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Leonhard Euler (
OY-lər;
[2] Swiss Standard German: [ˈɔɪlər] ( listen);
German Standard German: [ˈɔʏlɐ] ( listen); 15 April 1707 – 18 September 1783) was a Swiss
mathematician,
physicist,
astronomer,
logician and
engineer, who made important and influential discoveries in many branches of mathematics, such as
infinitesimal calculus and
graph theory, while also making pioneering contributions to several branches such as
topology and
analytic number theory. He also introduced much of the modern mathematical terminology and
notation, particularly for
mathematical analysis, such as the notion of a
mathematical function.
[3] He is also known for his work in
mechanics,
fluid dynamics,
optics,
astronomy, and
music theory.
[4]
Euler was one of the most eminent mathematicians of the 18th century
and is held to be one of the greatest in history. He is also widely
considered to be the most prolific mathematician of all time. His
collected works fill 60 to 80
quarto volumes,
[5] more than anybody in the field. He spent most of his adult life in
Saint Petersburg,
Russia, and in
Berlin, then the capital of
Prussia.
A statement attributed to
Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."
[6][7]
Life
Early years
Leonhard Euler was born on 15 April 1707, in
Basel, Switzerland to Paul III Euler, a pastor of the
Reformed Church, and Marguerite
née
Brucker, a pastor's daughter. He had two younger sisters: Anna Maria
and Maria Magdalena, and a younger brother Johann Heinrich.
[8] 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 was then regarded as Europe's foremost mathematician, and would eventually be the most important influence on young Leonhard.
Euler's formal education started in Basel, where he was sent to live
with his maternal grandmother. In 1720, aged thirteen, he enrolled at
the
University of Basel, and in 1723, he received a Master of Philosophy with a dissertation that compared the philosophies of
Descartes and
Newton. During that time, he was receiving Saturday afternoon lessons from
Johann Bernoulli, who quickly discovered his new pupil's incredible talent for mathematics.
[9] At that time Euler's main studies included theology,
Greek, and
Hebrew
at his father's urging in order to become a pastor, but Bernoulli
convinced his father that Leonhard was destined to become a great
mathematician.
In 1726, Euler completed a dissertation on the
propagation of sound with the title
De Sono.
[10] At that time, he was unsuccessfully attempting to obtain a position at the University of Basel. In 1727, he first entered the
Paris Academy Prize Problem competition; the problem that year was to find the best way to place the
masts on a ship.
Pierre Bouguer,
who became known as "the father of naval architecture", won and Euler
took second place. Euler later won this annual prize twelve times.
[11]
Saint Petersburg
Around this time Johann Bernoulli's two sons,
Daniel and
Nicolaus, were working at the
Imperial Russian Academy of Sciences in
Saint Petersburg. On 31 July 1726, Nicolaus died of appendicitis after spending less than a year in Russia,
[12][13]
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 Saint
Petersburg while he unsuccessfully applied for a physics professorship
at the University of Basel.
[14]
1957
Soviet Union
stamp commemorating the 250th birthday of Euler. The text says: 250
years from the birth of the great mathematician, academician Leonhard
Euler.
Euler arrived in Saint Petersburg 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 Saint Petersburg. He also took on an
additional job as a medic in the
Russian Navy.
[15]
The Academy at Saint 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 in order 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.
[11]
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 was suspicious of the academy's foreign scientists, and
thus cut funding and caused other difficulties for Euler and his
colleagues.
Conditions improved slightly after the death of Peter II, and Euler
swiftly rose through the ranks in the academy and was made a professor
of physics in 1731. Two years later, Daniel Bernoulli, who was fed up
with the censorship and hostility he faced at Saint Petersburg, left for
Basel. Euler succeeded him as the head of the mathematics department.
[16]
On 7 January 1734, he married Katharina Gsell (1707–1773), a daughter of
Georg Gsell, a painter from the Academy Gymnasium.
[17] The young couple bought a house by the
Neva River. Of their thirteen children, only five survived childhood.
[18]
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 25 years in
Berlin, where he wrote over 380 articles. In Berlin, he published the two works for which he would become most renowned: the
Introductio in analysin infinitorum, a text on functions published in 1748, and the
Institutiones calculi differentialis,
[19] published in 1755 on
differential calculus.
[20] In 1755, he was elected a foreign member of the
Royal Swedish Academy of Sciences.
In addition, Euler was asked to tutor
Friederike Charlotte of Brandenburg-Schwedt, the Princess of
Anhalt-Dessau
and Frederick's niece. Euler wrote over 200 letters to her in the early
1760s, which were later compiled into a best-selling volume entitled
Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess.
[21]
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 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.
[20]
Despite Euler's immense contribution to the Academy's prestige, he eventually incurred the ire of
Frederick
and ended up having to leave Berlin. The Prussian king had a large
circle of intellectuals in his court, and he found the mathematician
unsophisticated and ill-informed on matters beyond numbers and figures.
Euler was a simple, devoutly religious man who never questioned the
existing social order or conventional beliefs, in many ways the polar
opposite of
Voltaire,
who enjoyed a high place of prestige at Frederick's court. Euler was
not a skilled debater and often made it a point to argue subjects that
he knew little about, making him the frequent target of Voltaire's wit.
[20] Frederick also expressed disappointment with Euler's 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![22]
1753 portrait of Euler by
Emanuel Handmann, which indicates problems with Euler's right eyelid, possibly
strabismus. Euler's left eye, which here appears healthy, was later affected by a
cataract.
[23]
Eyesight deterioration
Euler's
eyesight
worsened throughout his mathematical career. In 1738, three years after
nearly expiring from fever, he became almost blind in his right eye,
but Euler rather blamed the painstaking work on
cartography
he performed for the St. Petersburg Academy for his condition. Euler's
vision in that eye worsened throughout his stay in Germany, to the
extent that Frederick referred to him as "
Cyclops". Euler later developed a
cataract
in his left eye, which was discovered in 1766. Just a few weeks after
its discovery, he was rendered almost totally blind. However, his
condition appeared to have little effect on his productivity, as he
compensated for it with his mental calculation skills and exceptional
memory. Upon losing the sight in both eyes, Euler remarked, "Now I will
have fewer distractions".
[24] 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.
[5] The Eulers bore a double name, Euler-Schölpi, the latter of which derives from
schelb and
schief, signifying squint-eyed, cross-eyed, or crooked. This suggests that the Eulers may have had a susceptibility to eye problems.
[25]
Return to Russia and death
In 1760, with the
Seven Years' War raging, Euler's farm in Charlottenburg was ransacked by advancing Russian troops. Upon learning of this event,
General Ivan Petrovich Saltykov paid compensation for the damage caused to Euler's estate, later
Empress Elizabeth of Russia added a further payment of 4000 roubles – an exorbitant amount at the time.
[26] The political situation in Russia stabilized after
Catherine the Great's
accession to the throne, so in 1766 Euler accepted an invitation to
return to the St. Petersburg Academy. His conditions were quite
exorbitant – a 3000 ruble annual salary, a pension for his wife, and the
promise of high-ranking appointments for his sons. All of these
requests were granted. He spent the rest of his life in Russia. However,
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 Katharina after 40 years of marriage.
Three years after his wife's death, Euler married her half-sister, Salome Abigail Gsell (1723–1794).
[27] This marriage lasted until his death. In 1782 he was elected a Foreign Honorary Member of the
American Academy of Arts and Sciences.
[28]
In St. Petersburg on 18 September 1783, after a lunch with his family, Euler was discussing the newly discovered planet
Uranus and its
orbit with a fellow
academician Anders Johan Lexell, when he collapsed from a
brain hemorrhage. He died a few hours later.
[29] Jacob von Staehlin-Storcksburg wrote a short obituary for the
Russian Academy of Sciences and Russian mathematician
Nicolas Fuss, one of Euler's disciples, wrote a more detailed eulogy,
[30] which he delivered at a memorial meeting. In his eulogy for the French Academy, French mathematician and philosopher
Marquis de Condorcet, wrote:
il cessa de calculer et de vivre—... he ceased to calculate and to live.[31]
Euler was buried next to Katharina at the
Smolensk Lutheran Cemetery on
Goloday Island. In 1785, the
Russian Academy of Sciences
put a marble bust of Leonhard Euler on a pedestal next to the
Director's seat and, in 1837, placed a headstone on Euler's grave. To
commemorate the 250th anniversary of Euler's birth, the headstone was
moved in 1956, together with his remains, to the 18th-century necropolis
at the
Alexander Nevsky Monastery.
Contributions to mathematics and physics
Euler worked in almost all areas of mathematics, such as
geometry,
infinitesimal 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.
[5] Euler's name is associated with a
large number of topics.
Euler is the only mathematician to have
two numbers named after him: the important
Euler's number in
calculus,
e, approximately equal to 2.71828, and the
Euler–Mascheroni constant γ (
gamma) sometimes referred to as just "Euler's constant", approximately equal to 0.57721. It is not known whether γ is
rational or
irrational.
[32]
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[3] 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 the
natural logarithm (now also known as
Euler's number), the Greek letter
Σ for summations and the letter
i to denote the
imaginary unit.
[33] 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 originated with
Welsh mathematician
William Jones.
[34]
Analysis
The development of
infinitesimal 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[35] (in particular his reliance on the principle of the
generality of algebra), his ideas led to many great advances. Euler is well known in
analysis for his frequent use and development of
power series, the expression of functions as sums of infinitely many terms, such as
Notably, Euler directly proved the power series expansions for
e and the
inverse tangent function. (Indirect proof via the inverse power series technique was given by
Newton and
Leibniz between 1670 and 1680.) His daring use of power series enabled him to solve the famous
Basel problem in 1735 (he provided a more elaborate argument in 1741):
[35]
Euler introduced the use of the
exponential function and
logarithms
in analytic proofs. He discovered ways to express various logarithmic
functions using power series, and he successfully defined logarithms for
negative and
complex numbers, thus greatly expanding the scope of mathematical applications of logarithms.
[33] He also defined the exponential function for complex numbers, and discovered its relation to the
trigonometric functions. For any
real number φ (taken to be radians),
Euler's formula states that the
complex exponential function satisfies
A special case of the above formula is known as
Euler's identity,
called "the most remarkable formula in mathematics" by
Richard P. 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
π.
[36] In 1988, readers of the
Mathematical Intelligencer voted it "the Most Beautiful Mathematical Formula Ever".
[37] In total, Euler was responsible for three of the top five formulae in that poll.
[37]
De Moivre's formula is a direct consequence of
Euler's formula.
In addition, Euler elaborated the theory of higher
transcendental functions by introducing the
gamma function and introduced a new method for solving
quartic equations. He also found a way to calculate integrals with complex limits, foreshadowing the development of modern
complex analysis. He also invented the
calculus of variations including its best-known result, the
Euler–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 of
hypergeometric series,
q-series,
hyperbolic trigonometric functions and the analytic theory of
continued fractions. For example, he proved the
infinitude of primes using the divergence of the
harmonic series, and he used analytic methods to gain some understanding of the way
prime numbers are distributed. Euler's work in this area led to the development of the
prime number theorem.
[38]
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 of
Pierre 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 to
Lagrange's four-square theorem. He also invented the
totient function φ(
n), the number of positive integers less than or equal to the integer
n that are
coprime to
n. Using properties of this function, he generalized Fermat's little theorem to what is now known as
Euler's theorem. He contributed significantly to the theory of
perfect numbers, which had fascinated mathematicians since
Euclid. He proved that the relationship shown between perfect numbers and
Mersenne primes earlier proved by Euclid was one-to-one, a result otherwise known as the
Euclid–Euler theorem. Euler also conjectured the law of
quadratic reciprocity. The concept is regarded as a fundamental theorem of number theory, and his ideas paved the way for the work of
Carl Friedrich Gauss.
[39] By 1772 Euler had proved that 2
31 − 1 =
2,147,483,647 is a Mersenne prime. It may have remained the
largest known prime until 1867.
[40]
Graph theory
Map of
Königsberg in Euler's time showing the actual layout of the
seven bridges, highlighting the river Pregel and the bridges.
In 1735, Euler presented a solution to the problem known as the
Seven Bridges of Königsberg.
[41] The city of
Königsberg,
Prussia was set on the
Pregel
River, and included two large islands that 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 possible: there is no
Eulerian circuit. This solution is considered to be the first theorem of
graph theory, specifically of
planar graph theory.
[41]
Euler also discovered the
formula relating the number of vertices, edges and faces of a
convex polyhedron,
[42] and hence of a
planar graph. The constant in this formula is now known as the
Euler characteristic for the graph (or other mathematical object), and is related to the
genus of the object.
[43] The study and generalization of this formula, specifically by
Cauchy[44] and
L'Huilier,
[45] is at the origin of
topology.
Applied mathematics
Some of Euler's greatest successes were in solving real-world
problems analytically, and in describing numerous applications of the
Bernoulli numbers,
Fourier series,
Euler numbers, the constants
e and
π, continued fractions and integrals. He integrated
Leibniz's
differential calculus with Newton's
Method of Fluxions, and developed tools that made it easier to apply calculus to physical problems. He made great strides in improving the
numerical approximation of integrals, inventing what are now known as the
Euler approximations. The most notable of these approximations are
Euler's method and the
Euler–Maclaurin formula. He also facilitated the use of
differential equations, in particular introducing the
Euler–Mascheroni constant:
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, did not receive
wide attention and was once described as too mathematical for musicians
and too musical for mathematicians.
[46]
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.
[47]
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
Christiaan Huygens would become the dominant mode of thought, at least until the development of the
quantum theory of light.
[48]
In 1757 he published an important set of equations for
inviscid flow, that are now known as the
Euler equations.
[49] In differential form, the equations are:
where
Euler is also well known in structural engineering for his formula giving the critical
buckling load of an ideal strut, which depends only on its length and flexural stiffness:
[50]
where
- F = maximum or critical force (vertical load on column),
- E = modulus of elasticity,
- I = area moment of inertia,
- L = unsupported length of column,
- K = column effective length factor, whose value depends on the conditions of end support of the column, as follows.
-
- For both ends pinned (hinged, free to rotate), K = 1.0.
- For both ends fixed, K = 0.50.
- For one end fixed and the other end pinned, K = 0.699…
- For one end fixed and the other end free to move laterally, K = 2.0.
- K L is the effective length of the column.
Logic
Euler is also credited with using
closed curves to illustrate
syllogistic reasoning (1768). These diagrams have become known as
Euler diagrams.
[51]
An Euler diagram is a
diagrammatic means of representing
sets and their relationships. Euler diagrams consist of simple closed curves (usually circles) in the plane that depict
sets. Each Euler curve divides the plane into two regions or "zones": the interior, which symbolically represents the
elements
of the set, and the exterior, which represents all elements that are
not members of the set. The sizes or shapes of the curves are not
important; the significance of the diagram is in how they overlap. The
spatial relationships between the regions bounded by each curve
(overlap, containment or neither) corresponds to set-theoretic
relationships (
intersection,
subset and
disjointness). Curves whose interior zones do not intersect represent
disjoint sets.
Two curves whose interior zones intersect represent sets that have
common elements; the zone inside both curves represents the set of
elements common to both sets (the
intersection of the sets). A curve that is contained completely within the interior zone of another represents a
subset of it. Euler diagrams were incorporated as part of instruction in
set theory as part of the
new math movement in the 1960s. Since then, they have also been adopted by other curriculum fields such as reading.
[52]
Music
Even when dealing with music, Euler’s approach is mainly
mathematical. His writings on music are not particularly numerous (a few
hundred pages, in his total production of about thirty thousand pages),
but they reflect an early preoccupation and one that did not leave him
throughout his life.
[53]
A first point of Euler’s musical theory is the definition of
"genres", i.e. of possible divisions of the octave using the prime
numbers 3 and 5. Euler describes 18 such genres, with the general
definition 2
mA, where A is the "exponent" of the genre (i.e. the sum of the exponents of 3 and 5) and 2
m (where "m is an indefinite number, small or large, so long as the sounds are perceptible"
[54]),
expresses that the relation holds independently of the number of
octaves concerned. The first genre, with A = 1, is the octave itself (or
its duplicates); the second genre, 2
m.3, is the octave divided by the fifth (fifth + fourth, C–G–C); the third genre is 2
m.5, major third + minor sixth (C–E–C); the fourth is 2
m.3
2, two fourths and a tone (C–F–B
♭–C); the fifth is 2
m.3.5 (C–E–G–B–C); etc. Genres 12 (2
m.3
3.5), 13 (2
m.3
2.5
2) and 14 (2
m.3.5
3) are corrected versions of the diatonic, chromatic and enharmonic, respectively, of the Ancients. Genre 18 (2
m.3
3.5
2) is the "diatonico-chromatic", "used generally in all compositions",
[55] and which turns out to be identical with the system described by Johann Mattheson.
[56] Euler later envisaged the possibility of describing genres including the prime number 7.
[57]
Euler devised a specific graph, the
Speculum musicum,
[58]
to illustrate the diatonico-chromatic genre, and discussed paths in
this graph for specific intervals, reminding his interest for the Seven
Bridges of Königsberg (see
above). The device knew a renewed interest as the
Tonnetz in neo-Riemannian theory (see also
Lattice (music)).
[59]
Euler further used the principle of the "exponent" to propose a derivation of the
gradus suavitatis
(degree of suavity, of agreeableness) of intervals and chords from
their prime factors – one must keep in mind that he considered just
intonation, i.e. 1 and the prime numbers 3 and 5 only.
[60] Formulas have been proposed extending this system to any number of prime numbers, e.g. in the form
- ds = Σ (kipi – ki) + 1
where
pi are prime numbers and
ki their exponents.
[61]
Personal philosophy and religious beliefs
Euler and his friend
Daniel Bernoulli were opponents of
Leibniz's monadism 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".
[62]
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 show that Euler was a devout Christian who believed the Bible to be inspired; the
Rettung was primarily an argument for the
divine inspiration of scripture.
[63]
There is a famous legend
[64]
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 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 this
non-sequitur: "Sir,
a+bn/n=
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 himself did research in mathematics.
[65] The legend was apparently first told by
Dieudonné Thiébault[66] with significant embellishment by
Augustus De Morgan.
[67][68]
Commemorations
Euler on the Old Swiss
10 Franc banknote
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 24 May—he was a devout Christian (and believer in
biblical inerrancy) who wrote
apologetics and argued forcefully against the prominent atheists of his time.
[63]
Selected bibliography
Illustration from
Solutio problematis... a. 1743 propositi published in
Acta Eruditorum, 1744
The title page of Euler's Methodus inveniendi lineas curvas.
Euler has an
extensive bibliography. His best-known books include:
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. A complete chronological list of Euler's works is available at the following page:
The Eneström Index (PDF).