Everything about Leonhard Euler totally explained
Leonhard Paul Euler (pronounced ; (OIL-ER)
April 15,
1707 – ) was a pioneering
Swiss mathematician and
physicist who spent most of his life in
Russia and
Germany.
Euler made important discoveries in fields as diverse as
calculus and
graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for
mathematical analysis, such as the notion of a
mathematical function. He is also renowned for his work in
mechanics,
optics, and
astronomy.
Euler is considered to be the preeminent mathematician of the 18th century and one of the greatest of all time. He is also one of the most prolific; his collected works fill 60–80
quarto volumes.
Euler was featured on the sixth series of the Swiss 10-
franc banknote and on numerous Swiss, German, and Russian
postage stamps. The
asteroid 2002 Euler was named in his honor. He is also commemorated by the
Lutheran Church on their
Calendar of Saints on
May 24th.
Biography
Early years
Euler was born in
Basel to Paul Euler, a
pastor of the
Reformed Church, and Marguerite Brucker, a pastor's daughter. He had two younger sisters named Anna Maria and Maria Magdalena. Soon after the birth of Leonhard, the Eulers moved from Basel to the town of
Riehen, where Euler spent most of his childhood. Paul Euler was a friend of the
Bernoulli family—
Johann Bernoulli, who was then regarded as Europe's foremost
mathematician, would eventually be the most important influence on young Leonhard. Euler's early formal education started in Basel, where he was sent to live with his maternal grandmother. At the age of thirteen he matriculated at the
University of Basel, and in 1723, received his
M.Phil with a dissertation that compared the philosophies of
Descartes and
Newton. At this time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupil's incredible talent for mathematics.
Euler was at this point studying
theology,
Greek, and
Hebrew at his father's urging, in order to become a pastor. Johann Bernoulli intervened, and convinced Paul Euler that Leonhard was destined to become a great mathematician. In 1726, Euler completed his Ph.D. dissertation on the
propagation of sound with the title
De Sono and in 1727, he entered the
Paris Academy Prize Problem competition, where the problem that year was to find the best way to place the
masts on a ship. He won second place, losing only to
Pierre Bouguer—who is now known as "the father of naval architecture". Euler subsequently won this coveted annual prize twelve times in his career.
St. Petersburg
Around this time Johann Bernoulli's two sons,
Daniel and
Nicolas, were working at the
Imperial Russian Academy of Sciences in
St Petersburg. In July 1726, Nicolas died of
appendicitis after spending a year in Russia, and when Daniel assumed his brother's position in the mathematics/physics division, he recommended that the post in physiology that he'd vacated be filled by his friend Euler. In November 1726 Euler eagerly accepted the offer, but delayed making the trip to St Petersburg while he unsuccessfully applied for a physics professorship at the University of Basel.
Euler arrived in the Russian capital on
May 17,
1727. He was promoted from his junior post in the medical department of the academy to a position in the mathematics department. He lodged with Daniel Bernoulli with whom he often worked in close collaboration. Euler mastered
Russian and settled into life in St Petersburg. He also took on an additional job as a medic in the
Russian Navy.
The Academy at St. Petersburg, established by
Peter the Great, was intended to improve education in Russia and to close the scientific gap with Western Europe. As a result, it was made especially attractive to foreign scholars like Euler. The academy possessed ample financial resources and a comprehensive library drawn from the private libraries of Peter himself and of the nobility. Very few students were enrolled in the academy so as to lessen the faculty's teaching burden, and the academy emphasized research and offered to its faculty both the time and the freedom to pursue scientific questions.
The Academy's benefactress,
Catherine I, who had continued the progressive policies of her late husband, died on the day of Euler's arrival. The Russian nobility then gained power upon the ascension of the twelve-year-old
Peter II. The nobility were suspicious of the academy's foreign scientists, and thus cut funding and caused other difficulties for Euler and his colleagues.
Conditions improved slightly upon the death of Peter II, and Euler swiftly rose through the ranks in the academy and was made professor of physics in 1731. Two years later, Daniel Bernoulli, who was fed up with the censorship and hostility he faced at St. Petersburg, left for Basel. Euler succeeded him as the head of the mathematics department.
On
January 7,
1734, he married Katharina Gsell, daughter of a painter from the Academy Gymnasium. The young couple bought a house by the
Neva River. Of their thirteen children, only five survived childhood.
Berlin
Concerned about the continuing turmoil in Russia, Euler left St. Petersburg on
June 19,
1741 to take up a post at the
Berlin Academy, which he'd been offered by
Frederick the Great of Prussia. He lived for twenty-five years in
Berlin, where he wrote over 380 articles. In Berlin, he published the two works which he'd be most renowned for: the
Introductio in analysin infinitorum, a text on functions published in 1748, and the
Institutiones calculi differentialis, published in 1755 on
differential calculus.
In addition, Euler was asked to tutor the Princess of Anhalt-Dessau, Frederick's niece. Euler wrote over 200 letters to her, which were later compiled into a best-selling volume entitled
Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess. This work contained Euler's exposition on various subjects pertaining to physics and mathematics, as well as offering valuable insights into Euler's personality 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.}}
Eyesight deterioration
Euler's eyesight worsened throughout his mathematical career. Three years after suffering a near-fatal fever in 1735 he became nearly blind in his right eye, but Euler rather blamed his condition on the painstaking work on
cartography he performed for the St. Petersburg Academy. Euler's sight in that eye worsened throughout his stay in Germany, so much so that Frederick referred to him as "
Cyclops". Euler later suffered a
cataract in his good left eye, rendering him almost totally blind a few weeks after its discovery. Even so, his condition appeared to have little effect on his productivity, as he compensated for it with his mental calculation skills and
photographic memory. For example, Euler could repeat the
Aeneid of
Virgil from beginning to end without hesitation, and for every page in the edition he could indicate which line was the first and which the last. With the aid of his scribes, Euler's productivity on many areas of study actually increased. He produced on average one mathematical paper every week in the year 1775.
Return to Russia
The situation in Russia had improved greatly since the accession to the throne of
Catherine the Great, and in 1766 Euler accepted an invitation to return to the St. Petersburg Academy and spent the rest of his life in Russia. His second stay in the country was marred by tragedy. A fire in St. Petersburg in 1771 cost him his home, and almost his life. In 1773, he lost his wife of 40 years. Three years after his wife's death Euler married her half sister. This marriage would last until his death.
On
September 18,
1783, Euler passed away in St. Petersburg after suffering a
brain hemorrhage, and was buried with his wife in the Smolensk Lutheran Cemetery on
Vasilievsky Island (the Soviets destroyed the cemetery after transferring Euler's remains to the Orthodox
Alexander Nevsky Lavra). His eulogy was written for the French Academy by the French mathematician and philosopher
Marquis de Condorcet, and an account of his life, with a list of his works, by Nikolaus von Fuss, Euler's son-in-law and the secretary of the
Imperial Academy of St. Petersburg.
Condorcet commented,
Contributions to mathematics
geometry,
calculus,
trigonometry,
algebra, and
number theory, as well as continuum physics, lunar theory and other areas of physics. He is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80
quarto volumes. The use of the Greek letter
π to denote the
ratio of a circle's circumference to its diameter was also popularized by Euler, although it didn't originate with him.
Analysis
The development of
calculus was at the forefront of 18th century mathematical research, and the Bernoullis—family friends of Euler—were responsible for much of the early progress in the field. Thanks to their influence, studying calculus became the major focus of Euler's work. While some of Euler's proofs are not acceptable by modern standards of
mathematical rigour, his ideas led to many great advances.
He is well known in analysis for his frequent use and development of
power series: that is, the expression of functions as sums of infinitely many terms, such as
»
One of Euler's more unusual interests was the application of mathematical ideas in
music. In 1739 he wrote the
Tentamen novae theoriae musicae, hoping to eventually incorporate
musical theory as part of mathematics. This part of his work, however, didn't receive wide attention and was once described as too mathematical for musicians and too musical for mathematicians.
Physics and astronomy
Euler helped develop the
Euler-Bernoulli beam equation, which became a cornerstone of engineering. Aside from successfully applying his analytic tools to problems in
classical mechanics, Euler also applied these techniques to celestial problems. His work in astronomy was recognized by a number of Paris Academy Prizes over the course of his career. His accomplishments include determining with great accuracy the orbits of comets and other celestial bodies, understanding the nature of comets, and calculating the
parallax of the sun. His calculations also contributed to the development of accurate
longitude tables.
In addition, Euler made important contributions in
optics. He disagreed with Newton's corpuscular theory of light in the
Opticks, which was then the prevailing theory. His 1740s papers on optics helped ensure that the
wave theory of light proposed by
Christian Huygens would become the dominant mode of thought, at least until the development of the
quantum theory of light.
Logic
He is also credited with using
closed curves to illustrate
syllogistic reasoning (1768). These diagrams have become known as
Euler diagrams.
Personal philosophy and religious beliefs
Euler and his friend Daniel Bernoulli were opponents of
Leibniz's monism and the philosophy of
Christian Wolff. Euler insisted that knowledge is founded in part on the basis of precise quantitative laws, something that monadism and Wolffian science were unable to provide. Euler's religious leanings might also have had a bearing on his dislike of the doctrine; he went so far as to label Wolff's ideas as "heathen and atheistic".
Much of what is known of Euler's religious beliefs can be deduced from his
Letters to a German Princess and an earlier work,
Rettung der Göttlichen Offenbahrung Gegen die Einwürfe der Freygeister (
Defense of the Divine Revelation against the Objections of the Freethinkers). These works present Euler as a staunch
Christian and a
biblical literalist (for example, the
Rettung was primarily an argument for the
divine inspiration of scripture).
There is a famous anecdote inspired by Euler's arguments with secular philosophers over religion, which is set during Euler's second stint at the St. Petersburg academy. The French philosopher
Denis Diderot was visiting Russia on Catherine the Great's invitation. However, the Empress was alarmed that the philosopher's arguments for
atheism were influencing members of her court, and so Euler was asked to confront the Frenchman. Diderot was later informed that a learned mathematician had produced a proof of the
existence of God: he agreed to view the proof as it was presented in court. Euler appeared, advanced toward Diderot, and in a tone of perfect conviction announced, "Sir,
(a + bn)⁄
z =
x, hence God exists—reply!". Diderot, to whom (says the story) all mathematics was gibberish, stood dumbstruck as peals of laughter erupted from the court. Embarrassed, he asked to leave Russia, a request that was graciously granted by the Empress. However amusing the anecdote may be, it's apocryphal, given that Diderot was a capable mathematician who had published mathematical treatises.
Selected bibliography
Euler has an
extensive bibliography but his best known books include:
Elements of Algebra
. This elementary algebra text starts with a discussion of the nature of numbers and gives a comprehensive introduction to algebra, including formulae for solutions of polynomial equations.
Introductio in analysin infinitorum (1748). English translation Introduction to Analysis of the Infinite by John Blanton (Book I, ISBN 0-387-96824-5, Springer-Verlag 1988; Book II, ISBN 0-387-97132-7, Springer-Verlag 1989).
Two influential textbooks on calculus: Institutiones calculi differentialis (1755) and Institutiones calculi integralis (1768–1770).
Lettres à une Princesse d'Allemagne (Letters to a German Princess) (1768–1772). Available online (in French). English translation, with notes, and a life of Euler, available online from Google Books: Volume 1, Volume 2
Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici latissimo sensu accepti (1744). The Latin title translates as a method for finding curved lines enjoying properties of maximum or minimum, or solution of isoperimetric problems in the broadest accepted sense.
A definitive collection of Euler's works, entitled Opera Omnia, has been published since 1911 by the Euler Commission of the Swiss Academy of Sciences.
Further Information
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