**Introduction**

Mathematics field has undergone a tremendous transformation which has been contributed by different people across the world such as Isaac Newton. The 84 years that Newton spent on earth, he used most of it learning extensively in trying to discover ways to solve different questions about nature (Todhunter and Isaac par 1). Although he learned some geometry at school, most of his discoveries were based on his extensive study from his fellow scientists and researchers such as John Wallis, Descartes and William Oughtred. He is especially renowned for his discovery of geometry of a point in a curved line. Although he is widely known for his contribution in various fields of education like mathematics and physics, most of his work was not published.

This research paper examines Newton’s contribution to the field of mathematics and also provides an analysis of his contribution to the past and future of mathematics.

**About the mathematician**

Isaac Newton was born in 1642 in Woolsthorpe Manor in England. He was raised by a single mother because his father had died three months before he was born. His mother married again to a second husband when Isaac was born and left Isaac with her mother. The second father of Newton died when Isaac was only fifteen years. Newton was enrolled at King’s School where was able to perform and top the entire school (Todhunter and Isaac par 1). After high school, Newton enrolled at Trinity College in Cambridge in 1661 where he studied mathematics and physics. Although he is known for his love for mathematics and physics, he also had a great interest in theology, a subject that influenced most of the discoveries. Newton lived for 84 years, and he never married, because his whole life was dedicated to reading and exploring different fields that are attached to nature, physics, and mathematics. It was at Cambridge that Newton was first exposed to the field of mathematics. His encounter with Euclid’s Elements in a bookstore came he was able to follow the mathematical concepts provided by Euclid with the help of his basic knowledge in mathematics (Newton Isaac par 3).

When Newton was enrolled at the University by his uncle, he was fascinated with mathematics, and he started mastering the work of Descartes in Geometry. Newton worked hard to learn as much knowledge on mathematics to the amazements of his peers and professors at the University. In the second year, he was given the opportunity to teach other students after the professor resigned from the institution. His breakthrough came during 1664-1666 when he discovered calculus during a compulsory holiday that was triggered by the outbreak of a plague in England (Kuhn p. 6). His discovery in calculus was contributed by his extensive study of different works from Galileo, Descartes, and Kepler. Despite his important discovery, Newton did not publish much of his work until later years of his study (Gleick and Gerald, p 75). After he had taken over the lecturing role at the University, Newton continued to lecture for twenty years trying to understand all the concepts of the discoveries that he had achieved. It was until when he was 41 years that he published his first book named Mathematical Principles of Natural Philosophy (Principia). The book focused on explaining various physical nature of the universe in mathematics concepts. Apart from the Principia, Newton also published other related books which include Newton’s Philosophy of Nature, The Mathematical Papers of Isaac Newton, The system of the World and The last Sorcerer. Apart from the books he published while he was alive, most of his other books and materials have been published by other people who used his knowledge and discoveries.

**The math**

The discovery of calculus formulas was based on his desire to calculate the slope at any point on a curve whose slope was varying at every point. Newton started exercising his mathematics prowess by working on calculus using geometrical perspective (Todhunter and Isaac par 1). This continuous work on calculus helped him to discover differentiation and integrations of mathematics’ formulas. He also proved that there were multiple colors in white light or sunlight, which was against the initial belief that light, only contained a single color. Newton’s innovations led to the discovery of the field of quantum physics by proving the theory that light is a wave. In 1687, Newton published the book ‘Principia’, one of the highly regarded scientific books ever written (Gleick et al pp 75). In this book, he applied different laws such as the law of motion and gravitation to the universe and proved the gravitational attraction between astronomical bodies.

**Calculus **

** **Calculus is one of the initial discoveries o f Isaac Newton. He discovered calculus when he was barely in his second year at the University. His discovery of the calculus was due to his desire to discover the slope of a point on a curvature (Todhunter and Isaac par 1). His knowledge in calculus led Newton to the discovery of integration and differentiation formulas to be used in the calculation of slope at a point by drawing a tangent line. In the year 1736, Newton released his book called Method of Fluxions which he completed writing in 1671 (Gleick et al pp 75). The book was released amid heated confrontation with Leibniz, a fellow mathematician who claimed to have discovered part of the information written in the book. The calculus book has been spread and read widely by other mathematicians and has contributed to the advancement of the later modification and application of calculus in other subjects such as physics, computer science, and chemistry. One of the facts that make calculus a significant contribution in the mathematics field is its changing nature that makes its formulas easily applicable to in different problems.

**Geometry**

Geometry is a branch of mathematics that deals with size, shape and relative position of the figure. In his study, Newton worked with different shapes and objects in order to get the actual figures for his calculations. The learning of geometry opened up to most of his discoveries and contributed to his success in calculus (De Gandt and François par 2). Geometry contributes to deep understanding of mathematics concepts that are related to different shapes. This also has a direct relation to the calculations in real life shapes such as in the field of architecture and engineering. Newton helped in the creation of symbols that are used in algebra due to his desire to explain nature by using numerical figures (Rickey and Frederick pp 247). Algebra was also a boost to the calculus because they both used symbols. The introduction of algebra during the 16^{th} and 17^{th} century also contributed to the success of calculus.

**Algebra**

The discovery of algebraic expression and figures by Isaac Newton has brought rise to numerous related formulas. During the plague period that struck England, Newton spent most of his time in solitude studying more calculations. It is during the time that Newton discovered binomial expansion. The binomial expansions follow algebraic expressions that can be used to solve other related calculations (Todhunter par 2). According to Todhunter (pp 5), algebra is the use of a symbol to perform different calculations and achieve the intended results.

**Isaac Contribution the past and future of the mathematics**

** **The discoveries of Newton have had a tremendous contribution to the field of mathematics because of the introduction of new formulas that are used to date. Although Newton had interest on a wide range of subjects, he majorly focused on geometry and calculus. Most of the concepts in mathematics he did not learn in school but taught himself through continuous learning and practices (Gleick et al pp 75). Although Newton did not publish much of his work, he contributed immensely to the development of mathematics by discovering a wide range of formulas.

At the time Newton started reading extensively about mathematics, there were scanty mathematic knowledge and numerous unanswered questions. Newton started with reading other writings from different mathematicians in order to trace and fill the gaps. The use of different objects and desire to explain various aspects of nature gave rise to new formulas and new signs in mathematics. Basically, Newton is the key player that connects the past, and the future of mathematics and its usage in different related fields (Todhunter pp 3).

Isaac Newton’s discoveries play a significant role in the future discoveries in mathematics. The future of different areas in the mathematics field such as calculus and geometry relies on the foundation that was laid by Newton and other mathematicians (Todhunter and Isaac par 3). The books that were written by Isaac Newton provide a profound knowledge in different fields related to mathematics. Although most of his work is not documented, Newton passed his knowledge by sharing it with his students. This was the beginning point of the spread of his knowledge which was later spread by the students to other parts of the country.

**Conclusion**

** **The contribution of Isaac Newton in mathematics is based on his deep understanding of nature and his desires to answer many questions about nature. Newton was born in 1642 and died in 1727, but he had already discovered a wide range of mathematics and physics theories and formulas. He always referred to himself a self-taught geometer by having discovered various formulas on geometry. He advanced his knowledge by reading work from other scientists such as William Oughtred and John Wallis. Along with his mathematics job, Newton criticized later works on algebra that were not rigorous and clear. Newton also had a confrontation with other scientists such as Leibniz based on some formulas such as fluxions. They also disagreed because of Newton‘s stance on God and creation, which even led to the delay in the reception and sharing of Newton’s work in the country and across the world.

*Work Cited*

De Gandt, François. *Force and Geometry in Newton’s” Principia”*. Princeton University Press, 2014.

Gleick, James, and Gerald L. Alexanderson. “Isaac Newton.” *The Mathematical Intelligencer* 27.3 (2005): 74-76.

Kuhn, Thomas. “The Scientific Revolution.” Philosophy of Science for Nursing Practice: Concepts and Application 87 (2010).

Newton, Isaac. *The mathematical papers of Isaac Newton*. Vol. 7. Cambridge University Press, 2008.

Rickey, V. Frederick. “Isaac Newton: Man, myth, and mathematics.” Sherlock Holmes in Babylon and Other Tales of Mathematical History (2004): 240-260.

Todhunter, Isaac. *A history of the mathematical theory of probability*. Cambridge University Press, 2014.