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The conjecture that Frey's elliptic curve was not modular. The conjecture was quickly proved by Ribet (Ribet's theorem) in 1986, and was an important step in the proof of ...

Let omega_1 and omega_2 be periods of a doubly periodic function, with tau=omega_2/omega_1 the half-period ratio a number with I[tau]!=0. Then Klein's absolute invariant ...

A prime factorization algorithm which uses residues produced in the continued fraction of sqrt(mN) for some suitably chosen m to obtain a square number. The algorithm solves ...

A method for mapping three-dimensional figures onto the plane.

Newton's term for a variable in his method of fluxions (differential calculus).

A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...

An fairly good numerical integration technique. The method is also available in the Wolfram Language using the option Method -> DoubleExponential to NIntegrate.

A method of computing the determinant of a square matrix due to Charles Dodgson (1866) (who is more famous under his pseudonym Lewis Carroll). The method is useful for hand ...

A Dirichlet L-series is a series of the form L_k(s,chi)=sum_(n=1)^inftychi_k(n)n^(-s), (1) where the number theoretic character chi_k(n) is an integer function with period k, ...

A method for finding roots which defines P_j(x)=(P(x))/((x-x_1)...(x-x_j)), (1) so the derivative is (2) One step of Newton's method can then be written as ...