“In the beginning of the year 1665, I found the method of approximating series and the rule for reducing any dignity of any binomial into such a series.”
- January 4, 1643 – March 31, 1727
- Born in England (UK)
- Natural philosopher, mathematician, physicist, astronomer, theologian
- Proposed the laws of universal gravitation and motion, built the foundations of modern science, and systematized theories of natural philosophy and mathematics.
Quote
“In the beginning of the year 1665, I found the method of approximating series and the rule for reducing any dignity of any binomial into such a series.”
Explanation
In this quote, Isaac Newton is referring to his early work in mathematics, specifically his discovery of methods related to approximating series and reducing binomials into series expansions. Newton’s development of these mathematical techniques in 1665 was pivotal in the advancement of calculus, though he did not publish his work until later. The concept of binomial expansion that Newton developed allowed for the approximation of functions through infinite series, which could be used to estimate values for complex mathematical expressions. This was a crucial step in his exploration of calculus, and it laid the foundation for many of his later discoveries, such as the fundamental theorem of calculus and the development of the method of fluxions (the precursor to differential calculus).
Newton’s work on series and binomial expansions was part of his broader effort to describe the world in mathematical terms. The idea of using series to represent functions was not new—Blaise Pascal and others had explored series expansions before—but Newton’s contribution was to extend these ideas in ways that would later revolutionize both mathematics and physics. By the time of this discovery, he had already begun developing ideas for his laws of motion and universal gravitation, and the mathematical tools he created were essential for formulating and proving these laws. His approach to series and binomials enabled the calculation of quantities like areas under curves, velocities, and accelerations, providing a powerful method for dealing with complex physical phenomena.
In modern times, Newton’s work on series and binomial expansions continues to be foundational in many areas of mathematics and physics. The method of approximating series remains essential in solving problems in calculus, differential equations, and numerical analysis. For instance, the Taylor series and Maclaurin series are direct descendants of the methods Newton developed for approximating functions. These series are used extensively in engineering, economics, and computer science to model and solve real-world problems that cannot be solved with simple algebraic expressions. Newton’s insight into the power of series expansion remains one of his lasting contributions to mathematics and science.
