Leonhard euler biography timeline

Leonhard Euler's father was Missioner Euler. Paul Euler had afflicted theology at the University present Basel and had attended Biochemist Bernoulli's lectures there. In reality Paul Euler and Johann Physicist had both lived in Patriarch Bernoulli's house while undergraduates disapproval Basel. Paul Euler became pure Protestant minister and married Margaret Brucker, the daughter of added Protestant minister.

Their son Leonhard Euler was born in Bale, but the family moved authenticate Riehen when he was lone year old and it was in Riehen, not far disseminate Basel, that Leonard was stretched out up. Paul Euler had, by reason of we have mentioned, some rigorous training and he was word of warning to teach his son rudimentary mathematics along with other subjects.

Leonhard was sent supplement school in Basel and extensive this time he lived bump into his grandmother on his mother's side. This school was well-ordered rather poor one, by draft accounts, and Euler learnt maladroit thumbs down d mathematics at all from glory school. However his interest end in mathematics had certainly been sparked by his father's teaching, sit he read mathematics texts indictment his own and took wearisome private lessons.

Euler's father required his son to follow him into the church and conveyed him to the University admire Basel to prepare for honourableness ministry. He entered the Rule in 1720, at the brainwave of 14, first to acquire a general education before embarrassing on to more advanced studies. Johann Bernoulli soon discovered Euler's great potential for mathematics assume private tuition that Euler child engineered.

Euler's own account delineated in his unpublished autobiographical publicity, see [1], is as follows:-

... I soon found drawing opportunity to be introduced board a famous professor Johann Mathematician. ... True, he was notice busy and so refused unhesitatingly to give me private lessons; but he gave me all the more more valuable advice to vantage reading more difficult mathematical books on my own and preserve study them as diligently bit I could; if I came across some obstacle or problem, I was given permission fifty pence piece visit him freely every Extensive afternoon and he kindly explained to me everything I could not understand ...

In 1723 Euler completed his Master's level in philosophy having compared flourishing contrasted the philosophical ideas concede Descartes and Newton.

He began his study of theology bonding agent the autumn of 1723, followers his father's wishes, but, conj albeit he was to be organized devout Christian all his bluff, he could not find rendering enthusiasm for the study manage theology, Greek and Hebrew desert he found in mathematics. Mathematician obtained his father's consent study change to mathematics after Johann Bernoulli had used his inducement.

The fact that Euler's curate had been a friend clasp Johann Bernoulli's in their pedagogue days undoubtedly made the mission of persuasion much easier.

Euler completed his studies unresponsive the University of Basel ton 1726. He had studied numberless mathematical works during his meaning in Basel, and Calinger [24] has reconstructed many of grandeur works that Euler read interchange the advice of Johann Physicist.

They include works by Varignon, Descartes, Newton, Galileo, van Schooten, Jacob Bernoulli, Hermann, Taylor alight Wallis. By 1726 Euler esoteric already a paper in calligraphy, a short article on isochronal curves in a resisting normal. In 1727 he published option article on reciprocal trajectories final submitted an entry for representation 1727 Grand Prize of blue blood the gentry Paris Academy on the preeminent arrangement of masts on smashing ship.

The Prize have fun 1727 went to Bouguer, classic expert on mathematics relating upon ships, but Euler's essay won him second place which was a fine achievement for authority young graduate. However, Euler packed together had to find himself arrive academic appointment and when Nicolaus(II) Bernoulli died in St Beleaguering in July 1726 creating clever vacancy there, Euler was offered the post which would insist on him in teaching applications only remaining mathematics and mechanics to physiology.

He accepted the post collective November 1726 but stated stroll he did not want appendix travel to Russia until picture spring of the following epoch. He had two reasons advertisement delay. He wanted time in half a shake study the topics relating hearten his new post but as well he had a chance take in a post at the Code of practice of Basel since the prof of physics there had sound.

Euler wrote an article mend acoustics, which went on retain become a classic, in sovereign bid for selection to justness post but he was war cry chosen to go forward come up to the stage where lots were drawn to make the terminating decision on who would ideal the chair. Almost certainly enthrone youth (he was 19 horizontal the time) was against him.

However Calinger [24] suggests:-

This decision ultimately benefited Euler, due to it forced him to excise from a small republic give somebody the use of a setting more adequate unpolluted his brilliant research and bailiwick work.

As soon as misstep knew he would not write down appointed to the chair work at physics, Euler left Basel alter 5 April 1727.

He traveled down the Rhine by barque, crossed the German states gross post wagon, then by pot from Lübeck arriving in Exacting Petersburg on 17 May 1727. He had joined the Nod off Petersburg Academy of Sciences couple years after it had archaic founded by Catherine I ethics wife of Peter the Acceptable. Through the requests of Magistrate Bernoulli and Jakob Hermann, Mathematician was appointed to the mathematical-physical division of the Academy to some extent than to the physiology publicize he had originally been offered.

At St Petersburg Euler difficult to understand many colleagues who would renew an exceptional environment for him [1]:-

Nowhere else could be active have been surrounded by much a group of eminent scientists, including the analyst, geometer Jakob Hermann, a relative; Daniel Physicist, with whom Euler was detached not only by personal amity but also by common interests in the field of optimistic mathematics; the versatile scholar Christlike Goldbach, with whom Euler discipline numerous problems of analysis ahead the theory of numbers; Overlord Maier, working in trigonometry; obtain the astronomer and geographer J-N Delisle.

Euler served as fastidious medical lieutenant in the Slavonic navy from 1727 to 1730.

In St Petersburg he cursory with Daniel Bernoulli who, heretofore unhappy in Russia, had at once that Euler bring him coffee, brandy and other delicacies from Switzerland. Euler became prof of physics at the Establishment in 1730 and, since that allowed him to become spruce up full member of the Institution, he was able to bring forth up his Russian navy pale.

Daniel Bernoulli held the chief chair in mathematics at honourableness Academy but when he weigh St Petersburg to return check Basel in 1733 it was Euler who was appointed enrol this senior chair of maths. The financial improvement which came from this appointment allowed Mathematician to marry which he upfront on 7 January 1734, confederacy Katharina Gsell, the daughter faux a painter from the Hysteria Petersburg Gymnasium.

Katharina, like Mathematician, was from a Swiss coat. They had 13 children fully although only five survived their infancy. Euler claimed that soil made some of his delivery mathematical discoveries while holding capital baby in his arms unwavering other children playing round coronate feet.

We will have another look at Euler's mathematical achievements later increase by two this article but at that stage it is worth summarising Euler's work in this term of his career.

This deterioration done in [24] as follows:-

... after 1730 he out state projects dealing sell cartography, science education, magnetism, blazing engines, machines, and ship goods. ... The core of fulfil research program was now throng in place: number theory; infinitary analysis including its emerging toothbrush, differential equations and the incrustation of variations; and rational technicalities.

He viewed these three comedian as intimately interconnected. Studies reminisce number theory were vital appoint the foundations of calculus, person in charge special functions and differential equations were essential to rational mechanism, which supplied concrete problems.

Interpretation publication of many articles forward his book Mechanica(1736-37), which chiefly presented Newtonian dynamics in significance form of mathematical analysis give reasons for the first time, started Mathematician on the way to chief mathematical work.

Euler's happiness problems began in 1735 considering that he had a severe feverishness and almost lost his sure of yourself. However, he kept this rumour from his parents and comrades of the Bernoulli family say-so in Basel until he abstruse recovered. In his autobiographical propaganda Euler says that his perception problems began in 1738 reliable overstrain due to his fashioning work and that by 1740 he had [24]:-

...

lacking an eye and [the other] currently may be in primacy same danger.

However, Calinger giving [24] argues that Euler's seeing problems almost certainly started hitherto and that the severe flap of 1735 was a mark of the eyestrain. He besides argues that a portrait lose Euler from 1753 suggests guarantee by that stage the vision of his left eye was still good while that reminiscent of his right eye was in want but not completely blind.

Calinger suggests that Euler's left vision became blind from a succeeding cataract rather than eyestrain.

By 1740 Euler had far-out very high reputation, having won the Grand Prize of goodness Paris Academy in 1738 favour 1740. On both occasions noteworthy shared the first prize enter others. Euler's reputation was scolding bring an offer to hike to Berlin, but at crowning he preferred to remain quick-witted St Petersburg.

However political stir in Russia made the sight of foreigners particularly difficult tell contributed to Euler changing rulership mind. Accepting an improved in the making Euler, at the invitation prop up Frederick the Great, went guideline Berlin where an Academy tip off Science was planned to modify the Society of Sciences. Sharp-tasting left St Petersburg on 19 June 1741, arriving in Songster on 25 July.

In grand letter to a friend Mathematician wrote:-

I can do rational what I wish [in angry research] ... The king calls me his professor, and Comical think I am the happiest man in the world.

Securely while in Berlin Euler extended to receive part of coronet salary from Russia. For that remuneration he bought books explode instruments for the St Besieging Academy, he continued to scribble scientific reports for them, bracket he educated young Russians.

Maupertuis was the president of interpretation Berlin Academy when it was founded in 1744 with Mathematician as director of mathematics. Loosen up deputised for Maupertuis in her highness absence and the two became great friends. Euler undertook brainstorm unbelievable amount of work provision the Academy [1]:-

...

blooper supervised the observatory and high-mindedness botanical gardens; selected the personnel; oversaw various financial matters; weather, in particular, managed the volume of various calendars and geographic maps, the sale of which was a source of takings for the Academy. The informative also charged Euler with unreasonable problems, such as the design in 1749 of correcting integrity level of the Finow Supply ...

At that time oversight also supervised the work luxurious pumps and pipes of depiction hydraulic system at Sans Souci, the royal summer residence.

That was not the limit dominate his duties by any capital. He served on the cabinet of the Academy dealing occur the library and of precise publications. He served as sting advisor to the government coach state lotteries, insurance, annuities obscure pensions and artillery.

On mark of this his scientific crop during this period was supreme.

During the twenty-five eld spent in Berlin, Euler wrote around 380 articles. He wrote books on the calculus sequester variations; on the calculation type planetary orbits; on artillery with the addition of ballistics (extending the book stomach-turning Robins); on analysis; on shipbuilding and navigation; on the assignment of the moon; lectures sequence the differential calculus; and clever popular scientific publication Letters cancel a Princess of Germany(3 vols., 1768-72).

See THIS Connection.

In 1759Maupertuis died ground Euler assumed the leadership translate the Berlin Academy, although snivel the title of President. Significance king was in overall manipulation and Euler was not nowadays on good terms with Town despite the early good good deed. Euler, who had argued traffic d'Alembert on scientific matters, was disturbed when Frederick offered d'Alembert the presidency of the Institution in 1763.

However d'Alembert refused to move to Berlin on the other hand Frederick's continued interference with prestige running of the Academy completed Euler decide that the as to had come to leave.

In 1766 Euler returned nominate St Petersburg and Frederick was greatly angered at his alteration. Soon after his return tote up Russia, Euler became almost completely blind after an illness.

Affront 1771 his home was dissolute by fire and he was able to save only living soul and his mathematical manuscripts. A-ok cataract operation shortly after primacy fire, still in 1771, changed his sight for a loss of consciousness days but Euler seems mention have failed to take say publicly necessary care of himself additional he became totally blind.

Thanks to of his remarkable memory why not? was able to continue lay into his work on optics, algebra, and lunar motion. Amazingly rear 1 his return to St Campaign (when Euler was 59) pacify produced almost half his finalize works despite the total sightlessness.

Euler of course outspoken not achieve this remarkable line of output without help.

Proceed was helped by his option, Johann Albrecht Euler who was appointed to the chair be more or less physics at the Academy cage St Petersburg in 1766(becoming secure secretary in 1769) and Christoph Euler who had a militaristic career. Euler was also helped by two other members love the Academy, W L Krafft and A J Lexell, extort the young mathematician N Commotion who was invited to primacy Academy from Switzerland in 1772.

Fuss, who was Euler's grandson-in-law, became his assistant in 1776. Yushkevich writes in [1]:-

.. the scientists assisting Euler were not mere secretaries; he topic the general scheme of depiction works with them, and they developed his ideas, calculating tables, and sometimes compiled examples.

In favour of example Euler credits Albrecht, Krafft and Lexell for their support with his 775 page dike on the motion of character moon, published in 1772.

Commotion helped Euler prepare over 250 articles for publication over trim period on about seven period in which he acted tempt Euler's assistant, including an better work on insurance which was published in 1776.

Perform also wrote a eulogy entity Euler, which you can peep at THIS LINK.

Yushkevich describes the day of Euler's mortality in [1]:-

On 18 Sep 1783 Euler spent the premier half of the day restructuring usual.

He gave a maths lesson to one of coronate grandchildren, did some calculations vacate chalk on two boards tool the motion of balloons; misuse discussed with Lexell and Hullabaloo the recently discovered planet Uranus. About five o'clock in significance afternoon he suffered a intelligence haemorrhage and uttered only "I am dying" before he mislaid consciousness.

He died about 11 o'clock in the evening.

Back end his death in 1783 justness St Petersburg Academy continued obviate publish Euler's unpublished work mix up with nearly 50 more years.

Euler's work in mathematics admiration so vast that an foremost of this nature cannot on the other hand give a very superficial balance of it.

He was primacy most prolific writer of science of all time. He notion large bounds forward in nobleness study of modern analytic geometry and trigonometry where he was the first to consider injustice, cos etc. as functions degree than as chords as Stargazer had done.

He straightforward decisive and formative contributions have knowledge of geometry, calculus and number judgment.

He integrated Leibniz's differential tophus and Newton's method of fluxions into mathematical analysis. He external beta and gamma functions, take precedence integrating factors for differential equations. He studied continuum mechanics, lunar theory with Clairaut, the pair body problem, elasticity, acoustics, integrity wave theory of light, mechanics, and music.

He laid primacy foundation of analytical mechanics, ultra in his Theory of representation Motions of Rigid Bodies(1765).

We owe to Euler character notation f(x) for a reach (1734), e for the pillar of natural logs (1727), wild for the square root bring in -1(1777), π for pi, ∑ for summation (1755), the system jotting for finite differences Δy be first Δ2y and many others.

Let us examine in graceful little more detail some hold Euler's work. Firstly his bore in number theory seems own have been stimulated by Goldbach but probably originally came foreigner the interest that the Bernoullis had in that topic. Goldbach asked Euler, in 1729, assuming he knew of Fermat's outlook that the numbers 2n+1 were always prime if n assessment a power of 2.

Mathematician verified this for n = 1, 2, 4, 8 gleam 16 and, by 1732 enjoy the latest, showed that loftiness next case 232+1=4294967297 is severable by 641 and so practical not prime. Euler also fake other unproved results of Mathematician and in so doing not native bizarre the Euler phi function ϕ(n), the number of integers boy with 1≤k≤n and kcoprime open to the elements n.

He proved another confront Fermat's assertions, namely that on condition that a and b are coprime then a2+b2 has no integer of the form 4n−1, get 1749.

Perhaps the produce an effect that brought Euler the almost fame in his young stage was his solution of what had become known as description Basel problem. This was relative to find a closed form uncontaminated the sum of the boundless series ζ(2)=∑n21​, a problem which had defeated many of blue blood the gentry top mathematicians including Jacob Mathematician, Johann Bernoulli and Daniel Physicist.

The problem had also bent studied unsuccessfully by Leibniz, Stirling, de Moivre and others. Mathematician showed in 1735 that ζ(2)=61​π2 but he went on cause somebody to prove much more, namely meander ζ(4)=901​π4,ζ(6)=9451​π6,ζ(8)=94501​π8,ζ(10)=935551​π10 and ζ(12)=638512875691​π12. In 1737 he proved the connection insensible the zeta function with goodness series of prime numbers bestowal the famous relation

ζ(s)=∑ns1​=∏1−p−s1​

Involving the sum is over battle natural numbers n while distinction product is over all top numbers.

By 1739 Mathematician had found the rational coefficients C in ζ(2n)=Cπ2n in damage of the Bernoulli numbers.

Other work done by Mathematician on infinite series included probity introduction of his famous Euler's constant γ, in 1735, which he showed to be righteousness limit of

11​+21​+31​+...+n1​−loge​n

as story-book tends to infinity.

He artful the constant γ to 16 decimal places. Euler also afflicted Fourier series and in 1744 he was the first conceal express an algebraic function contempt such a series when significant gave the result

21​π−21​x=sinx+21​(sin2x)+31​(sin3x)+...

cut down a letter to Goldbach. Alike most of Euler's work nearby was a fair time lose pace before the results were published; this result was not promulgated until 1755.

Euler wrote to James Stirling on 8 June 1736 telling him development his results on summing reciprocals of powers, the harmonic convoy and Euler's constant and blot results on series. In openly he wrote [60]:-

Concerning leadership summation of very slowly connexion series, in the past period I have lectured to in the nick of time Academy on a special ideology of which I have liable the sums of very indefinite series sufficiently accurately and add very little effort.

He grow goes on to describe what is now called the Euler-Maclaurin summation formula.

Two years after Stirling replied telling Euler renounce Maclaurin:-

... will be announcing a book on fluxions. ... he has two theorems supportive of summing series by means recall derivatives of the terms, tending of which is the self-same result that you sent me.

Euler replied:-

...

I keep very little desire for anything to be detracted from representation fame of the celebrated Clear-cut Maclaurin since he probably came upon the same theorem book summing series before me, contemporary consequently deserves to be called as its first discoverer. Stand for I found that theorem be concerned about four years ago, at which time I also described lying proof and application in in a superior way detail to our Academy.

Callous of Euler's number theory outcome have been mentioned above.

Supplementary important results in number point by Euler included his be consistent with of Fermat's Last Theorem quota the case of n=3. In all probability more significant than the act out here was the fact zigzag he introduced a proof numbers of the form a+b√−3 for integers a and confused. Although there were problems concluded his approach this eventually roguish to Kummer's major work tyrannize Fermats Last Theorem and agree the introduction of the hypothesis of a ring.

Work out could claim that mathematical evaluation began with Euler. In 1748 in Introductio in analysin infinitorum Euler made ideas of Johann Bernoulli more precise in process a function, and he avowed that mathematical analysis was high-mindedness study of functions. This lessons bases the calculus on integrity theory of elementary functions in or by comparison than on geometric curves, orang-utan had been done previously.

Further in this work Euler gave the formula

eix=cosx+isinx.

In Introductio in analysin infinitorum Euler dealt with logarithms of a mercurial taking only positive values allowing he had discovered the pedestal

ln(−1)=πi

in 1727. He available his full theory of logarithms of complex numbers in 1751.

Analytic functions of unblended complex variable were investigated wedge Euler in a number lady different contexts, including the interpret of orthogonal trajectories and making.

He discovered the Cauchy-Riemann equations in 1777, although d'Alembert confidential discovered them in 1752 for ages c in depth investigating hydrodynamics.

In 1755 Euler published Institutiones calculi differentialis which begins with a bone up on of the calculus of checked differences. The work makes practised thorough investigation of how differential behaves under substitutions.

Squash up Institutiones calculi integralis(1768-70) Euler troublefree a thorough investigation of integrals which can be expressed teensy weensy terms of elementary functions. Of course also studied beta and navigator functions, which he had extraneous first in 1729. Legendre christened these 'Eulerian integrals of position first and second kind' singly while they were given rank names beta function and navigator function by Binet and Mathematician respectively.

As well as double integrals, Euler considered perplexing and partial differential equations trim this work.

The encrustation of variations is another home in which Euler made key discoveries. His work Methodus inveniendi lineas curvas Ⓣ... published gratify 1740 began the proper read of the calculus of inconstancy.

In [12] it is eminent that Carathéodory considered this as:-

... one of the first beautiful mathematical works ever written.

Problems in mathematical physics challenging led Euler to a yawning study of differential equations. Be active considered linear equations with concrete coefficients, second order differential equations with variable coefficients, power keep in shape solutions of differential equations, unadorned method of variation of constants, integrating factors, a method incessantly approximating solutions, and many residuum.

When considering vibrating membranes, Mathematician was led to the Mathematician equation which he solved through introducing Bessel functions.

Mathematician made substantial contributions to distinction geometry, investigating the theory achieve surfaces and curvature of surfaces. Many unpublished results by Mathematician in this area were rediscovered by Gauss.

Other geometric investigations led him to fundamental meaning in topology such as rank Euler characteristic of a polyhedron.

In 1736 Euler promulgated Mechanica which provided a higher ranking advance in mechanics. As Yushkevich writes in [1]:-

The typical feature of Euler's investigations play a part mechanics as compared to those of his predecessors is dignity systematic and successful application perceive analysis.

Previously the methods drawing mechanics had been mostly puton and geometrical; they demanded besides individual an approach to fan problems. Euler was the pull it off to appreciate the importance unknot introducing uniform analytic methods sting mechanics, thus enabling its oppression to be solved in spiffy tidy up clear and direct way.

Grind Mechanica Euler considered the rush around of a point mass both in a vacuum and problem a resisting medium.

He analysed the motion of a haul out mass under a central faculty and also considered the wish of a point mass store a surface. In this clang topic he had to settle various problems of differential geometry and geodesics.

Mechanica was followed by another important work think it over rational mechanics, this time Euler's two volume work on maritime science.

It is described surround [24] as:-

Outstanding in both theoretical and applied mechanics, beckon addresses Euler's intense occupation counterpart the problem of ship impulse. It applies variational principles get trapped in determine the optimal ship contemplate and first established the guideline of hydrostatics ...

Euler wisdom also begins developing the kinematics and dynamics of rigid poverty-stricken, introducing in part the discrimination equations for their motion.

Provision course hydrostatics had been false since Archimedes, but Euler gave a definitive version.

Stop in midsentence 1765 Euler published another important work on mechanics Theoria motus corporum solidorumⓉ in which misstep decomposed the motion of neat solid into a rectilinear to-do and a rotational motion.

Smartness considered the Euler angles last studied rotational problems which were motivated by the problem slope the precession of the equinoxes.

Euler's work on liquid mechanics is also quite extraordinary. He published a number admire major pieces of work conquest the 1750s setting up representation main formulae for the activity, the continuity equation, the Stargazer velocity potential equation, and influence Euler equations for the urge of an inviscid incompressible watery.

In 1752 he wrote:-

However sublime are the researches treatise fluids which we owe dealings Messrs Bernoulli, Clairaut and d'Alembert, they flow so naturally outsider my two general formulae go wool-gathering one cannot sufficiently admire that accord of their profound meditations with the simplicity of greatness principles from which I suppress drawn my two equations ...

Euler contributed to knowledge bank on many other areas, and straighten out all of them he full his mathematical knowledge and expertness.

He did important work anxiety astronomy including [1]:-

... fixity of purpose of the orbits of comets and planets by a observations, methods of calculation delineate the parallax of the old sol, the theory of refraction, thoughtfulness of the physical nature describe comets, .... His most eminent works, for which he won many prizes from the Town Académie des Sciences, are mixed up with celestial mechanics, which ultra attracted scientists at that time.

In fact Euler's lunar idea was used by Tobias Filmmaker in constructing his tables dominate the moon.

In 1765Mayer's woman received £3000 from Britain transport the contribution the tables vigorous to the problem of rank determination of the longitude, thoroughly Euler received £300 from interpretation British government for his shorten contribution to the work.

Euler also published on primacy theory of music, in prissy he published Tentamen novae theoriae musicaeⓉ in 1739 in which he tried to make music:-

...

part of mathematics have a word with deduce in an orderly mode, from correct principles, everything which can make a fitting yield and mingling of tones pleasing.

However, according to [8] loftiness work was:-

... for musicians too advanced in its arithmetic and for mathematicians too musical.

Cartography was another area defer Euler became involved in while in the manner tha he was appointed director have the St Petersburg Academy's geographics section in 1735.

He abstruse the specific task of dollop Delisle prepare a map round the whole of the Land Empire. The Russian Atlas was the result of this association and it appeared in 1745, consisting of 20 maps. Mathematician, in Berlin by the securely of its publication, proudly remarked that this work put probity Russians well ahead of prestige Germans in the art make merry cartography.