Horner

Horner is a surname that can refer to several topics in science, mathematics, and medicine. The two most widely known uses are Horner's method for evaluating polynomials and Horner's syndrome, a neuro-ophthalmic condition.

Horner's method, also called Horner's scheme or Horner's rule, is an algorithm for evaluating polynomials with a minimum number of arithmetic operations. Introduced by William George Horner, an Irish mathematician, the method rewrites a polynomial in nested form to reduce multiplications. It is a fundamental technique in numerical analysis and underpins efficient polynomial evaluation in many computing systems.

Horner's syndrome is named after Johann Friedrich Horner, an ophthalmologist who described the condition. It results from disruption of the oculosympathetic pathway and is characterized by ptosis (drooping of the upper eyelid), miosis (constricted pupil), and often anhidrosis (reduced facial sweating) on one side of the face. The syndrome can arise from various etiologies, ranging from local nerve lesions to broader neurological or vascular issues, and is diagnosed primarily on clinical signs, with imaging as needed to identify underlying causes.

As a surname, Horner is borne by many individuals across diverse fields. Notable figures include William George Horner, associated with the polynomial evaluation method, and Johann Friedrich Horner, after whom Horner's syndrome is named. The name appears in different cultures and historical contexts.