Born: 4 January 1643 [O.S. 25 December 1642] · Woolsthorpe-by-Colsterworth, Lincolnshire, England

Died: 31 March 1727 (aged 84) [O.S. 20 March 1726] · Kensington, Middlesex, England

Education: Trinity College, Cambridge (BA, 1665; MA, 1668)

Politica party: Whig

Resting place: Westminster Abbey

Fields: Physics · natural philosophy · alchemy · theology · mathematics · astronomy · economics

Institutions: University of Cambridge · Royal Society · Royal Mint

Academic advisor: sIsaac Barrow · Benjamin Pulleyn

Major contributions of Isaac Newton include:

• The study of power series

• Generalizing the binomial theorem to non-integer exponents

• Developing a method for approximating the roots of a function

• Classifying most of the cubic plane curves

• Creating a new, specialized form of mathematics, known as calculus, to help explain his theories of gravity and motion

Problem/events that influence Isaac Newton's mathematical ideas:

Isaac Newton's mathematical ideas were influenced by a combination of intellectual, personal, and historical factors. The scientific revolution of the 17th century, marked by groundbreaking discoveries and a growing emphasis on empirical evidence and mathematical reasoning, provided the perfect environment for Newton's ideas to flourish. He was particularly inspired by the works of earlier mathematicians and scientists such as Euclid, René Descartes, and Johannes Kepler, whose studies on geometry, algebra, and planetary motion laid the groundwork for his investigations.

Newton's time at Cambridge University exposed him to advanced mathematical texts, and during the Great Plague of 1665–1666, he retreated to his family home in Woolsthorpe. This period of isolation became a productive time for Newton, during which he developed many of his most significant ideas. Faced with challenges in understanding motion, gravity, and planetary orbits, he sought to create mathematical tools to solve these problems. This led to his invention of calculus, which he called "the method of fluxions," to provide a systematic approach for analyzing change and motion.

Additionally, Newton's interest in physics and astronomy, particularly the questions surrounding celestial mechanics, pushed him to connect mathematics with natural phenomena. His desire to explain the laws governing the physical universe, such as the motion of planets and the behavior of light, deeply influenced his mathematical innovations. Newton's relentless curiosity and the challenges posed by unresolved scientific questions of his time played a critical role in shaping his mathematical legacy.

His Impact on the modern mathematics: 

Isaac Newton's impact on modern mathematics is immeasurable, as he is considered one of the greatest contributors to the field. His development of calculus, independently and alongside Gottfried Wilhelm Leibniz, revolutionized mathematics by providing a framework to study continuous change, motion, and growth. Calculus has since become a cornerstone of mathematics, essential in physics, engineering, economics, biology, and countless other disciplines. Newton's introduction of the method of fluxions (his term for calculus) offered tools to solve problems related to rates of change and areas under curves, enabling groundbreaking advancements in science and technology.

Beyond calculus, Newton's contributions to algebra, geometry, and mathematical analysis further expanded the understanding of mathematics. His work in Principia Mathematica, which used mathematical principles to describe the laws of motion and universal gravitation, demonstrated the power of mathematics in explaining the natural world. This established a foundation for modern physics and encouraged the integration of mathematics into other scientific fields.

Newton’s problem-solving methods, particularly his use of approximations and series expansions, continue to influence numerical analysis and computational methods today. His impact extends beyond his discoveries, as his approach to using mathematics to model and solve real-world phenomena set a standard for future generations of scientists and mathematicians.