In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include their own unique function, equation, formula, identity, number (single or sequence), or other mathematical entity. Many of these entities have been given simple and ambiguous names such as Euler's function, Euler's equation, and Euler's formula. Euler's work touched upon so many fields that he is often the earliest written reference on a given matter. In an effort to avoid naming everything after Euler, some discoveries and theorems are attributed to the first person to have proved them after Euler. Conjectures Euler's conjecture (Waring's problem) Euler's sum of powers conjecture Euler's Graeco-Latin square conjecture Equations Usually, Euler's equation refers to one of (or a set of) differential equations (DEs). It is customary to classify them into ODEs and PDEs. Otherwise, Euler's equation may refer to a non-differential equation, as in these three cases: Euler–Lotka equation, a characteristic equation employed in mathematical demography Euler's pump and turbine equation Euler transform used to accelerate the convergence of an alternating series and is also frequently applied to the hypergeometric series Ordinary differential equations Euler rotation equations, a set of first-order ODEs concerning the rotations of a rigid body. Euler–Cauchy equation, a linear equidimensional second-order ODE with variable coefficients. Its second-order version can emerge from Laplace equation in polar coordinates. Euler–Bernoulli beam equation, a fourth-order ODE concerning the elasticity of structural beams. Euler's differential equation, a first order nonlinear ordinary differential equation Partial differential equations Euler conservation equations, a set of quasilinear first-order hyperbolic equations used in fluid dynamics for inviscid flows. In the (Froude) limit of no external field, they are conservation equations. Euler–Tricomi equation – a second-order PDE emerging from Euler conservation equations. Euler–Poisson–Darboux equation, a second-order PDE playing important role in solving the wave equation. Euler–Lagrange equation, a second-order PDE emerging from minimization problems in calculus of variations. Formulas Functions The Euler function, a modular form that is a prototypical q-series. Euler's totient function (or Euler phi (φ) function) in number theory, counting the number of coprime integers less than an integer. Euler hypergeometric integral Euler–Riemann zeta function Identities Euler's identity . Euler's four-square identity, which shows that the product of two sums of four squares can itself be expressed as the sum of four squares. Euler's identity may also refer