The discovery of octonions by John T. Graves, who denoted them with a boldface O, was announced to his mathematician friend William Hamilton, discoverer of quaternions, in a letter on this date.

In mathematics, the octonions are a normed division algebra over the real numbers, a kind of hypercomplex number system. The octonions are usually represented by the capital letter O, using boldface O or blackboard bold . Octonions have eight dimensions; twice the number of dimensions of the quaternions, of which they are an extension. They are noncommutative and nonassociative, but satisfy a weaker form of associativity; namely, they are alternative. They are also power associative.

John Thomas Graves was an Irish jurist and mathematician. He was a friend of William Rowan Hamilton, and is credited both with inspiring Hamilton to discover the quaternions in October 1843 and then discovering their generalization the octonions himself later that same year. He was the brother of both the mathematician and bishop Charles Graves and the writer and clergyman Robert Perceval Graves.

Sir William Rowan Hamilton was an Irish mathematician, physicist, and astronomer who made numerous major contributions to abstract algebra, classical mechanics, and optics. His theoretical works and mathematical equations are considered fundamental to modern theoretical physics, particularly his reformulation of Lagrangian mechanics. His career included the analysis of geometrical optics, Fourier analysis, and quaternions, the last of which made him one of the founders of modern linear algebra.

In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. The set of all quaternions is conventionally denoted by , or if blackboard bold is not available, by H. Quaternions are not quite a field, because in general, multiplication of quaternions is not commutative. Quaternions provide a definition of the quotient of two vectors in a three-dimensional space. Quaternions are generally represented in the form