Leonhard Euler - DOC

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					Math 211 March 18, 2009

Leonhard Euler: The Forgotten Genius
Galileo Galilei, Isaac Newton, Johann Kepler, Blaise Pascal, Gauss, the list goes on of famous mathematicians and physicists. Ask any kid in middle school or high school about these men and a majority has at least heard of them. There are, however, many other men that have contributed greatly to math and physics. Maybe they aren’t as popular but they still left a lasting impression on our world. One of the many that are forgotten is Leonhard Euler. Euler had a diverse mind and contributed to many things throughout his life. From calculus to astronomy, Euler was a “jack of all trades” in every sense of the word. He was arguably the greatest mind of the 18th century. Euler’s contributions put him right up there with the stars of math and science. Euler carried integral calculus to a higher degree of perfection, developed the theory of trigonometric and logarithmic functions, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure mathematics (“Leonhard Euler (Swiss mathematician)”). He has numerous topics named after him including: Euler angles, Euler polynomials, Euler’s formula, Euler’s identity, an asteroid named 2002 Euler, Euler Medal, and even Euler’s number.

Personal Background
Of course, to really understand someone we need to know where they came from. Euler’s incredible skills were seemingly present from early in his life. Born in Basel, Switzerland in April of 1707, Euler’s parents were of strong religious background. His father was friends with Johann Bernoulli, one of the greatest mathematician’s of the time, so Leonhard had the distinct privilege of being exposed to math and science at an early age. He became lifelong friends with Bernoulli’s two sons, Daniel and Nicholas. Johann Bernoulli began teaching Euler on Saturdays and quickly discovered that Euler had a

talented mind. However, Euler’s father Paul wanted Leonhard to become a pastor. So Leonhard was studying languages and theology instead of math or physics. Bernoulli convinced Paul Euler that Leonhard was far too talented in math to be studying theology (“Leonhard Euler-“). In 1726, at the age of 19, Leonhard Euler achieved a Ph.D. About a year later, his good friend Nicolas Bernoulli, now working at the Imperial Russian Academy of Sciences with his brother Daniel, died of appendicitis. Euler then decided to move to St. Petersburg to work with Daniel Bernoulli. He and Daniel lived together in St. Petersburg as Euler got accustomed to Russian life. He quickly learned Russian. Euler became a professor of physics in 1731 and later the head the mathematics department in 1733.

The Works that Made Him Famous
At this point, Euler was considered a great mind. Those that worked with him, those that knew him, his students, they all knew that Euler was a brilliant man. But teaching in St. Petersburg meant a more modest, censored lifestyle. So when he moved in 1741 to work at Berlin Academy, Euler spread his wings. Euler would write the two most influential works of his life while working in Berlin, the Introductio in analysin infinitorum, a text on functions published in 1748, and the Institutiones calculi differentialis, published in 1755 on differential calculus (Dunham). In addition to these books, Euler wrote close to 400 articles on various topics. Another of Euler’s famous works was written at this time as well, Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess, a collection of letters written to the Princess of Anhalt-Dessau discussing physics and math and Euler’s personal opinions and religious beliefs. This book became more widely read than any of his mathematical works, and it was published across Europe and in the United States. The popularity of the 'Letters' testifies to Euler's ability to communicate scientific matters effectively to a lay audience, a rare ability for a dedicated research scientist (Dunham).Euler was eventually forced out of Berlin Academy

due to some differences with Frederick the Great. At that point, Euler decided to return to St. Petersburg Academy.

Specific Contributions
While on the subject of Euler’s works, let’s discuss his specific contributions to mathematics. Euler introduced the concept of a function, trigonometric functions, the letter e for the base of the natural logarithm, power series, exponential function, and the gamma function. In 1988, readers of the Mathematical Intelligencer voted Euler’s Identity "the Most Beautiful Mathematical Formula Ever" (Peterson).These, in addition to the many other contributions and discoveries, are the reason Euler deserves more credit than he receives. One of his greatest achievements is in the field of graph theory. He solved a problem called the Seven Bridges of Konigsberg. The city of Konigsberg, Prussia was located on the Pregel River. It was composed of two large islands which were connected to the mainland by a series of bridges. Euler coined the term Eulerian circuit to describe that there is no way to cross each bridge once and return to the starting point (“Leonhard Euler-“).There is no doubt that Euler had a great mind. But one of the things that are overlooked about him is how diverse his mind was. The number of fields that he let an impression on is astounding. From number theory, logic, and physics to astronomy, Euler was truly a visionary and genius.

Personal Life
Euler’s professional life was undoubtedly very interesting. His personal life, however, was also interesting. He was born and raised a Christian and kept those beliefs until the day he died. Euler was married to Katharina Gsell in 1734. He had thirteen children, but only 5 survived childhood (Rose Ball). Euler has many issues with his eyesight. In 1738 he lost almost all of his vision from his right eye. Frederick the Great called him “Cyclops” because his right eye was essentially blind and continued to

worsen as he got older. Then he got a cataract in his left eye, which made him almost totally blind. But amazingly enough, Euler continued to work “as he compensated for it with his mental calculation skills and photographic memory.” (“Leonhard Euler-“) Euler's productivity on many areas of study actually increased. He produced on average one mathematical paper every week in the year 1775 (“Leonhard Euler-“). His wife Katarina died in 1773 after 40 years of marriage. Three years later he married Katarina’s half-sister. He would be reunited with Katarina on September 18th 1783 when he passed away of a brain hemorrhage. He was buried with Katarina in the Smolensk Lutheran Cemetery on Vasilievsky Island. His remains now reside at Alexander Nevsky Lavra in St.Petersburg.

I, admittedly, did not know of Leonhard Euler before researching him for this paper. After reading about him and getting to know his works and his life story I have come to appreciate what he did for math and science. I’m sure there are many other men and women that have contributed as much if not more than Euler, but Leonhard Euler was a fascinating man and deserves to be talked about more than he is. His contributions made mathematics what it is today, and although he is popular in some fields, Euler should be put in the spotlight like Isaac Newton and Galileo Galilei for what he accomplished and what he battled to accomplish it. His ideas and discoveries are not only a part of our lives at school or at work, but in almost everything we do.

Works Cited Dunham, William. Euler the master of us all. [Washington, D.C.]: Mathematical Association of America, 1999. "Leonhard Euler -." Wikipedia, the free encyclopedia. 18 Mar. 2009 <>. "Leonhard Euler (Swiss mathematician) -- Britannica Online Encyclopedia." Encyclopedia Britannica Online Encyclopedia. 18 Mar. 2009 <>. "LEONHARD EULER." United States Naval Academy - Home Page. 18 Mar. 2009 <>. Peterson, Ivars. "The Mathematical Tourist - Euler's Beauties." Mathematical Association of America: MAA Online. 18 Mar. 2009 <>. Rouse Ball, W. W. "Leonhard Euler (1707 - 1783)." TCD School of Mathematics. 18 Mar. 2009 <>.

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