Newtonâ€™s special talent in mathematics started at an early age. By the age of 22, his passion in mathematics had grown even bigger when he started investigating into physics and geometry that later transpired into calculus. He devised various methods of dealing with mathematical problems based on ideas from past geometers like the Greek, Indians, Persians and even Arabs. His first mathematical discoveries were differential and integral calculus and gravitational law. He introduced his own theory of infinitely small numbers (infinitesimals) which was the best solution to finding the areas of derivatives or slopes. He also invented a mathematical symbolic language subsequently creating a new mathematical subject known us calculus which was part of his scientific inventions of motions and magnitudes (Sandnes & Rasmussen, 2005).
By 1666, Newton had developed a new form of mathematics known as the calculus subsequently developing into derivation and integration methods. Though afraid of criticism, his methods were never publicized and shifted his focus into tangent problems since he believed calculus was a metaphysical explanation of change he planned to look into in future. His central focus was to formalize the inverse properties between the integral and the differential; this was the first calculus system where he created new rhetoric and descriptive terms. Primarily due to his hard work and ability to synthesize the insights around him into a universal algorithmic process enabled him to form a new mathematical platform that influenced the direction of the modern mathematics (Sandnes & Rasmussen, 2005).
Through 18 century, calculus enlarged into mathematical application which is used today in natural and physical sciences. This involved a major shift away from working just with calculus towards working with integration and derivation (Chapter 3, 2005, p.11). Newtonâ€™s many mathematical discoveries established transition between the ancient calculus and the modern mathematics. Heâ€™s incredible aptitude was recognized by many geometers all over the world. At an early age he quickly learned about the current theories and by 1664 he had already advanced the binomial theorem formula which included fractions and negative exponents and extended this by applying algebra of finite quantities in an analysis of infinite series. His approach demonstrated how he viewed infinite series as alternative forms (Smith, 2007).
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