Leonhard Euler


Preacher’s kids commonly rebel, and Leonhard Euler is no exception. Son of a Calvinist pastor, he was expected to live the life of a clergyman. However, he admired numbers more than religion. It was not until his private tutor, Johann Bernoulli, convinced Euler’s father to allow him to become a mathematician that he was able to truly pursue the field. His brilliance and passion for mathematics would eventually give him the title as the greatest mathematician to come from Switzerland. He was one of the top mathematicians of the eighteenth century. In fact, he made contributions to nearly every field of mathematics. By the age of 16, Leonhard Euler had already received his Master’s degree from the University of Basel in Switzerland. Ten years later he became the professor of mathematics at the Academy of Sciences in St. Petersburg, Russia. In his lifetime, he would have thirteen children, but only five would survive to adulthood. And despite going completely blind by the age of 50, he continued his mathematical assertions. Modern mathematics owes a great deal to the “Analysis Incarnate.”

Insight and Influences


While in Russia, Euler discovered the Czar’s government was not the least bit democratic as he was being
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followed by secret police. In search of an escape, he and his family moved to Berlin. There, he took over as the director of mathematics at the Academy of Sciences under Frederick the Great. When the previous president of Prussia died, Euler should have been the obvious successor as he was held in high esteem. However, Frederick disliked him. D’alembert, a French mathematician, was instead asked to take the position. Although D’alembert fought against the injustice, it became clear that Leonhard should find a new home. He returned to St. Petersburg in 1766. Russia had then come under the rule of the more liberal Catherine the Great. He did much consulting work for the Russian government, publishing numerous results. Despite a nomadic lifestyle for him and his family, Euler continued to make enormous strides in mathematics. The world around him in the early eighteenth century, including the political turmoil, neither inspired nor ceased his genius. Gifted with a brilliant mind at an early age, he simply applied it. He knew his achievements would become important.

Major Contributions


These achievements are numerous and varied; Leonhard Euler’s contributions can be found in nearly all areas of mathematics. For example, he established a set of equations describing fluid mechanics that stemmed from Isaac Newton’s laws of motions. His particular interest in lunar motion led to significant improvements in the theory used to explain and predict such motion. This brought about more accurate lunar tables, commonly used by sailors to determine longitude during that time. In addition, he introduced the modern notation for the trigonometric functions, the letter e for the base of the natural logarithm (now also known as Euler’s number), the Greek letter ∑ for summations, and the letter i to denote the imaginary unit. Although the majority of his work was in pure mathematics, Leonhard did contribute to other disciplines as well. In the fields of physics and astronomy, Euler helped develop the Euler-Bernoulli beam equation, which later became a cornerstone for engineering. Not only did he have a remarkable ability to solve problems, he was also able to extend his knowledge on paper. He wrote book after book, article after article, becoming the most prolific writer of mathematics of all time. Such books included writings on the calculus of variations, the calculation of planetary orbits, artillery and ballistics, analysis, shipbuilding and navigation, the motion of the moon, and differential calculus.

Life and Works


Born on April 15, 1707 in Switzerland, Euler was the first of six children. Although he was born in Basel, he grew up in Riehen, Switzerland. He attended the University of Basel, and after graduating, he tried unsuccessfully to get a teaching job there. Instead, he took up a position at the Academy of Sciences in St. Petersburg, Russia. Like his parents, Leonhard followed Calvinist beliefs. He was a devout Christian all his life, despite his lack of enthusiasm for the study of theology, which has father pursued. His research stood alone in relevance to his religion. Married twice, he became a father to thirteen children with his second wife, Katharina Gsell. Five survived to adulthood, including sons Johann Albrecht and Christof. Johann did attain some fame in the field of physics. He was appointed to the chair of physics at the Academy in St. Petersburg in 1766. Christof, however, had a military career. One might assume that so many children would distract Leonhard Euler from his works, but with legendary power of memory and concentration, Euler was not troubled. In fact, he often times did much of his work with his young children playing at his feet.
In terms of publications, Mechanica was one of the most significant. This book started Euler on the way to major mathematical work, as it extensively presented Newtonian dynamics in the form of mathematical analysis for the first time. Another chief work was Introductio in Analysin Infinitorum (1748). It was intended to serve as an introduction to pure analytical mathematics. It contains the bulk of the matter that is to be found in modern textbooks on algebra, theory of equations, and trigonometry. Here, too we meet the symbols and
é, the incommensurable numbers 2.71828… and 3.14159…, respectively. The Analysis Infinitorum was followed by the Institutiones Calculi Differentialis in 1755. This is the first textbook on differential calculus that which has any claim to be regarded as complete. In short, he created a great deal of analysis, revising almost all of the branches of pure mathematics which were then known. He filled up the details, added proofs, and arranged the whole in a consistent form. Fortunately for science, such work fell into the hands of the extremely competent Leonhard Euler.

The Things He Left behind


In 2007, a public event took place to celebrate Euler’s 300th anniversary, demonstrating that his legacy lives on. Although he did not jump out of the bathtub and run through the streets like Archimedes, nor get hit in the head with an apple like Newton. He certainly did not discover how to add every number from 1 to 100 before age 10 either, like Gauss. He is not quite a household name, but he is undoubtedly one of the greatest mathematical scientists of all time. Today, Euler’s contributions shine through in Sudoku puzzles, terms such as “function, sine, cosine, and tangent,” as well as the calculus of variations. He is responsible for “the most remarkable formula in mathematics,” says Richard Feynman. This formula is: In addition, the asteroid 2002 Euler is named in his honor, and for nearly two decades, Euler was featured on a Swiss banknote. This is quite impressive, considering he was completely blind the last seventeen years of his life. His talents have done wonders for numerous mathematical fields! When he died, the mathematician and philosopher Marquis de Condorcet commented, “…il cessa de calculer et de vivre,” he ceased to calculate and ceased to live.


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