Leonhard Euler

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The following webpage is recognition for one of the greatest mathematicians of the eighteenth century. Leonhard Euler is said to be the most prolific mathematician of all times with the publishing of over 800 different books and papers. With his contribution to number theory, analysis, algebra, and geometry, there is hardly a branch of mathematics in which he did not play a significant role. In the following webpage, a tiny fraction of Euler’s life and achievements will be examined.

Biography

Born Leonard Euler in the spring of 1707 near Basil, Switzerland, little was known about the effect he would have on mathematics. With his father, Paul Euler, being a Protestant clergyman and his mother coming from a pastoral family, one would say young Euler was destined for ministry. As a youth, Euler became drawn to mathematics. At the age of fourteen, he entered the University of Basel in which he united with Johann Bernoulli, its most famous professor. Taking Euler under his wing, Bernoulli became a guide for Euler by allowing him to discuss topics that seemed especially difficult to understand. Bernoulli soon picked up on Euler’s intellect and was quick to realize he was something special. Upon graduating, Euler put aside mathematics and entered divinity school to study for the ministry. But the call of mathematics was too strong, forcing him to leave the ministry to others. Euler would soon become a mathematician. He accepted a position at the St. Petersburg Academy alongside Johann’s son Daniel Bernoulli in 1725 to teach physiology/medicine. The position was reassigned to physics upon his arrive to Russia, a subject Euler was much more familiar. Years later when Daniel departed from the Academy, the chair in mathematics was left open and then soon filled by Euler. With his comfortable life, he soon married Katharina Gsell. Together as a happy and productive couple, they had thirteen children; only five surpassed adolescence. Euler’s fame was increasing due to his many mathematical triumphs. Writing paper after paper into the journal of the St. Petersburg Academy, he continued his research. He seemed to be living the perfect life until his eyesight began to deteriorate. In 1738, he lost vision in his right eye; years to come, he would also suffer the failure to his remaining good eye. This impairment did not stop Euler in which he continued his research. Working through his physical disability, he made discoveries in classical number theory, analytic number theory and laid the groundwork for the theory of partitions. In 1741, Prussia’s Frederick the Great offered Euler membership to the Berlin Academy in which he accepted and moved to Germany. While living in Germany, Euler published two of his most famous works; Introductio in analysin infinitorum and Institutiones calculi differentialis. He also published a multi-volume (200 letters) masterpiece of exposition to the Princess of Anhalt Dessau providing instruction in elementary science topics such as light, sound, gravity, logic, language, magnetism, and astronomy. Becoming an international hit, Letters to a German Princess continues to be one of history’s finest works of popular science. Euler was forced out of the Berlin Academy and returned to St. Petersburg Academy in 1766 in which he would stay for good. They were more than willing to welcome back the greatest mathematician in the world. One might conclude that Euler’s productive days had come to in end with the recent death of his wife in 1783 and complete blindness in 1771 but nothing could stop his passion for research. This was shown by his increased output by writing on average, one mathematical paper per week. Searching for companionship, three years after the death of his wife, he married his half sister in which he spent for the remainder of his life. In 1773, Euler died instantly from a massive hemorrhage and was laid to rest in St. Petersburg.

Personality

Even though Euler was the greatest mathematician of the eighteenth century he never let his intelligence fill his head. He was a fairly conservative person filled with kindness and generosity. When looking at the eighteenth century’s better known figures (i.e. Benjamin Franklin or George Washington), one would say Euler lacked flair. Rather than commanding armies to victory, he worked behind the scenes by being devoted to his passion of mathematics. He was also a hardworking family man and a devout Protestant. Maybe not in the physical sense but Euler was a great adventurer. His adventures were of the intellectual sort, carrying him through a wonderful mathematical landscape. This was shown through his discoveries of mathematical topics in which never existed before. Even when his physical disability got the best of him, he was never one to let personal misfortune interfere with his attitude toward the wonders of the Nature. His blindness caused him to work even hard then before.

Achievements

Earned recognition in an international scientific competition for his analysis of the placement of masts on a sailing ship

Mathematics professor at St. Petersburg Academy

Provided a solution to the unsolved “Basal Problem”; The issue was to determine the exact value of the infinite series:

1+1/4+1/9+1/16+1/25+……+1/k^2+…

Wrote the text Mechanica, which has been called “a landmark in the history of physics”

Published Introductio in analysin infinitorum and Institutiones calculi differentialis

Published Letters of Euler on Different Subjects in Natural Philosophy Addressed to a German Princess to Princess of Anhalt Dessau

In 1775, wrote an average of one mathematical paper per week despite his blindness

Discovered Euler’s line (red line), which showed that in any triangle, four points are collinear

Discovered Euler’s Formula: cos(x) + isin(x) = e^(ix) , which shows the relationship between analysis, trignometry and imaginary numbers

Published over 800 different books and papers

Elected a foreign member of the Academy of Sciences at Paris

Euler's line

Contributions to the History of Computing

Leonhard Euler may not have contributed directly to the history of computing but he did provided expandable knowledge to mathematics which became the soul purpose of computers in the 17^th century. During this time, calculations were configured by human computers. Euler was a remarkable mental calculator in which he could complete difficult computations without the use of a pencil and paper. This process was found to be tedious and error prone which caused inventors to consider a simpler option. This is where Charles Babbage came into play by inventing two calculating machines, the Difference Engine and the Analytical Engine. The idea of how to eliminate human intervention became Babbage’s drive for these two machines. With Euler’s contribution to mathematics through number theory, analysis, algebra, and geometry and a drive for less tedious calculating approach, Euler has indirectly become a factor to the history of computing. With computers today based conceptually on the algebra of logic, they can be found applying commercial to banking, routine record keeping, engineering design, and quality control in manufacturing.

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Works Cited

Anna Sickler

Stony Brook University

CSE 301 – History of Computing

Spring 2007