually threatened not to publish Book III of the “Principia.” He even denounced the name of science stating that is “an impertinently litigious lady.” After finally starting to calm down, Newton gave his consent to finishing his publication. However, instead of mentioning hook or giving Hooke any kind of acknowledgement, he completely omitted every possible mention of his name. Newton’s hatred for Robert Hooke had consumed him. Newton later withheld the publication of "Opticks," waiting until after Hooke’s death in 1703.

“Principia” was a wild success, Newton finally got the recognition he deserved from his peers, well most of them that is. Isaac Newton became more involved in public affairs. In 1689, he was chosen to represent Cambridge in the Parliament. However, in 1693, he had a serious mental and emotional breakdown. This was similar to the instance in 1677 and 1678. No one knows the actual cause, but many think it could relate to overwork, stress, the fact that his work undertook a lot of criticism, or even mercury poisoning from the extended period of time that Newton undertook studying alchemy. Newton recovered from his mental state and found a new position in London. He became the Warden and eventually the Master of the Mint. He left Cambridge for an extended period of time to go to London.

Robert Hooke was reluctant to give up his title as head of the Royal Society, especially because he knew that if he did, the new head would be Newton. After Hooke’s death in 1703, Newton took the position of President immediately after Hooke’s death and published his book entitled, “Opticks.” A dead man can’t criticize his work after all. All of his work in this book was completed what is estimated to be a decade before its publication. He was obviously eternally bitter toward Hooke. After this, Isaac Newton was knighted by Queen Anne on April 16 1705.

Newton’s time as President was considered to be tyrannical. He used the Royal Society to his own personal affect. One case stands out in particular. Leibniz declared that he was the true inventor of calculus since he was the first to publish a work on the topic. The quarrel was taken to the Royal Society, of which Newton had full control. The result was a biased ruling in favor of Newton. The actions of the Royal Society acted on behalf of Newton. At the time, Newton was accredited with the founding of calculus. However, now they are both considered co-founders, having developed the ideas independently. As previously stated, Newton had founded calculus during his time at home during the plague, almost 20 years before Leibniz. Therefore, one could make the argument that Newton was the original inventor. Leibniz merely gets credit due to the fact that he published works on calculus before Newton.

Newton remained dominant in the fields of math and science until his death on March 31, 1727. He also remained the President of the Royal Society until his death. Isaac Newton is still considered one of the most intelligent people who have ever lived. He also made huge discoveries during his studies that made a major effect in math and science that were unprecedented at the time. His greatest discoveries are usually said to be that of infinitesimal calculus, series dealing with calculus (power series), physics, and of course gravity and planetary motion. Isaac Newton would be compared to no other mathematician or scientist until Albert Einstein. Newton is still widely considered to be one of the greatest scientists, mathematicians, and influential people of all time.

Inverse Square Law and Gravity

Isaac Newton was curious as to how gravity acted on objects such as an apple compared to other things such as the moon. Why doesn’t the moon come crashing down to Earth? Newton tested his theory using cannons. If you fire a cannon in an area without gravity or air resistance, the cannonball will continue in a straight path continuously unless acted upon by another force. If you were to fire a cannon on Earth with both of these factors, the cannonball wouldn’t travel in a straight line. It would actually travel in a parabola and the cannonball would eventually hit the ground due to the mysterious force of gravity. (Remember, gravity wasn’t discovered yet.) If you fired the cannonball so that it had a greater velocity, the cannonball would travel further before hitting the ground. He then theorized that if he could launch the cannonball at a fast enough speed, it would travel along the curved edges of the Earth. It would continue to circle the Earth, but never land on it. Newton thought that it was this same mysterious force that kept the moon in orbit with the Earth.

Hooke’s letter, as mentioned before, hinted towards planetary motion involving inverse squares. This was the missing piece Newton needed. He theorized that the force of gravity, F_g , was inversely proportional to the square of the distance between the objects, d². This can be denoted as: F_g  1/(d² )

Basically, this means that the farther away an object is, the less that gravity acts on that object. If an object is attracted to an object at a force of 16N, and the distance is doubled, with how much force will the objects be attracted? Well we can use the previous formula. if we substitute 2d in for d, then we know that the force will be one forth of what it was before. 16 (1/4) = 4, so the two objects will be attracted by a force of 4N.

It is for this reason that an apple falls to the ground, but the moon doesn't come crashing to the Earth and why we (being on the Earth) don’t crash into the Sun. The Earth exerts much less gravity on the moon than the apple since it is much further away. Gravity is also the mysterious force that keeps the Earth and other planets circling the Sun. This is what Newton determined during his experiments with gravity.

Here is a link to a youtube video that describes how the inverse square law works. This example is about the inverse square law in general, not just how it pertains to gravity.

_{https://www.youtube.com/watch?v=F-xNMdIXJIs}

Induction into the Royal Society and first Publications.

In 1672, Newton was elected into the Royal Society. His first paper dealt with color, light, and optics. This paper was very controversial at the time among fellow scientists and mathematicians. This sparked the first disputes that Isaac would have to undergo about his work. This also was the beginning of Newton’s greatest rivalry with the curator and head of the Royal Society, Robert Hooke. This controversy continued for about six years. Isaac Newton believed at this time that light was composed of particles. Hooke condemned Newton’s idea, for he theorized that they were composed of waves. Newton’s argument was that if light was in the form of a wave, then light should be able to bend around corners. If you have ever seen your shadow, you noticed that light does not bend around you, or you wouldn't have a shadow. Sound was known to be made up of waves and sound waves can bend. That is why you can hear someone talking in other rooms. Even though Newton wasn't entirely correct, his reasoning behind his theories did seem logical.

 During this time, Newton was publishing more and more papers, which again drew criticism, mostly from Hooke. Hooke accused Newton of plagiarism. The charges didn't hold water and were burned, but Newton withdrew. Isaac threatened to leave the Royal Academy, but decided to remain after some of the fellow members convinced him that he was held in high regard.

In 1678, Newton was emotionally distraught. The next year didn't bode much better for Newton with the passing of his mother. Isaac cut himself off from the rest of the world and all people. He began working on more research, a good part of which dealt with alchemy. Alchemy is more of a philosophical tradition than it is a science. People that practice alchemy attempt to use metals to do one of three things: create the mythical philosopher’s stone, transform metals into noble metals such as gold or silver, or create an elixir of life. All of these things are obviously mythical, but during this time period it was widely popular. Scholars of Newton don’t like to mention this usually since they consider it an embarrassment. However, practicing alchemy at this time could be considered an attempt to understand nature’s hidden forces.

These studies were not a complete loss for Newton though. Many link some of Newton’s ideas on mechanics to be traced back to his studies on alchemy. Newton changed this philosophical idea of mechanics by theorizing an invisible, yet measurable force, gravity. As mentioned before, Newton was said to have observed the falling of the apple in 1666. It is actually considered more accurate by scholars that Newton didn't fully understand gravity until almost twenty years after that event. Isaac Newton’s greatest rival at the time, Robert Hooke, was actually the person that helped Newton on the path to developing insights about gravity. Hooke had sent Newton a letter that mentioned a great question about planetary motion. Hooke suggested that the formula might involve the inverse squares.

"Prime of Age for Invention"

Newton had earned financial support for four more years at Trinity College. One thing held him back from his studies there, the Great Plague in 1664-1666. The Great Plague was considered the last major epidemic of the bubonic plague that had swept through London beginning in the 14th century. The bubonic plague (also known as Black Death) killed a number of Europeans during the 14th century. This epidemic killed less, but still took its toll. The Great Plague killed about 100,000 in London, this equated to about 15% of its population at the time. The disease spread by the bites of infected rats and fleas. The disease killed approximately two-thirds of infected people. The symptoms can be best described in the words of Boccaccio:

“The first sign of the plague was that swellings appeared in the groin or the armpits. Some of the swellings became as large as an apple, sometimes they were the size of an egg. The deadly swellings then began to spread in all directions over the body. Then the disease changed. Black or red spots broke out, sometimes on the thigh or arm. These spots were large in some cases; in other they were almost like a rash.”

It was for this reason that the University of Cambridge was forced to close. Isaac moved back to Woosthorpe. This would lead one to believe that Newton’s intellectual progress would remain stagnant. That assumption couldn’t be further from the truth. If one recalls, even during his undergraduate years, Newton spent more time pursuing his own academic interests and fascinations. During these eighteen months, Newton made a string of major and original contributions to science and mathematics. Newton considered himself to be, in his words, in his “prime age for invention.”

It was during this time that Newton conceived his idea of “method of fluxions” (what he called calculus) and discovered the generalized binomial theorem. This led to what is considered to be Newton’s biggest contribution to mathematics, that is, infinitesimal calculus. Infinitesimal calculus is a specific part of calculus that deals mostly with tangent lines to curves, areas lying under curves, minima and maxima, as well as other things. This portion of calculus is used mostly in problems involving physics, which was Newton’s strongest and favorite field of study. His ideas and applications of calculus were built on physics ideas. Instead of considering a change in "y" divided by a change in "x", he focused on changes in time.His ideas on calculus gave us numerous applications still used today. During his time off from the university, Newton found adequate time to develop ideas and theories on calculus. Newton did not publish any of his work regarding calculus at this time, which would eventually start a controversy on who actually developed calculus (Newton or Leibniz), but that comes later.

It was also during this time that Newton started to develop some ideas on optics and other things. This was also the time where legend has it; Newton observed an apple fall from a tree in his garden. It is true that Newton began to try to develop his own thoughts on gravity and the movement of planets, but it wasn't until later that Newton actually reached his epiphany on the laws of gravitation.

In 1667, the Great Plague had finally subsided, allowing Newton to return to his graduate studies at Cambridge. Against the odds, Newton was elected a minor fellow at Trinity College. Isaac Newton still wasn't considered a standout scholar. In the next year he became a senior fellow after he obtained his master’s degree. In 1669, Newton wrote “De Analysi,” which built upon Nicholas Mercator’s ideas on infinite series. Infinite series and sequences were major ideas that Newton studied and used to attribute to his theories on calculus (power series for instance). Isaac Newton shared his theories with his professor and friend, Isaac Barrow. Barrow took the work to British mathematician, John Collins. Barrow gave Newton great praise in his conversation of the paper to Collins. Barrow identified Newton as, “… a very young… but of an extraordinary genius and proficiency in these things.” This was the first time that one of Newton’s works was brought to the attention of the mathematical community at the time. Isaac Barrow resigned from his professorship at Cambridge shortly after this. Before his 27^th birthday, Newton became a professor at Cambridge, succeeding his mentor, Isaac Barrow.

College Years

Newton attended the King's school until he was around seventeen years old. Newton was encouraged by his uncle, Reverend William Ayscough, to seek admittance to Cambridge’s Trinity College. After being admitted into Trinity in 1661 (due to his uncle’s recommendation) Newton took part in a type of work study program at the university where he waited tables and took care of wealthier students’ rooms to pay for his schooling.

At the time, Trinity College mostly focused on the teachings of Aristotle. Newton himself also studied the works of Descartes and some astronomers, namely Galileo, Thomas Street, Copernicus and Kepler. During Newton's time is an undergraduate, he was still yet to become distinguished as a scholar. In fact Lucasian professor, Isaac Barrow questioned Newton on his knowledge of the works of Euclid and found his understanding to be lacking at best. 

Little is known about his undergraduate years at Cambridge. There is also little information regarding their curriculum at Trinity College. What is assumed is that it was mostly centered around Aristotle. Newton found himself captivated with mathematics and more so, advanced sciences. Most of his free time was devoted to reading about the theories of modern philosophers of the time period. Some believe this is why Isaac Newton's reputation as a student was still rather lackluster. He was more enthusiastic about other more advanced topics rather than that which was studied through the university's curriculum.

While attending Trinity College in his Undergraduate years, Newton kept a set of notes regarding some of his favorite scientific and mathematical topics. These notes were entitled, "Quaestiones quaedam philosophicae,” which means, “Certain philosophical questions.”  This is one of the most famous scientific notebooks of all time. It is currently in the Cambridge University Library. The note book has been assumed to have been written sometime between July 8, 1661 (when Newton arrived at the university) and before Decmeber 9, 1664.

 The notes dealt with several topics. The first topic was perpetual motion and was before Newton fully understood the idea of gravity. It was here where he began to theorize that gravity must act on the interiors of heavenly bodies. Newton’s thoughts regarding colors were also included in his notes. During this time, it was believed that colored light was the product of some mixture of light and darkness. Newton was one of the first to theorize that white light is a mixture of different colors of light. He proved this later using prisms. Although in this section, Newton also criticized Robert Hook’s theory of color which was based on the idea that light and color are in the form of waves. Newton argued that if light was a wave it would bend around objects much how sound waves do. His notes also touched on the idea of atoms and the motion of heavenly bodies.

After completing his undergraduate career, Newton won the title of scholar, but not much else. Isaac had still not become distinguished as a scholar nor did he graduate with any honors. The only thing he received after his four years at Trinity College was four more years of financial support for future education. 

Sir Isaac Newton

Sir Isaac Newton
(1643-1727)
By: Steve Boring

Isaac Newton was born prematurely on January 4, 1643 (according to the Gregorian Calendar) in Woolsthorpe, England (near Grantham in Lincolnshire). He was born to his mother, Hanna Ayscough Newton and his father who was also named Isaac. His father had died three months prior to Isaac Newton’s birth. Prior to 1582, most countries used the Julian Calendar. Some places may cite that Newton was born on Christmas day 1642. This date is according to the Julian Calendar which is why there is an eleven day difference between dates.

At three years old, Newton’s mother re-married to a wealthy minister named Barnabus Smith. Hanna moved in with Barnabus and wished to start a second family. She left Newton with his maternal grandmother until he was about twelve years old. Newton had a hatred toward his step-father being that he had taken Newton’s mother from him. Newton had an unhappy and resentful childhood. He was often angry which led to violent acts against others, friend or foe. This experience is thought of a cause to Newton’s complex character. In 1653, Barnabus died and Hanna returned to Woolsthorpe with three young children from her second marriage, though Newton denied any attention from her out of anger.

With the return of his mother, Newton was taken out of the King’s School in Grantham where he had attended become fascinated with chemistry, to chase his childhood dream of becoming a farmer. Newton was a failure at farming, but he wasn’t upset about it. He found farming to be monotonous. Newton returned to school to prepare for entrance to Trinity College in Cambridge. During his time in public school, Newton was considered to be absent-minded. Often his work was jaded and seemed to be lackluster in performance. Although, when he rejoined public school, he was motivated to be a better student by a school bully. During this time, it is said the he built sundials and windmills. At the King’s School, Isaac was mostly taught how to speak and write in Latin. Students did not learn much about mathematics in public schools at the time.