Sezibalo esikhulu Eyler Leonard: impumelelo kwi-mathematics, amanye amaqiniso athakazelisayo, Biography emfushane

Leonhard Euler - sezibalo Swiss kanye physics, omunye wabasunguli wezibalo okumsulwa. Akazange nje wenza iminikelo lokubalulekile formative geometry, calculus, omakhenikha kanye imfundiso yokuziphendukela izinombolo, kodwa futhi nezindlela ukuxazulula izinkinga yezinkanyezi elibukelayo futhi isicelo wezibalo kwezobunjiniyela imisebenzi yomphakathi.

Euler (sezibalo): Biography emfushane

Leonhard Euler wazalwa Apreli 15, 1707 Kwakuwusuku Paulus Euler noMargaret Brooker amazibulo. Ubaba livela uhlobo othobekile wezingcweti, futhi okhokho Margaret Brooker kwadingeka eziningi ososayensi abaziwayo. Paulus Euler wakhonza ngaleso umbambeli isikhathi Esontweni St uJakob. Njengoba isazi semfundiso yenkolo, uyise Leonard wayenesithakazelo wezibalo, futhi eminyakeni emibili yokuqala cwaningo eyunivesithi abahambele lo izifundo edumile Yakoba Bernulli. Ngemva cishe konyaka nengxenye ngemva nje kokuzalwa kwendodana yabo, umkhaya wathuthela Riehen, Basel Emaphethelweni lapho Paulus Euler baba umfundisi nebandla lendawo. Elapho futhi wakhonza ngokwethembeka kwaze kwaba sekufeni kwakhe.

Umndeni wawuhlala ezimweni enyinyekile, ikakhulukazi ngemva kokuzalwa komntwana wakhe wesibili, u-Anna-UMaria 1708. Lo mbhangqwana kuyoba izingane ezimbili - uMaria Magdalena kanye Johann Heinrich.

Izifundo zokuqala mathematics, uLeonard wathola ekhaya kuyise. Emhlabeni eneminyaka eyisishiyagalombili wathunyelwa esikoleni Latin e Basel, lapho ayehlala khona endlini kagogo ngasohlangothini lukanina. Ukuze bavale isikhala izinga abampofu imfundo esikoleni ngaleso sikhathi, ubaba waqasha komfundisi yangasese, isazi semfundiso yenkolo osemusha okuthiwa Johannes Burckhardt, umthandi abanothando wezibalo.

Ngo-October 1720 lapho ngineminyaka engu-iminyaka engu-13, uLeonard langena University of Basel-Faculty of Philosophy (okuyinto evamile ngesikhathi), lapho ubehambele khona ingqungquthela amakilasi ezethula mathematics aphansi Ioganna Bernulli, ungumfowabo omncane umufi ngesikhathi kaJakobe.

Euler Young wathatha ngentshiseko kuze izifundo zakhe, okuyinto ngokushesha yabakhanga nathishela, lokunguye wamkhuthaza ukufunda izincwadi eziyinkimbinkimbi lakhe, ngisho wazicelela ezifundweni zabo ngeMigqibelo. Ngo 1723, uLeonard igcwaliswe imfundo yakhe iziqu zeMasters futhi wabeka inkulumo yomphakathi ngesiLatini, lapho Descartes kuqhathaniswa uhlelo ne ifilosofi yemvelo ka Newton.

Ukulandela izifiso abazali bakhe, wabhalisa e-Theological Faculty, Kodwa nikela, iningi wezibalo isikhathi. Ekugcineni, cishe ngesikhathi ekufuna ka Ioganna Bernulli ubaba sakuthatha kalula nje indodana yakhe yenze injongo yesayensi, hhayi umsebenzi zenkolo.

Eminyakeni 19, Euler sezibalo nesibindi ukuze ancintisane ososayensi phezulu isikhathi, ngekubamba lichaza ukuncintisanela nesixazululo Paris Academy of Sciences on ukubekwa kahle umkhumbi insika. Ngaleso sikhathi ayenakho ngangingakaze ekuphileni kwami ukubonwa imikhumbi, umklomelo wokuqala awuwinanga, kodwa iwine endaweni yesibili yodumo. Komunye unyaka lapho kwakukhona letikhala uMnyango Physics e-University of Basel, uLeonard, ngokusekelwa umeluleki wakhe Ioganna Bernulli, wanquma ukulwa indawo, kodwa walahlekelwa ngenxa yobudala babo nokuntula i uhlu umxhwele izincwadi. Ngomqondo othile wayesembonile waba nenhlanhla ngoba wakwazi ukwamukela isimemo Petersburg Academy of Sciences, eyasungulwa eminyakeni embalwa ngaphambili by Tsar uPetru mina, lapho Euler wathola inkambu ethembisa ngaphezulu, okwamenza wakwazi ukuthuthukisa ngokugcwele. Iqhaza main kukhala ngu Bernoulli namadodana akhe amabili, futhi mina, Daniyeli, Nicklaus II, abakhuthalele ukusebenza lapho.

Petersburg (1727-1741): ukwanda meteoric

Euler wachitha ubusika ka 1726 e Basel, ukutadisha nokwakheka zomzimba belungiselela ekwenzeni imisebenzi yabo kulindeleke esikoleni. Lapho efika Petersburg wasebenza umhlobo, kwaba sobala ukuthi kumele azinikele wesayensi zezibalo. Ngaphezu kwalokho, ngo-Euler kwakudingeka iqhaza isinqumo-izivivinyo esikhathini ubusosha Corps, futhi ukweluleka Uhulumeni ezindabeni ezihlukahlukene zesayensi kanye lobuchwepheshe.

Leonard ingashintshwa kalula nezimo ezintsha ezinzima ekuphileni enyakatho yeYurophu. Ngokungafani namanye amalungu kakhulu sokusebenzelana namanye amazwe sokuqeqesha, ngokushesha waqala ukufunda isiRashiya futhi kahle ngokushesha futhi amafomu ezibhaliwe futhi ngomlomo. Kwaphela isikhathi ayephila nge Daniel Bernoulli futhi kwaba abangane nalabo Abathi bamaKrestu Goldbach, uNobhala Permanent of the Academy, namuhla eyaziwa ngokuthi namanje ngeke axazulula inkinga yayo, owawuthi iyiphi ngisho inombolo kusuka 4, kungenziwa emelelwa isamba primes ezimbili. Izincwadi olunzulu phakathi kwazo iwumthombo ebalulekile emlandweni wesayensi ekhulwini XVIII.

Leonhard Euler, impumelelo izibalo okuyinto kweso bamlethela udumo emhlabeni wonke futhi ngawakhulisa isimo sakhe, owawuse-Academy of iminyaka yabo ezikhiqiza kakhulu.

Ngo-January 1734, washada Katarine Gzel, indodakazi umculi Swiss, owafundisa nge Euler, base bethuthela emzini wabo siqu. Umshado wafika ukukhanyisa izingane ezingu-13, lapho, Nokho, emihlanu kuphela ufinyelelwe umuntu omdala. Izibulo, Johann Albrecht, naye waba sezibalo, futhi kamuva wasiza uyise emsebenzini wakhe.

Euler yehlelwa usizi. Ngo-1735, lapho wagula kakhulu futhi ngacishe ngafa. Ukuze impumuzo enkulu yazo zonke ukuthi walulama, kodwa ngemva kweminyaka emithathu emuva iyagula. Ngalesi sikhathi, lesi sifo kwamlahlekisela nasesweni lakhe lokunene, olubonakala ngokucacile kuzo zonke ekumeni of ososayensi kusukela ngaleso sikhathi.

Ukungazinzi kwezombusazwe eRussia, okwenzeka ngemva kokufa Queen Anna Ivanovna, Euler ephoqeleka ukuba ashiye izindlela Petersburg. Ikakhulukazi ngoba wabona isimemo esivela Prussian King Friedrich II ukuza Berlin nokusiza ukudala Academy of Sciences khona.

Ngo-June 1741, uLeonard nomkakhe Katarina, Johann Albrecht engu-6 ubudala kanye noCarl owayeneminyaka engu-ubudala ngemoto sisuka Petersburg ukuze Berlin.

Imisebenzi e Berlin (1741-1766)

Emkhankasweni wempi eSilesia noFrederick II usihlehlisile izinhlelo ukusungulwa sokuqeqesha. Futhi kuphela 1746 ekugcineni kwakhiwa. Waba umongameli Pierre-Lui Moro de Maupertuis futhi Euler waqokwa umqondisi woMnyango Mathematics. Kodwa kungakenzeki lokho, akazange ahlale angenzi lutho. Leonard wabhala izihloko mayelana 20 ngokwesayensi, azibhala ezinkulu 5 futhi wenza izincwadi ezingaphezu kuka-200.

Naphezu kweqiniso lokuthi Euler babenza khona imisebenzi eminingi - obangela Observatory kanye izingadi zezimila, ukuxazulula nabasebenzi kanye nezindaba zezimali ezihilelekile ukudayiswa ezincwadini zonyaka ezazisakazeka, akha lesi Umthombo oyinhloko wemali we Academy, ingasaphathwa amaphrojekthi ahlukahlukene kwezobuchwepheshe kanye zobunjiniyela, nokwenza kwayo zezibalo ayiphazamiseki.

Futhi, akulona kakhulu baphazanyiswa scandal we igunya kwatholakala isimiso isinyathelo okungenani, oqubuke kule 1750s zokuqala, amangalelwe ngohlelo Maupertuis ukuthi inselele usosayensi Swiss kanye academician elisanda kuqokwa Johann Samuel Koenig, khuluma ngezinto Ukukhuluma kwakhe Leibniz wabhalela sezibalo uJakobe Hermann. Koenig kwakuthandeka Maupertuis namacala ukusebenzisa umqondo womunye. Lapho ecelwa ukuba aveze incwadi, akakwazanga ukukwenza, futhi Euler wabelwa ukuba aphenye icala. Njengoba engenabo abangane uzwela ifilosofi Leibniz, ayengaba sohlangothini umongameli futhi esola wakwaKonig lokukhwabanisa. I abilayo yathinteka lapho uVoltaire, owathatha ohlangothini Koenig wabhala ukubhinqa ajivazayo, lampooned Maupertuis futhi Euler basindiswa. Umongameli wathukuthela kabi yashiya Berlin ngokushesha, Euler futhi kwadingeka abhekane, de empeleni waba ephethwe sokuqeqesha.

usosayensi umndeni

ULeonard waba mkhulu waze ayeyithenge ifa e Charlottenburg, nedlelo Berlin olusentshonalanga, enkulu ngokwanele ukuqinisekisa ukuhlala ukhululekile kunina ongumfelokazi, ubani owayebangele ukuba zonke eBerlin ngo-1750, ingxenye-udade nezingane zakhe.

Ngo 1754, amazibulo akhe Johann Albrecht ngesiphakamiso Maupertuis eneminyaka engu-iminyaka engu-20 futhi wakhethwa ukuba Berlin Academy. Ngo 1762, umsebenzi wayo perturbations we omise lezinkanyezi ezinomsila ukudonsa amaplanethi waklonyeliswa umklomelo we Petersburg Academy, futhi waxoxela Alexis-Klod Klero. indodana ka-Euler yesibili, uCarl, wafunda imithi ekhatsi Halle, nowesithathu, Christoph, baba isikhulu. Indodakazi yakhe Charlotte washada Aristocrat Dutch futhi udadewabo omdala Helena 1777 - isiphathimandla Russian.

inkosi izingobe

Usosayensi Ubuhlobo noFrederick II zazingelula. Ngokwengxenye lokhu okunemibandela on umehluko okukhulu kwenyama siqu nefilosofi Frederick - a, lokuxoxa uyaziqhenya ezethemba, nenhle futhi behlakaniphile, a sympathizer we French Ukukhanyiselwa; sezibalo Euler - engumProthestani nesizotha, neqondayo, engowenhlabathi futhi ozinikele. Esinye, isizathu mhlawumbe okubaluleke kakhulu kwaba Ukungasifuni kwama Leonard ukuthi akazange ahlinzekwa okuthunyelwe kukamongameli Berlin Academy. Lokhu kwabangela inzondo enkulu liye landa kuphela ngemva kokuhamba le Maupertuis nemizamo Euler ukugcina isikhungo ntanta, lapho Frederick yazama ukuvusa isithakazelo kwesitulo kamongameli Jean d'Alembert Leron. Lesi sakamuva, eqinisweni, wafika Berlin, kodwa kuphela ukutshela inkosi mayelana disinterest yakhe futhi Abelana uLeonard. Friedrich akugcini nje indiva iseluleko D'Alembert, kodwa engagwegwesi esezibeke njengenhloko ye Academy. Lokhu, kanye nabanye ukwehluleka eziningi iNkosi, ekugcineni, kwaholela yokuthi biography of sezibalo Euler wenza esejika emuva.

Ngo-1766, naphezu kwezithiyo ngehlangothini le nkosi, washiya Berlin. Leonard wamukele isimemo uCatherine II ukubuyela Petersburg, nalapho efike waphelela khona ngokusemthethweni yamukelwa.

Nalapha futhi, Petersburg (1766-1783)

Uhlonishwa futhi ehamba ekhulekelwa esikoleni esigodlweni Catherine sezibalo esikhulu Euler wasebenza okuthunyelwe ehlonishwa kakhulu futhi kwaba izilomo kwalokho sinqatshiwe isikhathi eside kangaka e-Berlin. Eqinisweni, yena wadlala indima Umholi kwezikamoya, uma hhayi inhloko sokuqeqesha. Nokho, Ngeshwa, impilo Akayena yini konke kwahamba kahle kakhulu. cataract esweni ngakwesokunxele, yona eyaqala ukwenza i uhlupho kuye Berlin laliya ungaguli kakhulu, futhi ngo-1771 Euler isinqumo akhuluma ngokuhlinza. okuwumphumela kwaba ukubunjwa ithumba, owabhubhisa cishe ngokuphelele umbono.

Ngasekupheleni kwalowo nyaka, ngesikhathi umlilo omkhulu Petersburg, indlu wakhe wokhuni yaphuka, Euler wawuyivelakancane ayikwazanga ashiswe ephila sibonga kuphela bophula nobuqhawe uPetru Grimm, i ingcweti kusukela Basel. Ukuze unciphise lokho usizi, iNdlovukazi usunike izimali ukwakhiwa ikhaya elisha.

Elinye igalelo esindayo waziqonda Euler ngo 1773 lapho kushona umkakhe. Ngemva kweminyaka engu-3, hhayi zincike izingane zabo, washada okwesibili ku udadewabo nengxenye, uSalome Abhigayili Gsell, (1723-1794).

Naphezu kwazo zonke lezi izenzakalo ebulalayo, sezibalo Leonhard Euler yayizimisele isayensi. Ngempela, cishe ingxenye yomsebenzi wakhe yanyatheliswa noma wazalwa Petersburg. Phakathi kwabo kukhona ezimbili yakhe "bestseller" - ". I-Algebra" "Izincwadi ku-Princess German" futhi Ngokwemvelo, wayengeke akwazi ukukwenza ngaphandle nonobhala ezinhle kanye nosizo lobuchwepheshe ukuthi alunikezile, phakathi kwezinye izinto, Nicklaus Fuss, a compatriot we Basel kanye umyeni ikusasa umzukulu Euler. Active iqhaza inqubo ukuthatha indodana yakhe Johann Albrecht. Lesi sakamuva wabuye wabakhumbuza owayebhala ngomshini Academy amaseshini lapho usosayensi othile, njengoba ilunga eliphelele omdala, kwadingeka ukuba bengamele.

ukufa

Sezibalo esikhulu Leonhard Euler ubulawe yisifo sohlangothi 18 Septhemba 1783 ngenkathi idlala umzukulu wakhe. Ngosuku kokufa zayo ezimbili ezinkulu amasleyithi atholakele amafomula ezichaza indiza ibhaluni, ephelele 5 Juni 1783 e Paris, Montgolfier abazalwane. Umqondo yasungulwa futhi uzilungiselele ukushicilelwa uJohann indodana. Kwakuwusuku lokugcina ube usosayensi, eyanyatheliswa ngo-1784 Memoires ivolumu. Leonhard Euler futhi iminikelo wakhe wezibalo sasisikhulu kangangokuba ukugeleza izihloko zilindele sako emaphephabhukwini zezemfundo, ishicilele iminyaka engu-50 ngemva kokufa usosayensi.

umsebenzi Scientific e Basel

Phakathi nenkathi emfushane Basel Euler umnikelo wezibalo kwakulula Curves isochronous kanye ne-mutual, kanye umsebenzi mncintiswano umklomelo we Paris Academy. Kodwa ubunzima main kulesigaba kwaba Dissertatio Physica de Sono, bafaka ekusekeleni igama lakhe kuze kube isihlalo kuyi-physics e-University of Basel, ubunjalo nokusatshalaliswa umsindo, ngokukhethekile, ijubane umsindo kanye nesizukulwane izinsimbi zomculo ezihlukahlukene.

Eyokuqala isikhathi Petersburg

Naphezu kwezinkinga zempilo olutholwa Euler, ukuthuthuka izibalo, usosayensi abakwazi kodwa ezibangela ukumangala. Phakathi nalesi sikhathi, ngaphezu imisebenzi eyisisekelo ku Mechanics, imfundiso yokuziphendukela umculo, kanye izakhiwo oluhle ngemikhumbi yempi, uye ebhaliwe izihloko 70 ngezihloko ezihlukahlukene kusukela umqulusizinda kanye nenombolo theory izinkinga ezithile kuyi-physics, omakhenikha nesayensi yokuhlolwa kwezinkanyezi.

imiqulu emibili ye "Mechanics" kwakuyisiqalo uhlelo ibanga elide ukubuyekeza olunzulu zonke izici Mechanics, kuhlanganise izihambisimshini okuqinile, nezimo futhi nokunwebeka emizimbeni, kanye uketshezi kanye Mechanics yasezulwini.

Njengoba singabona kusukela inothi-izincwadi Euler, namanje e Basel, wacabanga okuningi umculo komculo futhi wayehlela ukubhala incwadi. Lezi izinhlelo oye wabonisa ukuvuthwa kuso Petersburg emenza zabasebenzi Tentamen, elanyatheliswa ngo-1739. Umkhiqizo iqala ngengxoxo ubunjalo umsindo njengoba kunyakaza izinhlayiya komoya, okufaka ukusatshalaliswa kwayo, izitho zomzimba kanye nombono sokuzwa of isizukulwane komsindo yezinhlamvu kanye nezinsimbi zomculo ezifuthwayo.

Umnyombo umsebenzi imfundiso yokuziphendukela injabulo kubangelwa umculo Euler wadala ngekubeka amathoni isikhawu, ukulele noma ukulandelana kwezinhlamvu amanani ezinombolo, ubukhulu akha "ubuhle" isakhiwo zomculo: ephansi ezingeni, aba maningi ubumnandi. Umsebenzi kwenziwa umongo kumbhali ozithandayo diatonic Ubumnene chromatique, kodwa futhi ukunikeza ephelele theory nezibalo senhliziyo (basendulo nabanamuhla). Euler akuyena kuphela owazama ujike umculo ibe isayensi ngqo: Descartes, Mersenne, futhi benza okufanayo kuye, njengoba D'Alembert, nabanye abaningi emva kwakhe.

Yemiqulu emibili ye-Scientia Navalis - esigabeni yentuthuko yayo Mechanics okunengqondo yesibili. Incwadi sendlala imigomo futhi ithuthukisa hydrostatic yakhoibrium imfundiso yokuziphendukela kunyakaza nemizimba ngakuthathu ukuthi afakwa amanzi. Umsebenzi iqukethe esiqalweni Mechanics kwezinto eziqinile, okuyinto kamuva crystallizes encwadini Theoria Motus corporum solidorum seu rigidorum, wesithathu indatshana ezinkulu ku Mechanics. Umqulu kwemfundiso yokuziphendukela yesibili osebenza ku imikhumbi, shipbuilding lokuzula.

Akukholeki Leonhard Euler, impumelelo izibalo okuyinto kule sisethwe umxhwele, kwadingeka isikhathi namandla okukhuthazela ukuze ubhale umsebenzi amakhasi angu-300 izibalo aphansi ukusetshenziswa Petersburg ezikoleni zamabanga aphakeme. Indlela nenhlanhla labo abantwana abafundiswa isazi ezinhle!

umsebenzi Berlin

Ngaphezu izihloko 280, eziningi zazo zazibaluleke kakhulu kule nkathi sezibalo Leonard Euler wadala uchungechunge azibhala yesayensi eyingqopha.

Inkinga brachistochrone - ukuthola izindlela okuyilapho uhamba mass amandla adonsela phansi kusuka kwelinye iphuzu e indiza mpo komunye ngesikhathi lemfisha - isibonelo ekuseni yenkinga adalwe Johann Bernoulli search umsebenzi (noma ijika), okuyinto optimizes Inkulumo kohlaziyo kuye ngokuthi umsebenzi. Ngo 1744-m ke ngo-1766-m Euler tibalo kakhulu le nkinga ngokwakha legatsha elisha lonke wezibalo - "calculus yokwahlukahluka".

Amabili indatshana ezincane phezu trajectories amaplanethi lezinkanyezi ezinomsila kanye yokukhanya, yavela eminyakeni mayelana 1744 futhi 1746. Lesi sakamuva okuthakazelisayo ngokomlando, kusukela waqala ingxoxo izinhlayiya Newton futhi igagasi imfundiso yokuziphendukela ukukhanya Euler.

Ngo uhloniphe umqashi wakhe, iNkosi noFrederick II, uLeonard waphenduka umsebenzi obalulekile kuqhubeke eyiNgisi Benjamin Robins, nakuba bagxeka "Mechanics" Nokho e 1736 Wanezela, amazwana eziningi kangaka, amanothi achazayo kanye nokulungiswa, ngenxa incwadi "wezikhali" (1745) by volume lokhu izikhathi 5 ephakeme ukwedlula yasekuqaleni.

Yemiqulu emibili ye-"Isingeniso ukuhlaziya kuncane" (1748), isazi sezibalo Euler ukuma ukuhlaziywa njengenhlangano isiyalo ezimele, ifingqa ezitholwe zakhe eziningi emkhakheni uchungechunge obungapheli, imikhiqizo okungenamingcele amafraktjhini baqhubeka. Kutfutfukisa nombono umsebenzi okucacile amagugu zangempela futhi eziyinkimbinkimbi futhi ligcizelela ukuthi indima yomama ayisisekelo ukuhlaziywa e inombolo, lomchazi nemisebenzi logarithmic. Umqulu wesibili lunikezelwe geometry kohlaziyo: imfundiso yokuziphendukela algebraic Curves kanye evele.

"Calculus Ukwahlukaniswa" futhi liqukethe izingxenye ezimbili, eyokuqala Sizokwenza ukubala umehluko kanye nomehluko, kanti eyesibili - imfundiso yokuziphendukela amandla uchungechunge summation ifomula kanye inani elikhulu izibonelo. Lapha, ngenhlanhla elalinalo lokuqala olunyathelisiwe Fourier chungechunge.

Laba bobathathu omningi "calculus Integral" sezibalo Euler ucabangela quadrature (m. E. Endless kuphindelelwa) imisebenzi aphansi nobuchwepheshe ngibalethe lwento umehluko zibalo, zichazele kahle ngokuzokwenzeka imfundiso yokuziphendukela lwento umehluko zibalo oda yesibili.

Kuyo yonke le minyaka e Berlin, futhi kamuva Leonard wafunda yokukhanya yejeyomethri. izihloko lakhe nezincwadi eziphathelene nale ndaba, kuhlanganise nenqwaba emithathu ivolumu "Dioptrics" zaba amavolumu eziyisikhombisa Opera Omnia. Ekhuluma ngesici esiyinhloko lo msebenzi ukuthuthukisa amathuluzi okubona ezifana izibonakude kanye nangezibonakhulu, ingaxazululwa kanjani leyo impambuko ye-chromatic futhi eyindilinga ngokusebenzisa kwakha isimiso esiyinkimbinkimbi lens bese ugcwalisa eziwuketshezi.

Euler (sezibalo): Managing lesibili Petersburg kwesikhathi

Kwakuyisikhathi ezikhiqiza kakhulu, phakathi kwesikhathi lapho usosayensi ishicilele amaphepha angaphezu kuka-400 ngezihloko sekushiwo, kanye geometry, okungenzeka theory nezibalo, imephu, ngisho imali yempesheni abafelokazi kanye nezolimo. Kubo zingahlukaniswa zibe azibhala ezintathu ku-algebra, imfundiso yokuziphendukela Moon futhi isayensi asolwandle, kanye ngemfundiso yokuziphendukela izinombolo, ifilosofi yemvelo kanye dioptrics.

Lapha kwafika nomunye we "ethengwa kakhulu" yakhe - "Aljibhra." Igama sezibalo Euler ukuhlobisa lo msebenzi enamakhasi angu-500, okulotshiwe nge injongo yesiyalo ukufundisa i saqala ngokuphelele. Wamemezela ibhuku osafunda osemusha eyayibaphethe kusukela Berlin, futhi lapho umsebenzi usuphelile, waqonda wonke futhi wakwazi ukuxazulula kalula izinkinga algebraic ebhekiswa kuye.

"Imfundiso yokuziphendukela imikhumbi yesibili 'nayo eyenzelwe abantu abangenalo ulwazi mathematics, okungukuthi - amatilosi. Akumangazi ukuthi umsebenzi bekulokhu sibonga yimpumelelo kakhulu amakhono okungavamile didactic lembhali. UNgqongqoshe Navy kanye French Ezezimali Anne-Robert Turgot okuphakanyiswe iNkosi Louis XVI ukudinga bonke abafundi zasolwandle kanye wezikhali izikole ukufunda indatshana Euler. Kungenzeka kakhulu ukuthi omunye wabafundi kwenzakala Napoleon Bonaparte. Inkosi yaze ikhokhwe ruble 1,000 izibalo ngelungelo ukushicilela kabusha umsebenzi, kanye Umbusikazi uCatherine II engasafuni ukunikeza enkosini, liye laphindeka kabili lemali, nesazi sezibalo esikhulu Leonhard Euler ngaphezu kwalokho wathola ruble 2000!