"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.