- Leonhard Euler
Infobox Scientist

name = Leonhard Euler|box_width = 300px

|200px

image_width = 200px

caption = Portrait by Johann Georg Brucker

birth_date = birth date|df=yes|1707|4|15

birth_place =Basel ,Switzerland

death_date = 18 September (O.S 7 September) 1783, (aged 76)

death_place =St. Petersburg ,Russia

residence = Prussia,Russia

Switzerland

citizenship =

nationality = Swiss

ethnicity =

field =Mathematician andPhysicist

work_institutions = Imperial Russian Academy of Sciences

Berlin Academy

alma_mater =University of Basel

doctoral_advisor =Johann Bernoulli

doctoral_students = Johann HennertJoseph Lagrange

known_for =

author_abbrev_bot =

author_abbrev_zoo =

influences =

influenced =

prizes =

religion = Calvinist [*cite book|title=Scientists of Faith|author=Dan Graves|location=Grand Rapids, MI|year=1996|publisher=Kregel Resources|pages=85–86*] [*cite book|title=Men of Mathematics, Vol. 1|author=E. T. Bell|location=London|year=1953|publisher=Penguin|pages=155*]

footnotes =**Leonhard Paul Euler**(pronounced|ˈɔɪlɐ in German, IPAlink-en|ˈɔɪlɚ respell|OY|lər in English; [*The common English pronunciation IPAlink-en|ˈjuːlɚ respell|EW|lər is generally considered incorrect.*] 15 April 1707 – OldStyleDate|18 September|1783|7 September) was a pioneering Swissmathematician andphysicist who spent most of his life inRussia andGermany .Euler made important discoveries in fields as diverse as

calculus andgraph theory . He also introduced much of the modern mathematical terminology and notation, particularly formathematical analysis , such as the notion of a mathematical function.cite book| last = Dunham| first = William | authorlink=William Dunham (mathematician) | title = Euler: The Master of Us All| year = 1999| publisher =The Mathematical Association of America | pages = 17] He is also renowned for his work inmechanics ,optics , andastronomy .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. A statement attributed to

Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master [i.e., teacher] of us all."cite book| last = Dunham| first = William| title = Euler: The Master of Us All| year = 1999 | publisher =The Mathematical Association of America | pages = xiii | quote=Lisez Euler, lisez Euler, c'est notre maître à tous.]Euler was featured on the sixth series of the Swiss 10-franc banknote and on numerous Swiss, German, and Russian

postage stamp s. Theasteroid 2002 Euler was named in his honor. He is also commemorated by theLutheran Church on their Calendar of Saints on 24 May - he was a devout Christian (and believer inbiblical inerrancy ) who wrote apologetics and argued forcefully against the prominent atheists of his time.**Life****Early years**Euler was born in Basel to Paul Euler, a

pastor of theReformed 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 ofRiehen , where Euler spent most of his childhood. Paul Euler was a friend of theBernoulli family —Johann Bernoulli , who was then regarded as Europe's foremostmathematician , 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 theUniversity of Basel , and in 1723, received hisM.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.cite book |last= James |first= Ioan |title= Remarkable Mathematicians: From Euler to von Neumann |publisher= Cambridge |year= 2002|pages=2 |id= ISBN 0-521-52094-0]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" [*PDFlink| [*] 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*http://www.17centurymaths.com/contents/euler/e002tr.pdf Translation of Euler's Ph.D in English by Ian Bruce*] |232 KiBPierre Bouguer —who is now known as "the father of naval architecture". Euler subsequently won this coveted annual prize twelve times in his career.cite journal| author = Calinger, Ronald | year = 1996| title = Leonhard Euler: The First St. Petersburg Years (1727–1741)| journal = Historia Mathematica| volume = 23| issue = 2| pages = 156 | doi = 10.1006/hmat.1996.0015 ]**t. 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 ofappendicitis 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 had 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.cite journal| author = Calinger, Ronald | year = 1996| title = Leonhard Euler: The First St. Petersburg Years (1727–1741)| journal = Historia Mathematica| volume = 23| issue = 2| pages = 125 | doi = 10.1006/hmat.1996.0015 ]Euler arrived in the Russian capital on 17 May 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 .cite journal| author = Calinger, Ronald | year = 1996| title = Leonhard Euler: The First St. Petersburg Years (1727–1741)| journal = Historia Mathematica| volume = 23| issue = 2| pages = 127 | doi = 10.1006/hmat.1996.0015 ]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.cite journal| author = Calinger, Ronald | year = 1996| title = Leonhard Euler: The First St. Petersburg Years (1727–1741)| journal = Historia Mathematica| volume = 23| issue = 2| pages = 124 | doi = 10.1006/hmat.1996.0015 ]

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.cite journal| author = Calinger, Ronald | year = 1996| title = Leonhard Euler: The First St. Petersburg Years (1727–1741)| journal = Historia Mathematica| volume = 23| issue = 2| pages = 128–129 | doi = 10.1006/hmat.1996.0015 ]

On 7 January 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.cite web| url=http://www-history.mcs.st-and.ac.uk/~history/Extras/Euler_Fuss_Eulogy.html| title = Eulogy of Euler by Fuss| accessmonthday =30 August| accessyear =2006| last = Fuss| first = Nicolas]**Berlin**Concerned about the continuing turmoil in Russia, Euler left St. Petersburg on 19 June 1741 to take up a post at the "Berlin Academy", which he had been offered by

Frederick the Great of Prussia . He lived for twenty-five years inBerlin , where he wrote over 380 articles. In Berlin, he published the two works which he would be most renowned for: the "Introductio in analysin infinitorum", a text on functions published in 1748, and the "Institutiones calculi differentialis", [*[http://www.math.dartmouth.edu/~euler/pages/E212.html ".*] published in 1755 ondifferential calculus .cite book| last = Dunham| first = William | title = Euler: The Master of Us All | year = 1999| publisher =The Mathematical Association of America | pages = xxiv–xxv ]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.

Despite Euler's immense contribution to the Academy's prestige, he was eventually forced to leave Berlin. This was partly because of a conflict of personality with Frederick, who came to regard Euler as unsophisticated, especially in comparison to the circle of philosophers the German king brought to the Academy.

Voltaire was among those in Frederick's employ, and the Frenchman enjoyed a prominent position in the king's social circle. Euler, a simple religious man and a hard worker, was very conventional in his beliefs and tastes. He was in many ways the direct opposite of Voltaire. Euler had limited training inrhetoric , and tended to debate matters that he knew little about, making him a frequent target of Voltaire's wit. Frederick also expressed disappointment with Euler's practical engineering abilities:**Eyesight deterioration**Euler's

eyesight worsened throughout his mathematical career. Three years after suffering a near-fatalfever in 1735 he became nearly blind in his right eye, but Euler rather blamed his condition on the painstaking work oncartography 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 acataract 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 theAeneid ofVirgil 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.cite journal|last = Finkel|first = B.F.|year = 1897|title = Biography- Leonard Euler|journal = The American Mathematical Monthly| volume = 4| issue = 12| pages = 300|doi = 10.2307/2968971]**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 18 September 1783, Euler passed away in St. Petersburg after suffering a

brain hemorrhage , and was buried with his wife in the Smolensk Lutheran Cemetery onVasilievsky Island (the Soviets destroyed the cemetery after transferring Euler's remains to the OrthodoxAlexander Nevsky Lavra ). His eulogy was written for the French Academy by the French mathematician and philosopherMarquis 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**Euler worked in almost all areas of mathematics:

geometry ,calculus ,trigonometry ,algebra , andnumber theory , as well ascontinuum physics ,lunar theory and other areas ofphysics . 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. Euler's name is associated with a large number of topics.**Mathematical notation**Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks. Most notably, he introduced the concept of a function and was the first to write "f"("x") to denote the function "f" applied to the argument "x". He also introduced the modern notation for the

trigonometric functions , the letter "e" for the base of thenatural logarithm (now also known asEuler's number ), the Greek letter Σ for summations and the letter $i$ to denote theimaginary unit .cite book|title = A History of Mathematics|last= Boyer|first=Carl B.|coauthors= Uta C. Merzbach|publisher=John Wiley & Sons |id= ISBN 0-471-54397-7|pages = 439–445] 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 did not originate with him.cite web| url = http://www.stephenwolfram.com/publications/talks/mathml/mathml2.html| title = Mathematical Notation: Past and Future| accessmonth = August| accessyear=2006| last = Wolfram| first = Stephen]**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:$e^x\; =\; sum\_\{n=0\}^infty\; \{x^n\; over\; n!\}\; =\; lim\_\{n\; o\; infty\}left(frac\{1\}\{0!\}\; +\; frac\{x\}\{1!\}\; +\; frac\{x^2\}\{2!\}\; +\; cdots\; +\; frac\{x^n\}\{n!\}\; ight).$

Notably, Euler discovered the power series expansions for "e" and the

inverse tangent function. His daring (and, by modern standards, technically incorrect) use of power series enabled him to solve the famousBasel problem in 1735:cite book| last = Wanner| first = Gerhard| coauthors = Harrier, Ernst | title = Analysis by its history| edition = 1st| year = 2005| month = March| publisher = Springer| pages = 62]:$lim\_\{n\; o\; infty\}left(frac\{1\}\{1^2\}\; +\; frac\{1\}\{2^2\}\; +\; frac\{1\}\{3^2\}\; +\; cdots\; +\; frac\{1\}\{n^2\}\; ight)\; =\; frac\{pi\; ^2\}\{6\}.$

Euler introduced the use of the

exponential function andlogarithms in analytic proofs. He discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative andcomplex number s, thus greatly expanding the scope of mathematical applications of logarithms.cite book|title = A History of Mathematics|last= Boyer|first=Carl B.|coauthors= Merzbach, Uta C. |publisher=John Wiley & Sons |id= ISBN 0-471-54397-7|pages = 439–445] He also defined the exponential function for complex numbers, and discovered its relation to thetrigonometric function s. For anyreal number φ ,Euler's formula states that the complex exponential function satisfies:$e^\{ivarphi\}\; =\; cos\; varphi\; +\; isin\; varphi.,$

A special case of the above formula is known as

Euler's identity ,:$e^\{i\; pi\}\; +1\; =\; 0\; ,$called "the most remarkable formula in mathematics" byRichard Feynman , for its single uses of the notions of addition, multiplication, exponentiation, and equality, and the single uses of the important constants 0, 1, "e", "i" and πcite book |last= Feynman|first= Richard|title= The Feynman Lectures on Physics: Volume I |origyear=1970 |origmonth= June|pages=p.10 |chapter= Chapter 22: Algebra] . In 1988, the readers of theMathematical Intelligencer voted it "the Most Beautiful Mathematical Formula Ever". In total, Euler was responsible for three of the top five formulae in that pollcite journal | last= Wells | first= David | year= 1990 | title = Are these the most beautiful? | journal = Mathematical Intelligencer | volume = 12 | issue = 3 | pages= 37–41

cite journal | last= Wells | first= David | year= 1988 | title = Which is the most beautiful? | journal = Mathematical Intelligencer | volume = 10 | issue = 4 | pages= 30–31

See also: cite url | url = http://www.maa.org/mathtourist/mathtourist_03_12_07.html | title = The Mathematical Tourist | accessmonth = March | accessyear = 2008 | last = Peterson | first = Ivars ] .De Moivre's formula is a direct consequence ofEuler's formula .In addition, Euler elaborated the theory of higher

transcendental function s by introducing thegamma function and introduced a new method for solvingquartic equation s. He also found a way to calculate integrals with complex limits, foreshadowing the development of moderncomplex analysis , and invented thecalculus of variations including its best-known result, theEuler–Lagrange equation .Euler also pioneered the use of analytic methods to solve number theory problems. In doing so, he united two disparate branches of mathematics and introduced a new field of study,

analytic number theory . In breaking ground for this new field, Euler created the theory ofhypergeometric series ,q-series , hyperbolic trigonometric functions and the analytic theory of continued fractions. For example, he proved theinfinitude of primes using the divergence of the harmonic series, and he used analytic methods to gain some understanding of the wayprime numbers are distributed. Euler's work in this area led to the development of theprime number theorem .cite book| last = Dunham| first = William| title = Euler: The Master of Us All | year = 1999| publisher =The Mathematical Association of America | chapter = 3,4 ]**Number theory**Euler's interest in number theory can be traced to the influence of

Christian Goldbach , his friend in the St. Petersburg Academy. A lot of Euler's early work on number theory was based on the works ofPierre de Fermat . Euler developed some of Fermat's ideas, and disproved some of his conjectures.Euler linked the nature of prime distribution with ideas in analysis. He proved that the sum of the reciprocals of the primes diverges. In doing so, he discovered the connection between the Riemann zeta function and the prime numbers; this is known as the Euler product formula for the Riemann zeta function.

Euler proved

Newton's identities ,Fermat's little theorem ,Fermat's theorem on sums of two squares , and he made distinct contributions toLagrange's four-square theorem . He also invented thetotient function φ("n") which is the number of positive integers less than the integer "n" that arecoprime to "n". Using properties of this function, he generalized Fermat's little theorem to what is now known asEuler's theorem . He contributed significantly to the theory ofperfect numbers , which had fascinated mathematicians sinceEuclid . Euler also made progress toward theprime number theorem , and he conjectured the law ofquadratic reciprocity . The two concepts are regarded as fundamental theorems of number theory, and his ideas paved the way for the work ofCarl Friedrich Gauss .cite book| last = Dunham| first = William| title = Euler: The Master of Us All | year = 1999| publisher =The Mathematical Association of America | chapter = 1,4]By 1772 Euler had proved that 2

^{31}− 1 = 2,147,483,647 is aMersenne prime . It may have remained thelargest known prime until 1867. [*Caldwell, Chris. [*]*http://primes.utm.edu/notes/by_year.html "The largest known prime by year"*]**Geometry***

Euler line

*Euler's circle **Graph theory**In 1736, Euler solved the problem known as the

Seven Bridges of Königsberg .cite journal| last = Alexanderson| first = Gerald| year = 2006| month = July| title = Euler and Königsberg's bridges: a historical view| journal = Bulletin of the American Mathematical Society| doi = 10.1090/S0273-0979-06-01130-X| volume = 43| pages = 567] The city ofKönigsberg , Prussia was set on thePregel River, and included two large islands which were connected to each other and the mainland by seven bridges. The problem is to decide whether it is possible to follow a path that crosses each bridge exactly once and returns to the starting point. It is not: there is no Eulerian circuit. This solution is considered to be the first theorem ofgraph theory , specifically ofplanar graph theory.Euler also discovered the formula $V-E+F=2$ relating the number of edges, vertices, and faces of a convex

polyhedron [*cite book|title=Polyhedra|author=Peter R. Cromwell|location=Cambridge|year=1997|publisher=Cambridge University Press|pages=189-190*] , and hence of aplanar graph . The constant in this formula is now known as theEuler characteristic for the graph (or other mathematical object), and is related to the genus of the object. [*cite book|title=Algorithmic Graph Theory|author=Alan Gibbons|location=Cambridge|year=1985|publisher=Cambridge University Press|pages=72*] The study and generalization of this formula, specifically by Cauchycite journal|author=Cauchy, A.L.|year=1813|title=Recherche sur les polyèdres—premier mémoire|journal=Journal de l'Ecole Polytechnique|volume= 9 (Cahier 16)|pages=66–86] and L'Huillier,cite journal|author=L'Huillier, S.-A.-J.|title=Mémoire sur la polyèdrométrie|journal=Annales de Mathématiques|volume=3|year=1861|pages=169–189] is at the origin oftopology .**Applied mathematics**Some of Euler's greatest successes were in solving real-world problems analytically, and in describing numerous applications of Bernoulli's numbers,

Fourier series ,Venn diagrams ,Euler numbers , the constants e and π, continued fractions and integrals. He integrated Leibniz'sdifferential calculus with Newton'sMethod of Fluxions , and developed tools that made it easier to apply calculus to physical problems. He made great strides in improving thenumerical approximation of integrals, inventing what are now known as theEuler approximations . The most notable of these approximations areEuler's method and theEuler–Maclaurin formula . He also facilitated the use ofdifferential equations , in particular introducing theEuler-Mascheroni constant ::$gamma\; =\; lim\_\{n\; ightarrow\; infty\; \}\; left(\; 1+\; frac\{1\}\{2\}\; +\; frac\{1\}\{3\}\; +\; frac\{1\}\{4\}\; +\; cdots\; +\; frac\{1\}\{n\}\; -\; ln(n)\; ight).$

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 incorporatemusical theory as part of mathematics. This part of his work, however, did not receive wide attention and was once described as too mathematical for musicians and too musical for mathematicians.cite journal| author = Calinger, Ronald | year = 1996| title = Leonhard Euler: The First St. Petersburg Years (1727–1741)| journal = Historia Mathematica| volume = 23| issue = 2| pages = 144–145 | doi = 10.1006/hmat.1996.0015 ]**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 inclassical 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. [*Youschkevitch, A P; Biography in "Dictionary of Scientific Biography" (New York 1970–1990).*]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 thewave theory of light proposed byChristian Huygens would become the dominant mode of thought, at least until the development of the quantum theory of light.cite journal

author = Home, R.W.

year = 1988

title = Leonhard Euler's 'Anti-Newtonian' Theory of Light

journal = Annals of Science

volume = 45

issue = 5

pages = 521–533 | doi = 10.1080/00033798800200371 ]**Logic**He is also credited with using

closed curve s to illustrate syllogistic reasoning (1768). These diagrams have become known asEuler diagram s.Leibniz'smonism 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".cite journal| author = Calinger, Ronald | year = 1996| title = Leonhard Euler: The First St. Petersburg Years (1727–1741)| journal = Historia Mathematica| volume = 23| issue = 2| pages = 153–154 | doi = 10.1006/hmat.1996.0015 ]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 abiblical literalist (for example, the "Rettung" was primarily an argument for the divine inspiration of scripture).cite journal| last = Euler| first = Leonhard | editor = Orell-Fussli| year = 1960| title = Rettung der Göttlichen Offenbahrung Gegen die Einwürfe der Freygeister| journal = Leonhardi Euleri Opera Omnia (series 3)| volume = 12 ]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 foratheism 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 theexistence 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, $frac\{a+b^n\}\{z\}=x$, 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 is apocryphal, given that Diderot was a capable mathematician who had published mathematical treatises.cite journal| last = Brown | first = B.H.| year = 1942| month = May| title = The Euler-Diderot Anecdote| journal =The American Mathematical Monthly| volume = 49| issue = 5| pages = 302–303| doi = 10.2307/2303096; cite journal| last = Gillings | first = R.J.| year = 1954| month = February| title = The So-Called Euler-Diderot Incident| journal =The American Mathematical Monthly| volume = 61| issue = 2| pages = 77–80| doi = 10.2307/2307789]**elected bibliography**Euler has an extensive bibliography but his best known books include:

*" [*http://web.mat.bham.ac.uk/C.J.Sangwin/euler/ 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 [*http://perso.club-internet.fr/nielrowclub-internet.fr/nielrowbooks/euler.tif online*] (in French). English translation, with notes, and a life of Euler, available online fromGoogle Books : [*http://books.google.com/books?vid=09-Fi9xi6pUzqBOnQzlnRS&id=hAm5VsEeu1EC&printsec=titlepage&dq=%22Leonhard+Euler%22 Volume 1*] , [*http://books.google.com/books?vid=OCLC00826569&id=CZLPNtEnFRcC&printsec=titlepage&dq=%22Leonhard+Euler%22 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". [*[*]*http://math.dartmouth.edu/~euler/pages/E065.html E65 — Methodus… entry at Euler Archives*]A definitive collection of Euler's works, entitled "Opera Omnia," has been published since 1911 by the [

*http://www.leonhard-euler.ch/ Euler Commission*] of theSwiss Academy of Sciences .**See also***

List of topics named after Leonhard Euler **Notes****Further reading***"Lexikon der Naturwissenschaftler", 2000. Heidelberg: Spektrum Akademischer Verlag.

*Demidov, S.S., 2005, "Treatise on the differential calculus" in Grattan-Guiness, I., ed., "Landmark Writings in Western Mathematics". Elsevier: 191-98.

*Dunham, William (1999) "Euler: The Master of Us All", Washington: Mathematical Association of America. ISBN 0-88385-328-0.

*Fraser, Craig G., 2005, "Book on the calculus of variations" in Grattan-Guiness, I., ed., "Landmark Writings in Western Mathematics". Elsevier: 168-80.

*Gladyshev, Georgi, P. (2007) “ [*http://www.ceser.res.in/ijamas/cont/2007/ams-n07-cont.html Leonhard Euler’s methods and ideas live on in the thermodynamic hierarchical theory of biological evolution,*] ” "International Journal of Applied Mathematics & Statistics" (IJAMAS) 11 (N07), Special Issue onLeonhard Paul Euler ’s: Mathematical Topics and Applications (M. T. A.).

*cite journal | title= Leonhard Euler: his life, the man, and his works | author= W. Gautschi | year= 2008 | journal= SIAM Review | volume = 50 | issue= 1 | pages=3–33 | doi= 10.1137/070702710

*Heimpell, Hermann, Theodor Heuss, Benno Reifenberg (editors). 1956. "Die großen Deutschen", volume 2, Berlin: Ullstein Verlag.

*Krus, D.J. (2001) " [*http://www.visualstatistics.net/Statistics/Euler/Euler.htm Is the normal distribution due to Gauss? Euler, his family of gamma functions, and their place in the history of statistics,*] " "Quality and Quantity: International Journal of Methodology," 35: 445-46.

*Nahin, Paul (2006) "Dr. Euler's Fabulous Formula", New Jersey: Princeton, ISBN 978-06-9111-822-2

*Reich, Karin, 2005, " 'Introduction' to analysis" in Grattan-Guiness, I., ed., "Landmark Writings in Western Mathematics". Elsevier: 181-90.

*Sandifer, Edward C. (2007), "The Early Mathematics of Leonhard Euler", Washington: Mathematical Association of America. IBSN 10: 0-88385-559-3

*Simmons, J. (1996) "The giant book of scientists: The 100 greatest minds of all time", Sydney: The Book Company.

*Singh, Simon. (1997). "Fermat's last theorem", Fourth Estate: New York, ISBN 1-85702-669-1

*Thiele, Rüdiger. (2005). The mathematics and science of Leonhard Euler, in "Mathematics and the Historian's Craft: The Kenneth O. May Lectures", G. Van Brummelen and M. Kinyon (eds.), CMS Books in Mathematics, Springer Verlag. ISBN 0-387-25284-3.

*cite journal | year = 1983 | month = November | title = A Tribute to Leohnard Euler 1707-1783 | journal =Mathematics Magazine | volume = 56 | issue = 5**External links**wikiquote|Leonhard Euler

*MacTutor Biography|id=Euler

*ScienceWorldBiography | urlname=Euler | title=Euler, Leonhard (1707–1783)

* [*http://www.britannica.com/eb/article-9033216/Leonhard-Euler Encyclopedia Britannica article*]

*MathGenealogy|id=38586

* [*http://www.maa.org/news/howeulerdidit.html How Euler did it*] Website containing columns explaining how Euler solved various problems.

* [*http://www.eulerarchive.org/ Euler Archive*]

* [*http://www.leonhard-euler.ch/ Euler Committee of the Swiss Academy of Sciences*]

* [*http://www-history.mcs.st-andrews.ac.uk/References/Euler.html References for Leonhard Euler*]

* [*http://www.euler-2007.ch/en/index.htm Euler Tercentenary 2007*]

* [*http://www.eulersociety.org/ The Euler Society*]

* [*http://www.pdmi.ras.ru/EIMI/2007/AG/ Leonhard Euler Congress 2007*] —St. Petersburg, Russia

* [*http://www.gresham.ac.uk/event.asp?PageId=45&EventId=518 "Euler - 300th anniversary lecture"*] , given by Robin Wilson atGresham College , 9 May 2007 (available for download as video or audio files)

* [*http://www.projecteuler.net Project Euler*]

* [*http://www.math.dartmouth.edu/~euler/historica/family-tree.html Euler Family Tree*]

* [*http://friedrich.uni-trier.de/oeuvres/20/219/ Euler's Correspondence with Frederick the Great, King of Prussia*]Persondata

NAME= Euler, Leonhard

SHORT DESCRIPTION=Mathematician

DATE OF BIRTH=birth date|df=yes|1707|4|15

PLACE OF BIRTH=Basel ,Switzerland

DATE OF DEATH=death date|df=yes|1783|9|18

PLACE OF DEATH=St Petersburg ,Russia

*Wikimedia Foundation.
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**Leonhard Euler**— Leonhard Euler, Pastell von Emanuel Handma … Deutsch Wikipedia**Leonhard Euler**— nació el 15 de abril de 1707 en Basilea, Suiza. Murió el 18 de septiembre de 1783 en San Petersburgo, Rusia. Vivió en Rusia la mayor parte de su vida. Probablemente uno de los más grandes matemáticos de la historia, comparable a Gauss, Newton o … Enciclopedia Universal**Leonhard Euler**— « Euler » redirige ici. Pour les autres significations, voir Euler (homonymie). Leonhard Euler Portrait par Johann Georg Brucker Naissance … Wikipédia en Français**Leonhard Euler**— Retrato de Leonhard Euler, pintado por Johann Georg Bruck … Wikipedia Español**Leonhard Euler**— noun Swiss mathematician (1707 1783) • Syn: ↑Euler • Instance Hypernyms: ↑mathematician … Useful english dictionary**Leonhard Euler**— … Википедия**Leonhard Euler**— n. (1707 1783) Swiss mathematician … English contemporary dictionary**Contributions of Leonhard Euler to mathematics**— The 18th century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field. His seminal work had a profound impact in numerous areas of mathematics and he is widely… … Wikipedia**Liste des sujets nommés d'après Leonhard Euler**— En mathématiques et en physique, il existe un grand nombre de sujets nommés en l honneur de Leonhard Euler, dont beaucoup sont désignés par leur rôle : équation, formule, identité, nombre (unique ou séquence) ou une autre entité… … Wikipédia en Français**List of topics named after Leonhard Euler**— In mathematics and physics, there are a large number of topics named in honour of Leonhard Euler (pronounced Oiler ). As well, many of these topics include their own unique function, equation, formula, identity, number (single or sequence), or… … Wikipedia