Epitome of Eponyms: I Rest My Case!
Differing from the usual format for this section, one mathematician's name is associated with a great many topics. The common story is that mathematicians sometimes, trying to avoid naming everything after ***, name discoveries and theorems after the "first person after *** to discover it." Who is the mathematician ***?
 ***'s conjecture (or Waring's problem)
 ***'s sum of powers conjecture
 ***–Bernoulli beam equation, concerning the elasticity of structural beams
 ***–Cauchy equation, a secondorder linear differential equation
 ***–Lagrange equation, in regard to minimization problems in calculus of variations
 ***–Lotka equation (mathematical demography)
 ***–Poisson–Darboux equation
 *** transform used to accelerate the convergence of an alternating series and is also frequently applied to the hypergeometric series
 ***'s formula e^{ ix} = cos x + i sin x in complex analysis
 ***'s formula for planar graphs or polyhedra: v − e + f = 2
 ***'s formula for the critical load of a column
 ***'s continued fraction formula
 ***'s product formula for the Riemann zeta function
 ***–Maclaurin formula – relation between integrals and sums
 ***–Rodrigues formulas concern ***–Rodrigues parameters and 3D rotation matrices
 The *** function, a modular form that is a prototypical qseries
 ***'s homogeneous function theorem
 ***'s totient function (or *** phi (φ) function) in number theory, counting the number of coprime integers less than an integer
 *** hypergeometric integral
 ***'s identity e^{ iπ} + 1 = 0
 ***'s foursquare identity, which shows that the product of two sums of four squares can itself be expressed as the sum of four squares
 ***'s number, e ≈ 2.71828, the base of the natural logarithm, also known as Napier's constant
 ***'s idoneal numbers
 *** numbers are an integer sequence
 *** characteristic
 ***'s Lucky numbers
 *** integers are the numbers of form a + bω where ω is a complex cube root of 1
 ***'s homogeneous function theorem, a theorem about homogeneous polynomials
 ***'s infinite tetration theorem
 ***'s rotation theorem
 ***'s theorem (differential geometry) on the existence of the principal curvatures of a surface and orthogonality of the associated principal directions
 ***'s theorem in geometry, relating the circumcircle and incircle of a triangle
 ***–Fermat theorem, that a^{φ(m)} ≡ 1 (mod m) whenever a is coprime to m, and φ is ***'s totient function
 *** angles defining a rotation in space
 *** brick
 ***'s line – relation between triangle centers
 *** operator – set of functions to create polygon meshes
 ***'s rotation theorem
 *** squares, usually called GraecoLatin squares
 *** cycle – a path through a graph that takes each edge once
 *** class
 *** diagram – likely better (but wrongly) known as Venn diagrams, its subclass
 *** pseudoprime
 ***'s Disk – a toy consisting of a circular disk that spins, without slipping, on a surface
Now, who is the mathematician *** and what do each of these eponymic ideas/formulas mean?
Answer:
Leonhard Euler!
