Biography of Leonard Euler

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Humble Beginnings St. Petersburg Berlin Academy Back to Russia: The Most Prolific Period Interesting Facts/Last Years Works Cited

Leonard Euler was one of history’s most prolific mathematicians. Born on April 15, 1707 in Basel, Switzerland, Euler was the first of six children. His father was a Protestant priest, and expected Euler to follow in his footsteps. His father had also studied mathematics under the tutelage of Jacob Bernoulli, and he wanted his son to do the same. Euler obeyed his father’s wishes by studying theology and taking weekly mathematics lessons from Johann Bernoulli, Jacob’s younger brother. Gifted with a brilliant mind at an early age, he received his master’s degree at the age of 16 from the University of Basel. Witnessing this accomplishment, the Bernoulli’s suggested he pursue a mathematics career, which met with much resistance from Euler’s father. His love of math eventually won out, and Euler decided to pursue mathematics and put the ministry aside (“Euler,” Notable Mathematicians 2). His mathematical contributions came later in life, and helped advance the field of calculus, trigonometry, and even topology. It was Euler’s genius that led to his writings and discoveries, which is why he is such an integral part of the history of mathematics.

Euler’s connections helped him attain his first teaching position at St. Petersburg. Euler had been trying unsuccessfully to get a teaching job at the University of Basel, when he received help from Daniel and Nicholas Bernoulli. They were able to get Euler a position at the St. Petersburg Academy of Sciences teaching physiology, a subject which he had no prior knowledge. Despite this inconvenience, Euler was determined to learn as much as he could about the subject in the three months before he began the job. Fortunately for him, his arrival at St. Petersburg coincided with the death of the wife of Peter the Great. Amidst the turmoil, the young mathematician slipped quietly into a mathematics position at the Academy in the early 1730s (“Euler,” Math and Mathematicians 2).

Euler had already been producing high-quality mathematical papers when in 1733 Daniel Bernoulli left the Academy because of political turmoil. Daniel Bernoulli commanded the top mathematical position at the Academy, and when he left it was Euler who took over. It was here where Euler met his wife, Katharina Gsell. The two had 13 children, but unfortunately only five made it to maturity. Additionally, Euler went blind in his right eye in 1735 from staring at the sun trying to figure out an astronomy problem (“Euler,” Notable Mathematicians 2).

While in St. Petersburg, Euler performed many important calculations for the Russian government as well as several mathematical advancements. One of his most important works came with the problem of the Konigsberg bridge. The town of Konigsberg had a river running through it, with two islands in the center of the river. The townsfolk built a series of seven bridges connecting the two islands and the two sides of the river. It was set where three bridges connected to both sides of the river, four bridges connected to the first island, and three connected to the second island. It was asked whether or not it was possible to cross all the bridges only once in just one trip. Euler figured that if “k” represented the number of bridges approaching a region, then (k+1)/2 and k/2 represented the number of times a region with an odd and even number of bridges respectfully could be crossed without violating the rules. He then figured that if the sum of these numbers was greater than the total number of bridges plus one (in this case 8, since 7+1=8), then it was impossible to cross all the bridges only once in one trip, which was the case of the Konigsberg bridges. Euler’s accomplishments with this problem led to the modern field of graph theory in topology (Katz 636).

Still in St. Petersburg, Euler published his ideas on differential equations and their relation to trigonometric equations. At the time, higher-order equations could be solved with exponential functions. But when given a problem dealing with vibrations of an elastic band, Euler realized that exponential functions would not be sufficient. He was able to solve the problem with a power series, but did not realize until 1739 that this series could be represented with a sine or cosine function. The equation he came up with was both the earliest use of sine as a function of time, and the earliest use of the sine function in a differential equation (Katz 555). Top

In 1741, Euler left St. Petersburg for Germany where he made several important achievements in calculus and its applications. He grew tired of the political turmoil in Russia, and accepted an invitation from Frederick the Great to teach at the Berlin Academy. It was here that Euler published his ideas on the calculus of variations. In 1748 he published the first of three volumes of calculus analysis. Entitled Introduction to Analysis of the Infinite, the work concentrated mainly on precalculus and worked with transcendental and algebraic functions. All modern treatments of exponential, logarithmic, and trigonometric functions are derived from Euler’s publication. For example, in this book he was the first to define the inverse of the log function as an exponential function. In 1755 the second volume of this series, Calculus of Differentiation, was published. Here Euler gave a purely analytical view on differentiation (Katz 567-73).

Outside of this highly analytical standpoint, Euler also worked on many practical mathematical projects while at Berlin. Among the projects he worked on for Frederick the Great were: pension plans, navigation calculations, national coinage, and water supply systems. More importantly, Euler published important work on mechanics of solid bodies. He was able to arrive at a general equation of motion, as well as did work concerning bodies rotating around a center of mass. He later introduced the term “moment of inertia” to represent this type of motion (“Euler,” Encyclopedia of World Biography 30). Today this term is an integral part of physics and dynamics.

Euler eventually made it back to St. Petersburg, where he entered the most prolific period of his life, despite a heavy handicap. While in Berlin, Euler opposed the opinions of Voltaire and became disfavored by Frederick the Great, who would often call him a “mathematical Cyclops" (“Euler,” Math and Mathematicians 3). In July of 1766 he moved back to St. Petersburg at the invitation of Catherine the Great, who had recently come into power. Unfortunately, Euler went completely blind when he returned due to a cataract in his left eye. Amazingly, nearly half of his 886 books and manuscripts were created during this period. For example, he calculated the motion and positioning of the Moon and resulting tides, and was able to calculate the orbit of Uranus. Probably the most important manuscript he created was a classical treatise on integral calculus, called Methods of Integral Calculus. In the third installment of his examination of calculus, he examined integration in-depth. Interestingly, although much of his work has applications in real-world scenarios, this book dealt with integration on a purely analytical level. Euler never thought of integration in terms of tangent lines, normal lines, or area; he only thought of it as antidifferentiation. It was in this treatise that Euler also gave the first detailed explanation of a double integral (Katz 573-5).

Aside from his mathematics, Euler was also known for other talents and qualities that remained with him until his death. It is difficult for anyone to achieve the mathematical comprehension of Euler, but it is even more difficult to be able to communicate that knowledge to others. Nonetheless, he established a reputation as a superior educator, with one of his best-known qualities being his willingness to explain his discoveries in great detail. He was also kind and generous, and loved playing with children. Ironically, Euler died on September 18, 1783 from a sudden heart attack while playing with his grandson (“Euler,” Notable Mathematicians 3).

Leonard Euler was an important mathematician for his contributions and discoveries in both pure and applied mathematics. Thanks to his connections to the Bernoulli family, Euler was able to get a strong foundation in math, and attained a teaching position at the prestigious St. Petersburg Academy of Sciences. Euler’s genius and seemingly inexhaustible energy led him to make great discoveries in geography at St. Petersburg, and in physics and calculus while in Berlin. This energy and genius was further exemplified when Euler entered his most prolific period while blind. Euler’s outstanding contributions in both pure and applied mathematics have greatly influenced the math of today and will no doubt do the same for the future.

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Works Cited

“Euler, Leonard.” Encyclopedia of World Biography. 12 vols. New York:

McGraw-Hill, 1973.

“Euler, Leonard.” Math and Mathematicians: The History of Math Discoveries around

the World. Biography Research Center. 1999.

http://galenet.galegroup.com/servlet/BioRC?c=2/ (1 September 2002).

“Euler, Leonard.” Notable Mathematicians: from Ancient Times to the Present.

Biography Research Center. 1998.

http://galenet.galegroup.com/servlet/BioRC?c=3/ (1 September 2002).

Katz, Victor. A History of Mathematics: An Introduction. 2^nd ed. New York:

Addison Wesley Longman, 1998.