Leonhard Euler was a leading Swiss mathematician and physicist who made significant discoveries in varied fields such as graph theory and infinitesimal calculus. He also defined a substantial amount of contemporary mathematical terminology and notation, specifically for mathematical analysis, such as the notion of a mathematical function. He is also well renowned for his works in fluid dynamics, astronomy, mechanics and optics. Euler worked on his subjects mostly in St. Petersburg (Russia) and in Berlin, during his adulthood. All his collections, if printed, would occupy 60-80 quarto volumes reflecting his outstanding mathematical abilities. Euler was a versatile mathematician who worked on a spectrum of topics such as number theory, algebra, geometry and trigonometry and in different areas of physics such as continuum physics, lunar theory, etc. Contrary to Monadism and Wolffian science, Euler firmly believed in knowledge found on the basis of exact quantitative laws.
Childhood And Early Life
Euler was born on April 15, 1707, in Basel, Switzerland. His father Paul Euler was a pastor of the Reformed Church. His mother, Marguerite Brucker was a pastor's daughter. Euler had two younger sisters - Anna Maria and Maria Magdalena. Soon after Euler was born, his family relocated to the town of Riehen. Euler’s father was a friend of Johann Bernoulli, who was a renowned European mathematician and had a great influence on Euler. At thirteen, Euler entered the University of Basel and received his Master of Philosophy in 1723. He prepared a thesis that compared the philosophies of Newton and Descartes. Johann Bernoulli, who gave him Saturday afternoon lessons, quickly recognized Euler’s exceptional mathematical skills persuaded him to discontinue young theology and shift to mathematics.
In 1727, Euler participated in the Paris Academy Prize Problem competition to search for the best technique to place masts on a ship. He stood second and the first place won by Pierre Bouguera, who later came to be known as ‘the father of naval architecture’. Euler participated each year, subsequently winning this popular annual prize twelve times in his life.
On 17 May 1727, Euler joined the medical department at Imperial Russian Academy of Sciences in St Petersburg and was promoted to the mathematics department in no time. However, due to chaos in Russia, Euler joined the Berlin Academy on 19 June 1741. Euler stayed there for around 25 years and authored over 380 articles. He was elected as a foreign member of the Royal Swedish Academy of Sciences in 1755.
Euler was then requested to teach the Princess of Anhalt-Dessau and, in early 1760s, Euler wrote over 200 letters to her which were later published as a best-selling volume entitled ‘Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess’. The book not only illustrated Euler’s skills in different topics related to mathematics and physics, but also a reflection of his personality and religious beliefs. Interestingly, this book became more popular than any of his mathematical works and it was published across Europe as well as in United States. The reason behind the fame of these letters was that they revealed Euler’s unique ability to convey scientific subjects in a simplified form to a layman. Adding to this was the fact that Euler had become almost blind in the right eye in 1735 and his left eye was also blinded by cataract in 1766. Despite this drawback, Euler kept up with his work and wrote one mathematical paper every week on an average in 1755.
In 1766, Euler accepted an invitation to return to the St. Petersburg Academy and spent the rest of his life in Russia. However, his second stay in Russia didn’t prove to be lucky for him as he lost his home in a fire in St. Petersburg in 1771 and then his wife Katharina in 1773.
On 7 January 1734, Euler married Katharina Gsell. In 1773, after 40 years of marriage, Katharina died. After three years, Euler married her half sister, Salome Abigail Gsell, who remained his wife for the rest of his life.
Death And Legacy
On 18th September 1783, after a lunch with his family in St Petersburg, Euler suffered a brain hemorrhage and expired a few hours later. He was buried at the Smolensk Lutheran Cemetery on Vasilievsky Island, next to his first wife Katharina. The Russian Academy of Sciences put a marble bust of Leonhard Euler on a pedestal adjacent to the Director's seat in 1785 and placed a headstone on Euler's grave in 1837. To pay tribute to the 250th anniversary of Euler's birth, the headstone, along with his remains, was relocated to the 18th-century necropolis at the Alexander Nevsky Monastery in 1956.
To honor Euler for his stupendous achievements, he was marked on the sixth series of the Swiss 10-franc banknote and on several Russian, Swiss and German postage stamps. Even the asteroid ‘2002 Euler’ was named after him. He is also venerated by the Lutheran Church on their Calendar of Saints on 24 May as he was a committed Christian and a strong believer of Bible.
Contributions To Mathematics And Physics
Among his diverse works, the most notable was the introduction of the concept of functions. Euler also pioneered in writing f(x) to signify the function ‘f’ applied to the argument ‘x’. He also defined the contemporary notation for the trigonometric functions, the letter ‘e’, for the base of the natural logarithm (known as Euler's number), the Greek letter ‘Σ' for summations and the letter ‘i’ to signify the imaginary unit.
Euler defined the use of the exponential functions and logarithms in analytic proofs. He discovered ways to state various logarithmic functions using power series, and he effectively defined logarithms for negative and complex numbers. Through these accomplishments, he enlarged the scope of mathematical applications of logarithms to a great extent.
Euler also explained in detail the theory of higher transcendental functions by inventing the gamma function and introduced a novel approach for solving quartic equations. He also discovered a technique to calculate integrals with complex limits, aiding the development of modern complex analysis. He also invented the calculus of variations along with the Euler–Lagrange equation.
Euler proved Fermat's little theorem, Newton's identities, Fermat's theorem on sums of two squares, and he also distinctively contributed to Lagrange's four-square theorem. He supplied significant value addition to the theory of perfect numbers, which had always been a captivating topic for several mathematicians.
Physics And Astronomy
Euler made a noteworthy contribution in explaining the Euler–Bernoulli beam equation, which became the foundation of engineering. He not only applied his analytical techniques in classical mechanics but also in solving the celestial problems. He was awarded with numerous Paris Academy Prizes for his contributions in the field of astronomy. He found out the orbits of comets and other celestial bodies with exactness, understanding the nature of comets and calculating the parallax of the sun. This aided in preparing precise longitude tables.