Leonhard Euler

NAME Leonhard Euler

WHAT FAMOUS FOR Euler is renowned as one of the most prolific and influential mathematicians and physicists in history, making foundational contributions to geometry, calculus, mechanics, number theory, graph theory, and mathematical notation. 

BIRTH Euler was born on April 15, 1707, in Basel, Switzerland.

FAMILY BACKGROUND Leonhard Euler was born to Paul Euler, a pastor of the Reformed Church, and Marguerite (née Brucker), the daughter of another pastor. He was the eldest of four children, with two younger sisters, Anna Maria and Maria Magdalena, and a younger brother, Johann Heinrich. 

The family was devoutly religious and scholarly, with both parents coming from backgrounds steeped in theology and learning. Shortly after Leonhard's birth, the family moved to Riehen, near Basel, where his father became the local pastor and where Leonhard spent most of his childhood. Paul Euler had studied theology and mathematics, having attended lectures by the renowned mathematician Jacob Bernoulli, and maintained a friendship with the Bernoulli family, which would later be influential in Leonhard's education

CHILDHOOD Euler grew up in the parsonage at Riehen, a suburb of Basel, in a household that valued both religious devotion and intellectual pursuit. His father taught him elementary mathematics, and he developed an early passion for the subject. 

EDUCATION His early education was provided at home: his mother taught him classics, while his father introduced him to mathematics, sparking his lifelong passion for the subject. Around the age of eight, Euler moved to Basel to live with his maternal grandmother and attended a Latin grammar school. The school did not offer mathematics, so his father arranged for private tutoring by Johannes Burckhardt, a young theologian with a strong interest in mathematics. Euler’s early schooling was thus a blend of formal classical education and informal, but rigorous, mathematical training at home and through private lessons.

At just 13 years old, Euler entered the University of Basel in 1720, which was not unusual for the era. He began his studies in the Philosophical Faculty, taking courses in elementary mathematics taught by Johann Bernoulli, the leading mathematician in Europe at the time and a close friend of his father. Bernoulli quickly recognized Euler's extraordinary talent but, due to his busy schedule, declined to give him private lessons. Instead, Bernoulli encouraged Euler to tackle advanced mathematical texts on his own and invited him to discuss any difficulties every Saturday or Sunday afternoon—a mentorship that proved invaluable.

Euler completed his Master’s degree in philosophy in 1723, presenting a dissertation comparing the philosophies of Descartes and Newton. Following his father’s wishes, he then began theological studies, but his enthusiasm for mathematics, supported by Bernoulli’s encouragement, led his father to consent to a change in focus. Euler completed his studies at the University of Basel in 1726, having read widely in mathematics and already published his first scientific paper. In 1727, he entered the Paris Academy prize competition, marking the beginning of his international recognition. (1)

CAREER RECORD 1727: Moved to St. Petersburg, Russia, joining the Academy of Sciences, initially in physiology, then mathematics.

1730: Became professor of physics at the Academy.

1733: Succeeded Daniel Bernoulli as head of the mathematics department.

1741–1766: Worked at the Berlin Academy at the invitation of Frederick the Great, producing a prolific body of work.

1766–1783: Returned to St. Petersburg, where he continued to publish extensively, even after becoming almost completely blind.

APPEARANCE  Portraits depict Euler as a typical 18th-century scholar, often wearing a cap or cloth on his head, which was common at the time and not unusual or eccentric. Later in life, he was often shown with a bandage over his eyes due to his declining eyesight. 

Leonhard Euler - Jakob Emanuel Handmann

FASHION Euler dressed in the standard scholarly attire of his era, including the aforementioned head covering, which was a practical and fashionable item among academics.

CHARACTER Contemporaries described Euler as cheerful, sociable, modest, generous, and kind. He was animated, charming, and occasionally playful, with a strong sense of humor and a reputation for being approachable and good-natured, even after losing his sight.

SPEAKING VOICE Euler was known for being a lively conversationalist and engaging storyteller, suggesting a pleasant and animated speaking style.

SENSE OF HUMOUR Euler was known for his sense of humor, being playful and able to laugh at himself and his profession. For instance, he once quipped, "Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different." (2)

He was also a good storyteller, and his sociability made him popular among colleagues and acquaintances.

RELATIONSHIPS Leonhard Euler married Katharina Gsell on January 7, 1734 in St. Petersburg, Russia. Katharina was the daughter of Georg Gsell, a Swiss painter associated with the St. Petersburg Academy Gymnasium. Their marriage lasted nearly 40 years, until Katharina's death in 1773. Together, they had 13 children, though only five survived childhood. Euler often credited his family life for providing a supportive and lively environment, and he was known to work on mathematics while surrounded by his children.

Three years after Katharina's death, in 1776, Euler married her half-sister, Salome Abigail Gsell. This second marriage lasted until Euler's death in 1783. Salome Abigail outlived Euler, dying after 1790.

His oldest son Johann Euler was a prolific astronomer and mathematician in his own right, winning seven international academy prizes over his lifetime. 

Johann Euler

Euler maintained correspondence with many mathematicians and scientists of his time. The Bernoulli family were particularly important.

MONEY AND FAME Euler earned a good income from his positions at the academies, publications, and involvement in projects such as mapmaking and tutoring. He was widely celebrated in his lifetime and honored posthumously with commemorations, such as appearing on currency and stamps.

FOOD AND DRINK  Euler spent most of his adult life in St. Petersburg, Russia, and Berlin, Prussia. In 18th-century Russia, the diet commonly included bread, porridge (kasha), cabbage, root vegetables, fish, and meats such as beef and pork. Dairy, especially raw milk, was a staple, as noted by historians discussing the Russian diet of Euler’s time. Swiss cuisine, from Euler’s childhood, would have featured bread, cheese, and hearty soups.

Raw milk was an essential part of the Russian diet during Euler’s lifetime. This is relevant because some researchers believe Euler’s health problems (including his eventual blindness and final illness) may have been linked to brucellosis, a disease often contracted from consuming unpasteurized milk. (3)

Correspondence shows he occasionally requested delicacies like tea, coffee, and brandy from Switzerland, suggesting a taste for such comforts.

MUSIC AND ARTS Leonhard Euler had a deep and sustained interest in music throughout his life. Music was not only a personal relaxation for him, but also a serious subject of scientific and mathematical inquiry. He devoted significant time to understanding the mathematical foundations of musical harmony and sound, and his very first book was on music theory.

Euler’s work, Tentamen novae theoriae musicae (1739), attempted to create a new mathematical theory of music. He developed the concept of a "degree of agreeableness," a numerical index to measure the pleasure derived from musical intervals and chords. This was a novel approach, replacing ancient canons of numerical simplicity with criteria based on sensory pleasure. Euler’s investigations included the mathematical structure of scales, the nature of consonance and dissonance, and the physiological perception of sound. He also wrote about the generation of sound by musical instruments and the speed of sound.

Euler was not just a theorist; he enjoyed music-making as a leisure activity. According to his student and son-in-law, Nicolas Fuss, Euler’s chief relaxation was music, and he would often calculate the mathematical proportions of tones during performances. He played the piano, though even at the keyboard he approached music with a mathematician’s mindset. (2)

Image by Chat GBT

LITERATURE Euler was a prolific writer. His works fill 60 to 80 quarto volumes, more than anybody in the field. His works include numerous books, treatises, and articles on a wide range of scientific and mathematical subjects. One of his notable works was "Letters to a Princess of Germany".

Euler was highly erudite, with a deep knowledge of the classics.  His memory was said to have been so great that he was able to recite Virgil's Aeneid from beginning to end without hesitation - a text that is over 9000 lines long

NATURE Euler’s scientific work often involved natural phenomena.

HOBBIES AND SPORTS Euler’s primary passion was mathematics, and he was known for returning to mathematical problems repeatedly, always seeking simpler or more elegant solutions. He also enjoyed solving practical problems in physics, engineering, and astronomy.

SCIENCE AND MATHS Euler was a polymath, contributing to mathematics, physics, astronomy, logic, geography, and engineering. He was known for his encyclopedic knowledge and ability to work across disciplines.

CONTRIBUTIONS TO MATHEMATICS AND PHYSICS If you were to sit down and write a list of all the cleverest things a human being could possibly think of in one lifetime—and then imagine someone ticking every single one off before tea—you’d be describing Leonhard Euler.

Let’s start with his habit of taking messy, ill-defined ideas and turning them into neat, beautiful tools of infinite usefulness. Power series, for example. Euler practically lived in them. With the serene confidence of someone rearranging their sock drawer, he expressed complicated functions—like the exponential and inverse tangent—using infinite sums. Then, as if just to show off, he cracked the infamous Basel problem: the exact sum of 1 + 1/4 + 1/9 + 1/16 + … You’d think the answer would be some gnarly irrational soup, but no—it’s π²⁄6. And Euler casually pulls it out like it’s the price of bread.

He also changed the way math looks. Not figuratively—literally. Most of the symbols we use today—f(x) for functions, e for that oddly ubiquitous number (~2.718), i for the square root of −1, π, Σ, even ϕ(n) for his totient function—were popularized or invented by Euler. If math is a language, he was its Gutenberg.

In number theory, he took Fermat’s speculative doodles and built them into a solid, sprawling mansion. He didn’t just prove Fermat’s Little Theorem; he gave us the totient function and generalized it all into what we now call Euler’s Theorem. He also showed that adding up the reciprocals of prime numbers never settles down—it just keeps going, a discovery that eventually helped define the prime numbers’ haunting patterns through the zeta function.

As if that weren’t enough, Euler practically founded graph theory when he solved the Seven Bridges of Königsberg problem. “Can you walk across each bridge exactly once?” the townsfolk asked. Euler looked at their map and said, “No,” and in doing so, invented an entire field. While he was at it, he noticed a curious relationship in polyhedra: vertices minus edges plus faces always equals 2. Euler characteristic, they now call it—topology’s cornerstone.

In geometry and trigonometry, he was just as annoying (in the best way). He showed that triangles contain a secret line—the Euler line—connecting several important points, and that the so-called "nine-point circle" elegantly cradles them. Then he casually tossed out Euler’s formula:

eⁱθ = cos(θ) + i·sin(θ)

Richard Feynman later called it the most remarkable formula in mathematics, but Euler just slipped it into a letter.

He also invented the calculus of variations. If you’ve ever asked, “What’s the best way to do something?” you’ve entered his territory. His Euler–Lagrange equation is still how physicists and economists find optimum paths, shapes, or strategies.

In physics, he translated Newton’s laws into a crisp, analytic framework and gave us equations describing the motion of rigid bodies—essential for understanding how planets spin or bicycles wobble. His Euler buckling formula helps prevent buildings from falling over, and in fluid dynamics, he wrote down the first serious equations describing inviscid flow.

Oh, and he improved telescope design, worked out better theories of planetary motion, and made suggestions about the nature of light. All while going completely blind in his right eye, and later both, yet somehow becoming more productive.

So in sum, Euler wasn’t just prolific—he was transformative. He turned mathematics into a system you could teach, write in, and build with. He did for numbers what Shakespeare did for words: gave them depth, structure, and endless possibility. And he did it all with the quiet, devastating charm of someone who makes genius look routine.

PHILOSOPHY & THEOLOGY  Leonhard Euler was a devout and orthodox Christian throughout his life, remaining committed to the Calvinist tradition in which he was raised. He believed firmly in the divine inspiration of the Bible, the divinity of Christ, and the truth of Christian doctrine. Euler regularly led family prayers and maintained a deep personal devotion, conducting himself with piety and spiritual discipline.

His writings, particularly Letters to a German Princess and Rettung der Göttlichen Offenbahrung gegen die Einwürfe der Freygeister (Defense of the Divine Revelation against the Objections of the Freethinkers), reveal his theological convictions. Euler argued for the omnipotence, omniscience, and omnipresence of God, describing the Creator as possessing "infinite wisdom" and "most consummate wisdom". He insisted that the works of God infinitely surpass human achievements and that the world had a definite beginning and would have an end, countering the views of deists and rationalists.

Euler also maintained a dualistic view of body and soul, seeing the soul as immaterial, free, and independent from the body—a position consistent with traditional Christian spiritualism. He rejected materialist and monadist philosophies, such as those of Leibniz and Wolff, considering them "heathen and atheistic".

Euler's philosophy of knowledge recognized three sources: sense perception, reason, and belief. He argued that each source required careful discernment, and he advocated a "middle course" between credulity and skepticism. While he accepted the use of reason and scientific investigation, Euler held that religious truths ultimately rest on revelation, not on natural theology or rational deduction alone.

Euler was an active participant in the intellectual and theological debates of his time. He wrote against the anti-religious and deist thinkers of the Enlightenment, defending the Christian faith against their critiques. He was known for his willingness to challenge secular philosophers and to engage in public controversies over religion and science.

A famous (though apocryphal) anecdote recounts Euler confronting the French philosopher Denis Diderot at the Russian court with a mock-mathematical "proof" of God's existence, illustrating his reputation as a defender of faith in an age of skepticism.

For Euler, scientific inquiry and religious faith were not at odds but were mutually reinforcing. He saw his mathematical and scientific work as an expression of worship and service to God, believing that exploring the natural world was a way to honor the Creator. Euler’s worldview recognized Jesus as the logos, or the sum of all knowledge and truth, and he approached every area of life as worthy of exploration under God's sovereignty. (4)

POLITICS Euler's life was intertwined with the politics of his time, serving under Catherine the Great in Russia and Frederick the Great in Prussia. However, he was not politically active and was described as conventional in his social and political views, never questioning the existing order.

SCANDAL Euler's life was largely free of scandal. He was known for his dedication to his work and his family.

MILITARY RECORD Euler served briefly as a medical lieutenant in the Russian navy from 1727 to 1730 before fully transitioning to academia.

HEALTH AND PHYSICAL FITNESS Euler's eyesight deteriorated over the course of his life. In 1738, he became nearly blind in his right eye, earning the nickname "Cyclops" from Frederick II; by 1766, he lost vision in his left eye as well. Despite becoming functionally blind, his productivity actually surged: in 1775, he wrote on average one mathematical paper per week.

HOMES Euler lived in Basel and Riehen as a child, then in St. Petersburg and Berlin during his academic career. He owned a house by the Neva River in St. Petersburg.

TRAVEL Euler moved between Switzerland, Russia, and Prussia (Berlin) for his academic positions, but there is no evidence of extensive travel beyond these relocations.

DEATH Leonhard Euler died on 18 September 1783 in St. Petersburg, Russia, at the age of 76. On the day of his death, Euler spent the morning as usual: he gave a mathematics lesson to his grandchild, performed calculations on the motion of balloons, and discussed the recently discovered planet Uranus with his colleagues Anders Johan Lexell and Nicolas Fuss. In the late afternoon, around five o'clock, Euler suffered a brain hemorrhage, reportedly uttering only "I am dying" before losing consciousness. He passed away later that evening, around eleven o'clock.

Euler was buried next to his first wife, Katharina, at the Smolensk Lutheran Cemetery on Vasilievsky Island in St. Petersburg. This cemetery was designated for foreigners and notable figures in the city. His funeral was attended by colleagues, friends, and members of the St. Petersburg Academy of Sciences, reflecting his high standing in both the scientific and local communities.

In 1837, the Russian Academy of Sciences installed a new monument to replace Euler’s overgrown grave plaque at the Smolensk Lutheran Cemetery.

In 1957, to mark the 250th anniversary of Euler’s birth, his remains were moved to the Lazarevskoe Cemetery at the Alexander Nevsky Monastery (also known as the Necropolis of Alexander Nevsky Lavra) in St. Petersburg. This cemetery is the final resting place for many of Russia’s most distinguished figures, including Alexander Suvorov, Fyodor Dostoevsky, and Pyotr Tchaikovsky, signifying the highest national recognition for Euler’s legacy.

Today, his tombstone, made of red granite and featuring an angel statue, stands as a prominent memorial in the Necropolis of Alexander Nevsky Lavra, visited by admirers from around the world. (1)

Euler's grave at the Alexander Nevsky Monastery

APPEARANCES IN MEDIA Euler has been commemorated on banknotes, stamps, and in numerous biographies and academic works. His name is attached to countless mathematical concepts, and he is frequently referenced in popular and academic discussions of mathematics.

ACHIEVEMENTS Euler is considered one of the greatest mathematicians of all time, rivaled only by figures like Newton and Gauss. He was elected to numerous academies and societies, and his collected works fill over 70 volumes, representing a significant portion of 18th-century mathematical research

Sources (1) Maths History (2) Leonardeuler.com (3) International Ophthalmology Conference (4) Breakpoint.org