Leonhard Euler

1707 — 1783

royaume de Prusse, Empire russe, ancienne Confédération suisse

SciencesMathématicien(ne)ScientifiqueInventeur/triceEarly Modern18th century (Early Modern Period, Age of Enlightenment)

Les Lumières

Swiss mathematician, physicist, and engineer (1707–1783), Euler is one of the greatest scientists of the 18th century. Prolific and innovative, he contributed to nearly every field of mathematics and physics, despite the blindness that affected him from 1738 onward.

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Inspiré

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Surpris

Triste

Fier

Key Facts

1727: Joins the Saint Petersburg Academy of Sciences at the invitation of Bernoulli
1735: Solves the Seven Bridges of Königsberg problem, founding graph theory
1738: Gradually loses his sight, but continues his work with the help of collaborators
1755–1771: Produces his major works in analysis, differential and integral calculus
1783: Dies in Saint Petersburg having published more than 800 scientific papers

Works & Achievements

Introductio in analysin infinitorum (1748)

Foundational work that established the bases of modern analysis and introduced the exponential notation e^x. This treatise revolutionized the way infinitesimal functions are studied.

Euler's formula (e^(ix) = cos(x) + i*sin(x)) (1748)

Famous equation linking exponential functions, trigonometric functions, and complex numbers. It is one of the most beautiful mathematical formulas, unifying several branches of mathematics.

Methodus inveniendi lineas curvas (1744)

Founding work of the calculus of variations that solves the brachistochrone problem and develops methods for finding optimal curves.

Graph theory - The Seven Bridges of Königsberg problem (1736)

Solution to the famous problem that laid the foundations of graph theory. Euler proves that it is impossible to cross all seven bridges exactly once, thereby creating a new mathematical field.

Contributions to number theory (1770s)

Euler considerably deepened number theory, establishing results on prime numbers, Euler's totient function φ, and the properties of congruences.

Elementa doctrinae solidorum (1758)

Work on the geometry of solids that introduces the Euler-Descartes characteristic (V - E + F = 2), a fundamental formula in topology.

Contributions to mechanics and physics (1736-1760)

Euler develops the equations of fluid mechanics, the theory of elasticity, and solves numerous problems in applied mechanics, enriching mathematical physics.

Anecdotes

Euler lost vision in his right eye in 1738, likely due to an infection, but continued working with remarkable productivity. After becoming completely blind in 1766, he dictated his discoveries to his assistants and produced nearly half of his scientific works during this period of total blindness, demonstrating extraordinary determination.

Euler was so prolific that he published on average one scientific paper every three days throughout his life. The Saint Petersburg Academy of Sciences had to continue publishing his memoirs for thirteen years after his death, so vast was his catalogue of works.

In 1735, Euler solved the famous Seven Bridges of Königsberg problem in a matter of days, thereby laying the foundations of graph theory. This elegant solution demonstrated how mathematics could solve concrete practical problems, revolutionizing the scientific approach of the era.

Euler had 13 children with his first wife Katerina, and led a very active family life while pursuing his intense mathematical research. He would jokingly remark that some of his best ideas came to him while playing with his children or walking in the academy gardens.

In 1761, Euler predicted the transit of Venus across the Sun with remarkable precision, demonstrating the power of his astronomical calculations. This prediction helped establish the precise distances between the planets and the Sun, a major breakthrough for the astronomy of his time.

Primary Sources

Introductio in analysin infinitorum (1748)

A function is an analytical expression composed in any way from this variable and numbers or constants.

Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes (1744)

Since the nature of the universe is most perfect and nothing happens without reason, it is extremely probable that everything occurs in such a way that some quantity always remains a maximum or minimum.

Correspondence with Daniel Bernoulli (1740-1750)

I am ceaselessly occupied with finding new properties of curves and deepening the mysteries of infinitesimal calculus.

Solutio problematis ad geometriam situs pertinentis (1741)

The solution of this problem has no relation to ordinary geometry, but seems to belong to a new branch of geometry, which Leibniz once called geometry of position.

Letters to a German Princess (1768-1772)

Mathematics is the science of magnitudes and numbers, and all natural phenomena can be reduced to relationships of magnitudes.

Key Places

Basel, Switzerland

Euler's birthplace on April 15, 1707. Basel is a major city in German-speaking Switzerland where he grew up and received his first mathematical training from his father Paul Euler.

Saint Petersburg Academy of Sciences, Russia

Euler's main place of activity from 1727 to 1741 and from 1766 to 1783. It was in Saint Petersburg that he produced a large part of his prolific mathematical work, despite his progressive blindness.

Berlin Academy of Sciences, Germany

Euler worked there from 1741 to 1766 as director of the mathematics section under the reign of Frederick II. This period was highly productive for his research in analysis and number theory.

University of Basel, Switzerland

Euler's initial place of study, where he studied mathematics and theology. The university played a foundational role in the intellectual development of the young scholar.

Potsdam, Germany

Royal residence of Frederick II where Euler spent time during his stay in Prussia. The Berlin Academy, where he conducted his scientific work, was located nearby.

Typical Objects

Quill and inkwell

Essential tools of Euler's work, who wrote thousands of pages of mathematics and physics. Despite his progressive blindness, he continued to produce works by dictating to assistants, using these instruments until the end of his life.

Blackboard and chalk

Teaching instruments used by Euler during his lectures in Switzerland, Russia, and Prussia. They represent his role as a professor and his part in transmitting mathematical knowledge in the 18th century.

Corrective spectacles

Everyday objects of the 18th century, symbolizing Euler's struggle against poor eyesight and then blindness. Despite this disability from 1738 onwards, he never ceased his remarkable scientific research.

Compass and set square

Fundamental geometric tools for mathematicians of the early modern period, indispensable for the geometric drawings and proofs that Euler carried out.

Mathematics book or scientific treatise

Euler published more than 500 works and memoirs. These volumes represent his immense intellectual legacy and his major contribution to the building of modern mathematics (algebra, analysis, number theory).

Terrestrial globe or astronomical instrument

Symbols of 18th-century science and Euler's interests in physics, astronomy, and celestial mechanics. They illustrate the broad and empirical approach of Enlightenment scholars.

Handwritten correspondence

Euler was a prolific letter writer, exchanging with the greatest scholars in Europe. These letters bear witness to the intense intellectual life of scientific networks in the Age of Enlightenment.

School Curriculum

LycéeMathématiques — Histoire des mathématiques modernes

LycéeMathématiques — Fonction exponentielle et nombre e

LycéeMathématiques — Logarithmes et propriétés des fonctions exponentielles

LycéeMathématiques — Calcul différentiel et intégral

LycéeMathématiques — Théorie des graphes et chemins eulériens

LycéeMathématiques — Nombres complexes et formule d'Euler

LycéeMathématiques — Séries infinies et convergence

Vocabulary & Tags

Key Vocabulary

Euler's number eEuler's formula (e^(ix) = cos(x) + i·sin(x))Exponential functionGraph and edgeDifferential calculusInfinite seriesNatural logarithm

Daily Life

Morning

Euler rises early, as was customary in the 18th century. Despite his progressive and then total blindness from 1738 onward, he begins his day by dictating his mathematical observations to his assistants or his sons. He has a light breakfast of bread, cheese, and herbal tea before immersing himself in his work.

Afternoon

The afternoon is devoted to intensive sessions of intellectual work: mental calculations, dictating scientific memoirs to secretaries, and correspondence with other European scholars. Euler maintains remarkable productivity by relying on his prodigious memory and his collaborators as interlocutors, discussing complex mathematical problems.

Evening

In the evening, Euler may receive other scholars or academy members for scientific discussions, or enjoy time with his family. He goes to bed relatively early to preserve his energy, as the intense intellectual work and his physical condition require regular rest.

Food

As a member of the scientific elite of 18th-century Northern Europe, Euler consumes rye or wheat bread, local cheeses, fish, and butcher's meat. His diet includes seasonal fruits and vegetables, as well as wine or beer, common beverages of the era across all social classes.

Clothing

Euler wears the typical attire of an 18th-century scholar: a dark-colored coat, breeches, woolen stockings, and buckled shoes. With age and especially after losing his sight, he adopts a simpler and more comfortable style, with little concern for fashion, favoring practicality.

Housing

Euler lives in residences befitting his academic standing, notably in Saint Petersburg (1727–1741), then Berlin (1741–1766), and finally Saint Petersburg again (1766–1783). These homes provide dedicated spaces for intellectual work, a library, and the reception of scientific peers, characteristic of the households of prestigious academicians.

Historical Timeline

1707Naissance de Leonhard Euler à Bâle, en Suisse.

1727Euler devient académicien à Saint-Pétersbourg, à l'Académie des sciences de Russie.

1738Euler perd la vision de son œil droit et devient partiellement aveugle.

1740Début de la guerre de succession d'Autriche, conflit majeur en Europe.

1741Euler s'installe à Berlin et rejoint l'Académie royale des sciences de Prusse.

1748Publication de l'Introductio in analysin infinitorum, ouvrage fondamental d'Euler sur l'analyse mathématique.

1751Diderot et d'Alembert publient le premier volume de l'Encyclopédie, symbole des Lumières.

1755Tremblement de terre de Lisbonne, catastrophe majeure qui marque l'époque des Lumières.

1766Euler retourne à Saint-Pétersbourg et devient complètement aveugle.

1768Euler publie ses Lettres à une princesse d'Allemagne, vulgarisation scientifique importante.

1770Publication de l'Algèbre d'Euler, traité influent sur la théorie algébrique.

1776Déclaration d'indépendance des États-Unis, événement politique majeur du siècle.

1783Décès de Leonhard Euler à Saint-Pétersbourg le 18 septembre.

1789Révolution française, bouleversement politique marquant la fin de l'époque moderne.

Period Vocabulary

Infinitesimal calculus — Branch of mathematics studying infinitely small variations, developed by Newton and Leibniz. Euler was one of its greatest masters.

Pure mathematics — Theoretical study of mathematics without immediate practical application, as opposed to applied mathematics.

Algebraic notation — System of symbols and signs to represent mathematical operations. Euler popularized several notations still in use today, such as the symbols π and f(x).

Rational mechanics — Theoretical study of motion and forces based on mathematical principles, a key discipline in 18th-century science.

Age of Enlightenment — Period of the 18th century marked by confidence in reason, science, and progress, in which education and scientific knowledge were highly valued.

Scientific academy — Institution bringing together scholars and learned individuals to advance the sciences. Euler worked for the Academy of Sciences in Saint Petersburg and Berlin.

Analytic geometry — Method combining algebra and geometry to solve problems, making it possible to represent figures through equations.

Complex number — Number containing a real part and an imaginary part (involving the square root of -1). Euler greatly contributed to their mathematical understanding.

Graph theory — Mathematical study of networks and connections. Euler is considered its founder through his Seven Bridges of Königsberg problem.

Polyhedral — Relating to polyhedra (geometric solids). Euler stated the famous formula relating vertices, edges, and faces: V - E + F = 2.

Scientific correspondence — Exchange of letters between scholars to discuss discoveries and theories. This was the primary mode of international scientific communication in the 18th century.

Gallery

Leonhard Euler (1707-1783)

Joseph frédéric auguste darbès, ritratto del matematico léonard euler, 1778

Euler 1778

Leonhard Euler 1741-1766 by F B Frey

Portrait of Leonhard Euler (1707-1783)label QS:Len,"Portrait of Leonhard Euler (1707-1783)"label QS:Lde,"Porträt des Leonhard Euler (1707-1783)"

Leonhard Euler (image from Opera postuma mathematica et physica, 1862)

Paul Heinrich Fuss (image from Opera postuma mathematica et physica, 1862)

A History of Mathematics (1893)

A history of mathematics

Visual Style

Un style d'illustration scientifique du XVIIIe siècle inspiré des gravures de l'Époque des Lumières, combinant la précision mathématique avec la chaleur baroque, entre lumière de chandelle et obscurité, reflétant le génie créatif d'Euler malgré sa cécité tardive.

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AI Prompt

18th century scientific illustration in the style of Enlightenment engravings, featuring mathematical diagrams, celestial charts, and geometric patterns. Golden warm lighting with deep shadows, reminiscent of candlelit study rooms. Baroque ornamentation mixed with precise mathematical precision. Fine cross-hatching and detailed line work typical of period scientific publications. Color palette of aged parchment, bronze, deep blues, and burnt sienna. Atmosphere of intellectual rigor and wonder, with elements suggesting both vision and blindness - sharp geometric forms alongside softer, ethereal mathematical curves.

Sound Ambience

Une ambiance sonore immersive du cabinet d'étude d'un savant du XVIIIe siècle, mêlant les bruits de la composition mathématique (grattement de plume, froissement de parchemin) aux sons discrets de l'environnement européen de l'époque, créant une atmosphère de concentration intellectuelle et de découverte scientifique.

AI Prompt

18th century Swiss study ambience with a focus on mathematical and scientific work. Background sounds include quill pen scratching on parchment, pages turning, subtle candlelight flickering, and occasional wood creaking from an old desk. Distant church bells from a European town, muffled voices of scholars in conversation, the soft rustle of papers and mathematical instruments. Incorporate gentle ambient sounds of a period study room: subtle footsteps on wooden floors, the faint sound of a fireplace, and the quietness that evokes focused intellectual work. The atmosphere should convey the deliberate pace of 18th century scientific discovery, with an underlying sense of thoughtful concentration and the passage of time.

Portrait Source

Wikimedia Commons — domaine public — Jakob Emanuel Handmann — 1753