Euler, L
Achievements: A founder of pure mathematics. He made decisive contributions to geometry, calculus, mechanics, and the number theory.
Born: April 15, 1707; Basel, Switzerland
Died: September 18, 1783; St. Petersburg, Russia (Aged 76)
Field & Discipline: Mathematics; Mathematician
Language: French; German
Education: Riehen Gymnasium; mathematics tuition from Johann Burckhardt; University of Basel
Major Work:
"Letters of Euler on Different Subjects in Natural Philosophy, Addressed to a German Princess"
Life & Times:
One of Euler’s teachers at the University of Basel was [taught by] Johann I Bernoulli*, one of the greatest mathematicians in Europe at the time. Euler soon became an intimate of the Bernoulli family. He formed close friendships with Johann I's gifted sons, Nikolaus II and [close pal of] Daniel Bernoulli*.
In 1725, at 18 Euler gave up the study of theology and began independent mathematical investigations. In 1727 Euler took a post in the physics department at the newly organized St. Petersburg Academy of Sciences. From this time on, Euler's life and work were closely connected with the St. Petersburg Academy and with Russia. In 1731, Euler became professor of physics, and in 1733 succeeded Daniel Bernoulli as professor of mathematics when Bernoulli returned to Basel. Euler was frequently called upon by the Russian government to advise on scientific matters. He prepared maps, advised the navy, and even tested designs for fire engines. His main efforts, however, were in mathematical sciences, and, because of his correspondence with scientists from many countries, his discoveries often became known long before his results were published, and he gained fame rapidly.
During his 14 years in St. Petersburg, Euler made brilliant discoveries in mathematical analysis, the theory of numbers, and mechanics. He also wrote on ship-building, acoustics, and the theory of musical harmony. He also made seminal discoveries in classical number theory, and pushed into the uncharted waters of analytic number theory and the theory of partitions. He carried integral calculus to a higher degree of perfection, developed the theory of trigonometric and logarithmic functions, reduced analytical operations to a greater simplicity, and threw new light on nearly all parts of pure mathematics.
Because he overworked himself, he eventually lost the sight in one eye. By age 34, he had prepared about 90 works for publication and had published 55 books and articles, including the two-volume "Mechanica", which presented the Newtonian laws of motion within a framework of calculus, and was a landmark in the history of physics.
In late 1740 Euler accepted a post in Berlin at the reorganized Berlin Society of Sciences. It had been established by Leibniz, but had declined until [hired by] Frederick II of Prussia*, who had just succeeded to the Prussian throne, revived it.
Euler lived in Berlin for the next 25 years. He was appointed director of mathematics at the Berlin Society, and also substituted for the president, [succeeded] Maupertuis*, when the latter was absent. When Maupertuis died in 1759, Euler took over the running of the Academy.
During his years in Berlin, Euler published two of his greatest works: "Introductio in analysin infinitorum" (1748), in which he developed the concept of function in mathematical analysis, through which variables are related to each other and in which he advanced the use of infinitesimals and infinite quantities; and a volume on differential calculus, the "Institutiones calculi differentialis" (1755), which is still important for its formulas of differentiation and methods of indefinite integration. Euler also made advances in the theory of linear differential equations, which are useful in solving problems in physics. This period also saw him investigate complex numbers, as well as offer a proof of the fundamental theorem of algebra.
Euler agreed to give lessons in elementary science to the Princess of Anhalt Dessau. The result was a multi-volume masterpiece of exposition, published on his return to St. Petersburg as: "Letters of Euler on Different Subjects in Natural Philosophy Addressed to a German Princess" The compilation of over 200 "letters" introduced subjects as diverse as light, sound, gravity, logic, language, magnetism, and astronomy.
He also ventured into the philosophical field, discussing the origin of evil, the conversion of sinners, and the "Electrization of Men and Animals". The work became an international sensation and was Euler's most widely read book. While in Berlin, Euler prepared 380 works, of which about 275 were published.
Euler had several disputes with other scientists, particularly with his mathematical rival, [was mathematical rival of] d'Alembert*, on the problem of logarithms of negative numbers. He also disagreed with d'Alembert and Daniel Bernoulli on the solution of the equation of a vibrating string, and had an argument with the English optician [optical argument with] Dollond* on several optical problems.
Frederick II refused to appoint Euler as President of the Berlin Society and invited Euler's rival d'Alembert to take the post, (d'Alembert turned it down.) In addition, Frederick's favorite at the Society, [was disliked by] Voltaire*, took a dislike to Euler and began to ridicule him for his bookish ways. By 1766, Frederick and Euler were arguing heatedly about the Society's finances.
Euler saw the writing on the wall, and when [hired by] Catherine the Great* invited him back to St. Petersburg, he happily accepted, arriving in 1766. But he began losing the sight in his other eye, and by 1771 was totally blind; he lost his house and almost all his property in a fire; and, in 1773, his wife died. During his descent into blindness, Euler wrote an influential textbook on algebra, a 775-page treatise on the motion of the moon, and a massive, three-volume development of integral calculus, the "Institutiones calculi integralis".
In 1783 Euler suffered a massive stroke. On the day of his death, he worked on mathematical questions associated with the flight of balloons, a topic that fascinated him after the Montgolfier brothers' ascent over Paris in a hot-air balloon.
Extra Connections: In efforts to replace synthetic by analytic methods, Euler was succeeded by [his work advanced by] Lagrange*, though Lagrange did not agree totally with Euler's theories.
[eulogy written by] Condorcet* wrote Euler's eulogy
He corresponded with [corresponded with] Venturi*
He beat [won competition ahead of] Boscovich* in a Paris Academy of Sciences competition regarding the mutually perturbations of Saturn and Jupiter
Assessment: Euler was one of the most important mathematicians after Newton.
Oneliner: Leonhard Euler, a founder of modern math
Bibliography:
- Dictionary of Scientific Biography.
- Dunham, William, Euler: The Master of Us All,Washington, D.C: The Mathematical Association of America, 1999.
- Encyclopedia Britannica.
Father: Paul Euler
Mother: Margarete Brucker
Siblings: Johann Heinrich (painter)
Spouse: 1) Katharina Gsell; 2) Salome Abigail Gsell
Children: Johann Albrecht; Karl; Christoph; 2 daughters survived infancy; 8 died in infancy