I was born on April 1707 in Basel, Switzerland. My father Paul Euler was a pastor of the Reformed Church and my mother, Marguerite Brucker, was a pastor’s daughter. I had two younger sisters named Anna Maria and Maria Magdalena. After I was born my family moved to Riehen where I spent most of my childhood. Johann Bernoulli, a family friend, and one of the most highly regarded mathematicians of our time, was my biggest influence and pushed me into the world of mathematics and science (“Leonhard Euler”, Wikipedia: The Free Encyclopedia).
My academic career started at age 13 when I enrolled in the University of Basel. In 1723 I received a master’s degree of philosophy with a dissertation that compared the philosophies of Descartes and Newton. My obvious professonal path at this point was clergy or at least that was what my father desired, so I studied theology, Greek and Hebrew. If it wasn’t for Johann Bernoulli to convince my father that I have a future in mathematics I would have spent my days serving god’s wishes. My carreer turn allowed me to complete my Ph.D. dissertation in propagandation of sound in 1926. A year later I entered the annual Paris Academy Prize Problem competition that tries to find the best way to place the masts on a ship. I came second, but won the competition 12 times after that (“Leonhard Euler”, Wikipedia: The Free Encyclopedia).
July 1726 brought a very saddening moment in my life when my friend and son of Johann Bernoulli, Nicholas, died. At that time he and his brother Daniel were working at the Imperial Russian Academy of Sciences in St Petersburg. After his brother’s death Daniel invited me to take his own position because he was to take over the position of Nicholas in the mathematics/ physics division. Eager to take on a position in the Academy in St Petersburg I accepted the offer and came to Russia in May 1726. I mastered Russian, worked closely with Daniel Bernoulli, and even took a second job as a medic for the Russian Navy. At this time the Academy in St Petersburg was a very attractive place to many scholars. It was the perfect place to pursue research and scientific questions. Unfortunately, shortly after my arrival, the Academy’s benefactress, Catherine I, died and with the rise of the power of the suspicious Russian nobility the funding was decreased and caused me numerous problems. In 1731 I was made professor of physics after the conditions in the academy had improved following the death of Peter II. In 1733 I became the head of the mathematics department because my friend Daniel Bernoulli left for Basel (“Leonhard Euler”, Wikipedia: The Free Encyclopedia).
During January of the following year I married the daughter of a painter from the Academy Gymnasium, Katharina Gsell. Our marriage brought us thirteen children but only five of them were able to survive childhood. 1735 brought me a near-fatal fever which also affected my eyesight and I became nearly blind in my right eye. During later years, my vision became progressively worse but I was able to compensate with my mental calculation skills and photographic memory. I have been known to easily recite the Aeneid of Virgil from beginning to end and I can also indicate which line is first and which line is last on each page (“Leonhard Euler”, Wikipedia: The Free Encyclopedia).
The turmoil in Russia concerned me and in 1741 I accepted a position at the Berlin academy offered to me by Frederick the Great of Prussia. The next twenty five years of my life I spent in Berlin where I wrote over three hundred and eighty articles. Some of them I contributed to the St Petersburg Academy which later granted me my pension (“Euler, Leonhard.” Encyclopædia Britannica). While in Berlin, I was also asked to tutor Frederick’s niece, the Princess of Anhalt- Dessau. For years I wrote to her over 200 letters about different subjects, raging from my own personal believes to physics and mathematics. After my long stay in Berlin I was finally forced to leave. Difference in thinking and personality brought me further apart from Frederick. He had become much closer with other philosophers, especially Voltaire, who enjoyed a very favorable position among Frederick’s circle. I often got into conflicts with Voltaire and Frederick because I had little training in rhetoric but I did not hesitate to argue about things that I did not necessarily know much about. On one occasion Frederick even expressed his disappointment with my practical engineering abilities:
“I wanted to have a water jet in my garden: Euler calculated the force of the wheels necessary to raise the water to a reservoir, from where it should fall back through channels, finally spurting out in Sanssouci. My mill was carried out geometrically and could not raise a mouthful of water closer than fifty paces to the reservoir. Vanity of vanities! Vanity of geometry!” (“Leonhard Euler”, Wikipedia: The Free Encyclopedia).
In 1766 I returned to Russia where I spent the rest of my life. Even though conditions in the country had improved drastically after the ascension of Catherine the Great, my life there was more tragic than it had been in my previous years there. Soon after my arrival at St. Petersburg, a cataract formed in my remaining good eye and I spent the rest of my life in total blindness (“Euler, Leonhard.” Encyclopædia Britannica). A fire in St Petersburg in 1771 almost cost me my life and then two years later I lost my dear wife of forty years (“Leonhard Euler”, Wikipedia: The Free Encyclopedia).
As far as my contributions to mathematics go, I spent a lot of time throughout my life working on different areas ranging from geometry, trigonometry, algebra, and number theory to calculus. My works introduced the concept of function, and the notation f(x) to denote the function f to the argument x. I also introduced the letter e to denote the base of a natural logarithm, the ∑ for summations, and i for imaginary unit. I also tried to simplify trigonometric values as ratios and represented the angles of a triangle by A, B, and C and the corresponding sides by a, b, and c (“Leonard Euler.”, Encyclopedia of World Biography” ; Leonhard Euler”, Wikipedia: The Free Encyclopedia). I published my first book in 1748- Introductio in Analysin Infinitorum. The first volume of the book talks about the theory of functions, in particular, that of exponential, logarithmic, and trigonometric functions. I developed these functions as infinite series and solved the problem of logarithms of negative and imaginary numbers, probing that e is irrational. The second volume of my book was concerned with the analytical study of curves and surfaces (“Leonard Euler.”, Encyclopedia of World Biography”).
One of my greatest interests in my work has been number theory. A lot of my early work on it was based on the works of Pierre de Fermat. One of his most famous propositions states that the equation xn + yn = zn has no solutions for n greater than 2. I was able to demonstrate the theorem for n = 3 and n = 4 (“Leonard Euler.”, Encyclopedia of World Biography”).
Another contribution to number theory was my generalization of Fermat’s little theory where I have concluded that if n is a positive integer and a is coprime to n, then aφ(n) ≡ 1(mod n). Obviously I had to invent the totient function φ(n) which assigns to a positive function of n the number of positive integers less than n and coprime to n (“Leonhard Euler”, Wikipedia: The Free Encyclopedia).
| In the year 1736 I was able to solve the Seven Bridges of Königsberg problem and showed that there was no way to find a path through the town that crosses each bridge exactly once and returns to the starting point. |
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(“Leonhard Euler”, Wikipedia: The Free Encyclopedia)
One of my many other interests involved the use of mathematics in music. My work in this field was never taken very seriously and remained unappreciated by the public. Many thought that it was just “too much mathematical for musicians and too musical for mathematicians” (“Leonhard Euler,” Wikipedia: The Free Encyclopedia). As I mentioned before, my interests often span beyond pure mathematics. Working with Bernoulli we developed what came to be known as the Euler-Bernoulli equation. I also worked on astronomical problems and my work was recognized many times by prizes from the Paris Academy. These prizes were given to me for determining the orbits of comets and other celestial bodies, calculating the parallax of the sun, and understanding the nature of comets (“Leonhard Euler”, Wikipedia: The Free Encyclopedia).
Bibliography:
“Euler, Leonhard.” Encyclopædia Britannica. 2007. Encyclopædia Britannica Online. 24 Mar. 2007 http://www.britannica.com/eb/article-9033216.
“Leonard Euler.” Encyclopedia of World Biography. Ed. Paula K. Byers. Vol. 5. 2nd ed. Detroit: Gale, 1998. 331-332. 23 vols. Gale Virtual Reference Library. Thomson Gale. Nassau Community College Library – SUNY. 24 Mar. 2007 http://find.galegroup.com/gvrl/infomark.do?&contentSet=EBKS&type=retrieve&tabID=T001&prodId=GVRL&docId=CX3404702050 &source=gale&userGroupName=sunynassau&version=1.0.
“Leonhard Euler.” Wikipedia, The Free Encyclopedia. 24 Mar 2007, 08:27 UTC. Wikimedia Foundation, Inc. 24 Mar 2007 http://en.wikipedia.org/w/index.php?title=Leonhard_Euler&oldid=117481390
Information Literacy for MAT 225 