92 Facts About Leonhard Euler

Leonhard Euler founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus.

Leonhard Euler introduced much of modern mathematical terminology and notation, including the notion of a mathematical function.

Leonhard Euler is known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory.

Leonhard Euler spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Prussia.

Leonhard Euler gave the current definition of the constant, the base of the natural logarithm, now known as Euler's number.

Leonhard Euler made contributions to applied mathematics and engineering, such as his study of ships which helped navigation, his three volumes on optics contributed to the design of microscopes and telescopes, and he studied the bending of beams and the critical load of columns.

Leonhard Euler is credited with being the first to develop graph theory.

Leonhard Euler became famous for, among many other accomplishments, solving several unsolved problems in number theory and analysis, including the famous Basel problem.

Leonhard Euler has been credited for discovering that the sum of the numbers of vertices and faces minus the number of edges of a polyhedron equals 2, a number now commonly known as the Leonhard Euler characteristic.

In physics, Leonhard Euler reformulated Isaac Newton's laws of motion into new laws in his two-volume work Mechanica to better explain the motion of rigid bodies.

Leonhard Euler contributed to the study of elastic deformations of solid objects.

Leonhard Euler formulated the partial differential equations for the motion of inviscid fluid, and laid the mathematical foundations of potential theory.

Leonhard Euler is regarded as arguably the most prolific contributor in the history of mathematics and science, and the greatest mathematician of the 18th century.

Leonhard Euler was the oldest of four children, with two younger sisters, Anna Maria and Maria Magdalena, and a younger brother, Johann Heinrich.

From a young age, Leonhard Euler received schooling in mathematics from his father, who had taken courses from Jacob Bernoulli some years earlier at the University of Basel.

Around the age of eight, Leonhard Euler was sent to live at his maternal grandmother's house and enrolled in the Latin school in Basel.

In 1720, at age 13, Leonhard Euler enrolled at the University of Basel.

Johann Bernoulli and Leonhard Euler soon got to know each other better.

In 1723, Leonhard Euler received a Master of Philosophy with a dissertation that compared the philosophies of Rene Descartes and Isaac Newton.

In 1726, Leonhard Euler completed a dissertation on the propagation of sound titled De Sono, with which he unsuccessfully attempted to obtain a position at the University of Basel.

Pierre Bouguer, who became known as "the father of naval architecture", won and Leonhard Euler took second place.

Leonhard Euler was promoted from his junior post in the medical department of the academy to a position in the mathematics department.

Leonhard Euler lodged with Daniel Bernoulli with whom he worked in close collaboration.

Leonhard Euler mastered Russian, settled into life in Saint Petersburg and took on an additional job as a medic in the Russian Navy.

Leonhard Euler swiftly rose through the ranks in the academy and was made a professor of physics in 1731.

Leonhard Euler left the Russian Navy, refusing a promotion to lieutenant.

Leonhard Euler succeeded him as the head of the mathematics department.

Leonhard Euler lived for 25 years in Berlin, where he wrote several hundred articles.

Leonhard Euler became the tutor for Friederike Charlotte of Brandenburg-Schwedt, the Princess of Anhalt-Dessau and Frederick's niece.

Leonhard Euler wrote over 200 letters to her in the early 1760s, which were later compiled into a volume entitled Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess.

Leonhard Euler was a simple, devoutly religious man who never questioned the existing social order or conventional beliefs.

Leonhard Euler was, in many ways, the polar opposite of Voltaire, who enjoyed a high place of prestige at Frederick's court.

Leonhard Euler was not a skilled debater and often made it a point to argue subjects that he knew little about, making him the frequent target of Voltaire's wit.

Leonhard Euler assisted students from the St Petersburg academy and at times accommodated Russian students in his house in Berlin.

Leonhard Euler decided to leave Berlin in 1766 and return to Russia.

Leonhard Euler wrote 380 works, 275 of which were published.

Leonhard Euler was even involved in the design of the water fountains at Sanssouci, the King's summer palace.

The political situation in Russia stabilized after Catherine the Great's accession to the throne, so in 1766 Leonhard Euler accepted an invitation to return to the St Petersburg Academy.

Three years after his wife's death in 1773, Leonhard Euler married her half-sister, Salome Abigail Gsell.

Early in his life, Leonhard Euler memorized Virgil's Aeneid, and by old age, he could recite the poem and give the first and last sentence on each page of the edition from which he had learnt it.

Leonhard Euler knew the first hundred prime numbers and could give each of their powers up to the sixth degree.

Leonhard Euler was known as a generous and kind person, not neurotic as seen in some geniuses, keeping his good-natured disposition even after becoming entirely blind.

Leonhard Euler blamed the cartography he performed for the St Petersburg Academy for his condition, but the cause of his blindness remains the subject of speculation.

Leonhard Euler's condition appeared to have little effect on his productivity.

Jacob von Staehlin wrote a short obituary for the Russian Academy of Sciences and Russian mathematician Nicolas Fuss, one of Leonhard Euler's disciples, wrote a more detailed eulogy, which he delivered at a memorial meeting.

Leonhard Euler was buried next to Katharina at the Smolensk Lutheran Cemetery on Vasilievsky Island.

Leonhard Euler worked in almost all areas of mathematics, including geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory, and other areas of physics.

Leonhard Euler is a seminal figure in the history of mathematics; if printed, his works, many of which are of fundamental interest, would occupy between 60 and 80 quarto volumes.

Leonhard Euler's name is associated with a large number of topics.

Leonhard Euler wrote over 4500 letters and hundreds of manuscripts.

Leonhard Euler introduced and popularized several notational conventions through his numerous and widely circulated textbooks.

Leonhard Euler is well known in analysis for his frequent use and development of power series, the expression of functions as sums of infinitely many terms, such as.

Leonhard Euler introduced the use of the exponential function and logarithms in analytic proofs.

Leonhard Euler discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers, thus greatly expanding the scope of mathematical applications of logarithms.

Leonhard Euler defined the exponential function for complex numbers and discovered its relation to the trigonometric functions.

Leonhard Euler elaborated the theory of higher transcendental functions by introducing the gamma function and introduced a new method for solving quartic equations.

Leonhard Euler found a way to calculate integrals with complex limits, foreshadowing the development of modern complex analysis.

Leonhard Euler pioneered the use of analytic methods to solve number theory problems.

In breaking ground for this new field, Leonhard Euler created the theory of hypergeometric series, q-series, hyperbolic trigonometric functions, and the analytic theory of continued fractions.

Leonhard Euler developed some of Fermat's ideas and disproved some of his conjectures, such as his conjecture that all numbers of the form are prime.

Leonhard Euler linked the nature of prime distribution with ideas in analysis.

Leonhard Euler proved that the sum of the reciprocals of the primes diverges.

Leonhard Euler contributed significantly to the theory of perfect numbers, which had fascinated mathematicians since Euclid.

Leonhard Euler contributed major developments to the theory of partitions of an integer.

In 1735, Leonhard Euler presented a solution to the problem known as the Seven Bridges of Konigsberg.

Leonhard Euler discovered the formula relating the number of vertices, edges, and faces of a convex polyhedron, and hence of a planar graph.

Leonhard Euler integrated Leibniz's differential calculus with Newton's Method of Fluxions, and developed tools that made it easier to apply calculus to physical problems.

Leonhard Euler made great strides in improving the numerical approximation of integrals, inventing what are now known as the Euler approximations.

Besides successfully applying his analytic tools to problems in classical mechanics, Leonhard Euler applied these techniques to celestial problems.

Leonhard Euler's accomplishments include determining with great accuracy the orbits of comets and other celestial bodies, understanding the nature of comets, and calculating the parallax of the Sun.

Leonhard Euler's calculations contributed to the development of accurate longitude tables.

Leonhard Euler disagreed with Newton's corpuscular theory of light, which was the prevailing theory of the time.

In fluid dynamics, Leonhard Euler was the first to predict the phenomenon of cavitation, in 1754, long before its first observation in the late 19th century, and the Leonhard Euler number used in fluid flow calculations comes from his related work on the efficiency of turbines.

Leonhard Euler is well known in structural engineering for his formula giving Leonhard Euler's critical load, the critical buckling load of an ideal strut, which depends only on its length and flexural stiffness.

Leonhard Euler is credited with using closed curves to illustrate syllogistic reasoning.

An Leonhard Euler diagram is a diagrammatic means of representing sets and their relationships.

Leonhard Euler diagrams consist of simple closed curves in the plane that depict sets.

Leonhard Euler diagrams were incorporated as part of instruction in set theory as part of the new math movement in the 1960s.

Leonhard Euler later envisaged the possibility of describing genres including the prime number 7.

Leonhard Euler devised a specific graph, the Speculum musicum, to illustrate the diatonico-chromatic genre, and discussed paths in this graph for specific intervals, recalling his interest in the Seven Bridges of Konigsberg.

Leonhard Euler opposed the concepts of Leibniz's monadism and the philosophy of Christian Wolff.

Leonhard Euler insisted that knowledge is founded in part on the basis of precise quantitative laws, something that monadism and Wolffian science were unable to provide.

The Empress was alarmed that Diderot's arguments for atheism were influencing members of her court, and so Leonhard Euler was asked to confront him.

Leonhard Euler appeared, advanced toward Diderot, and in a tone of perfect conviction announced this non sequitur:.

Leonhard Euler is widely recognized as one of the greatest mathematicians of all time, and more likely than not the most prolific contributor to mathematics and science.

Mathematician Francois Arago said, "Leonhard Euler calculated without any apparent effort, just as men breathe and as eagles sustain themselves in air".

Leonhard Euler is generally ranked right below Carl Friedrich Gauss, Isaac Newton, and Archimedes among the greatest mathematicians of all time, while some rank him as equal with them.

French mathematician Andre Weil noted that Leonhard Euler stood above his contemporaries and more than anyone else was able to cement himself as the leading force of his era's mathematics:.

Leonhard Euler had read all the best Roman writers, knew perfectly the ancient history of mathematics, held in his memory the historical events of all times and peoples, and could without hesitation adduce by way of examples the most trifling of historical events.

Leonhard Euler knew more about medicine, botany, and chemistry than might be expected of someone who had not worked especially in those sciences.

Leonhard Euler was featured on both the sixth and seventh series of the Swiss 10-franc banknote and on numerous Swiss, German, and Russian postage stamps.

The Leonhard Euler Archive was started at Dartmouth College before moving to the Mathematical Association of America and, most recently, to University of the Pacific in 2017.