Method of Fluxions

The Method of Fluxions is an important book about mathematics written by Sir Isaac Newton. In this book, Newton explained his ideas about a new way to understand change and motion. This new way of thinking later became known as calculus, which is a major part of modern mathematics.

Newton finished writing this book in 1671, but it was not published until after he passed away, in 1736. Even though it came out many years later, the ideas in the book were some of Newton’s earliest work on calculus. His ideas helped change how scientists and mathematicians solve problems about movement, growth, and many other changing processes.

The book’s full Latin title is De Methodis Serierum et Fluxionum, which means “On the Methods of Series and Fluxions.” It shows how Newton used special methods to describe very small changes, which are like tiny steps that help us understand big movements or changes over time. Thanks to Newton’s work, calculus became a powerful tool used in many areas of science and engineering today.

Background

Fluxion is the name Isaac Newton used for what we now call a derivative. He thought of this idea while he was living at Woolsthorpe Manor. This was during a time when Cambridge was closed because of the Great Plague of London between 1665 and 1667. Newton did not share his work for many years.

Later, a mathematician named Gottfried Leibniz made his own version of calculus around 1673. Leibniz told others about his ideas in 1684. Newton shared his version in 1693. Both men helped create what we now know as calculus.

Impact

The way we write calculus today mainly comes from a mathematician named Leibniz. However, a special kind of notation created by Isaac Newton, shown as x with a dot over it (x˙), is still often used when dealing with changes over time.

Rivalry with Leibniz

Newton’s Method of Fluxions was published after he died. When Leibniz published his version of calculus first, the two mathematicians began to disagree. They argued about who had come up with the ideas of calculus first. This led Newton to share his work on fluxions.

Main article: bitter rivalry

Newton's development of analysis

For many years, Newton and other mathematicians tried to solve important math problems. These problems included finding the area under curves, known as quadrature, and figuring out the slopes of curves, or finding tangents. While these new methods worked, they sometimes used very small numbers, called infinitesimal values, which were hard to explain with old geometry. Newton, like some of his peers such as Isaac Barrow, was careful about these ideas. Over time, Newton found better ways to support his methods, coming close to what we now call the modern definition of limits.