Leonhard Euler

Leonhard Euler was a Swiss <a href="/facts/Polymath/eqIfjQRu">polymath</a> who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a> and <a href="/facts/Topology/2EqW47cU">topology</a> and made influential discoveries in many other branches of mathematics, such as <a href="/facts/Analytic_number_theory/mrHbWwrx">analytic number theory</a>, <a href="/facts/Complex_analysis/hgCoQlH0">complex analysis</a>, and <a href="/facts/Infinitesimal_calculus/MEmUTYoz">infinitesimal calculus</a>. He also introduced much of modern mathematical terminology and <a href="/facts/Mathematical_notation/vHgEE8cE">notation</a>, including the notion of a <a href="/facts/Mathematical_function/CdReEKCh">mathematical function</a>. He is known for his work in <a href="/facts/Mechanics/A3yHLQA5">mechanics</a>, <a href="/facts/Fluid_dynamics/y7uzSCfg">fluid dynamics</a>, optics, astronomy, and music theory. Euler has been called a "universal genius" who "was fully equipped with almost unlimited powers of imagination, intellectual gifts and extraordinary memory". He spent most of his adult life in <a href="/facts/Saint_Petersburg/pNuCBxaM">Saint Petersburg</a>, Russia, and in <a href="/facts/Berlin/pMTIRNXK">Berlin</a>, then the capital of <a href="/facts/Kingdom_of_Prussia/x796l7vx">Prussia</a>.
Euler is credited for popularizing the Greek letter 
 
 
 
 π
 
 
 {\displaystyle \pi }
 
 (lowercase <a href="/facts/Pi_(letter)/4UpopgBE">pi</a>) to denote <a href="/facts/Pi/vC0UBj1q">the ratio of a circle's circumference to its diameter</a>, as well as first using the notation 
 
 
 
 f
 (
 x
 )
 
 
 {\displaystyle f(x)}
 
 for the value of a function, the letter 
 
 
 
 i
 
 
 {\displaystyle i}
 
 to express the <a href="/facts/Imaginary_unit/1SCllQlU">imaginary unit</a> 
 
 
 
 
 
 −
 1
 
 
 
 
 {\displaystyle {\sqrt {-1}}}
 
, the Greek letter 
 
 
 
 Σ
 
 
 {\displaystyle \Sigma }
 
 (capital <a href="/facts/Sigma/DWcCDzou">sigma</a>) to express <a href="/facts/Summation/V2WUxoKn">summations</a>, the Greek letter 
 
 
 
 Δ
 
 
 {\displaystyle \Delta }
 
 (capital <a href="/facts/Delta_(letter)/otPsSYj6">delta</a>) for <a href="/facts/Finite_difference/aY1txFhj">finite differences</a>, and lowercase letters to represent the sides of a triangle while representing the angles as capital letters. He gave the current definition of the constant 
 
 
 
 e
 
 
 {\displaystyle e}
 
, the base of the <a href="/facts/Natural_logarithm/PnreKEzI">natural logarithm</a>, now known as <a href="/facts/Euler%2527s_number/coEtSBk8">Euler's number</a>. Euler made contributions to <a href="/facts/Applied_mathematics/qyqklXXm">applied mathematics</a> and <a href="/facts/Engineering/RFVg8H3I">engineering</a>, such as his study of ships which helped navigation, his three volumes on optics contributed to the design of <a href="/facts/Microscope/ldJp0CI3">microscopes</a> and <a href="/facts/Telescope/BDwYahhR">telescopes</a>, and he studied the bending of beams and the critical load of columns.
Euler is credited with being the first to develop <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a> (partly as a solution for the problem of the <a href="/facts/Seven_Bridges_of_K%25C3%25B6nigsberg/r95CwL9f">Seven Bridges of Königsberg</a>, which is also considered the first practical application of topology). He also became famous for, among many other accomplishments, solving several unsolved problems in number theory and analysis, including the famous <a href="/facts/Basel_problem/2PManmlC">Basel problem</a>. Euler has also been credited for discovering that the sum of the numbers of vertices and faces minus the number of edges of a <a href="/facts/Polyhedron/UC0p9FTF">polyhedron</a> equals 2, a number now commonly known as the <a href="/facts/Euler_characteristic/JCjzWUr2">Euler characteristic</a>. In physics, Euler reformulated <a href="/facts/Isaac_Newton/4L7gTncN">Isaac Newton</a>'s <a href="/facts/Newton%2527s_laws_of_motion/XKzGTXK1">laws of motion</a> into <a href="/facts/Euler%2527s_laws_of_motion/2KymtP2P">new laws</a> in his two-volume work <a href="/facts/Mechanica/S353xzMa">Mechanica</a> to better explain the motion of <a href="/facts/Rigid_bodies/THezBlq2">rigid bodies</a>. He contributed to the study of <a href="/facts/Euler%25E2%2580%2593Bernoulli_beam_theory/3DyQV9do">elastic deformations</a> of solid objects. Euler formulated the <a href="/facts/Euler_equations_(fluid_dynamics)/EYW5lerl">partial differential equations</a> for the motion of <a href="/facts/Inviscid_flow/GRNloKQ6">inviscid fluid</a>, and laid the mathematical foundations of <a href="/facts/Potential_theory/3sXGIcDA">potential theory</a>.
Euler is regarded as arguably the most prolific contributor in the history of mathematics and science, and the greatest mathematician of the 18th century. His 866 publications and his correspondence are being collected in the <a href="/facts/Opera_Omnia_Leonhard_Euler/vDrEcmAz">Opera Omnia Leonhard Euler</a> which, when completed, will consist of 81 <a href="/facts/Quarto/p9l8ygjR">quartos</a>. Several great mathematicians who worked after Euler's death have recognised his importance in the field: <a href="/facts/Pierre-Simon_Laplace/6ktp0txb">Pierre-Simon Laplace</a> said, "Read Euler, read Euler, he is the master of us all"; <a href="/facts/Carl_Friedrich_Gauss/f4eSMBD7">Carl Friedrich Gauss</a> wrote: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it."

Leonhard Euler open-in-new

Leonhard Euler