-
Period: to
FIRST PERIOD
This period can be characterized as the time when mathematicians investigated, discovered, and developed hyper-complex number systems that could be used in analysis in space. In this period, the two largest traditions emerged: the Grassmann tradition and the Hamilton tradition, which, due to its importance, is separated into a special chapter. -
Peter Guthrie Tait
Tait was born in 1831 near Edinburgh, Scotland. In 1841 he entered the Edinburgh Academy where a year before the young Maxwell had been where a friendship between them was established. After his graduation in 1852, he was appointed a Fellow of Peterhouse College, Cambridge where he began the production of his many books. -
Period: to
Peter Guthrie Tait (importance)
(1) He was the leader in the knowledge of the quaternion system from 1865 until his death (2) Tait developed quaternion analysis as a tool for research in the physical sciences, and created many new theorems in quaternion analysis to be translated into modern vector analysis. (3) Through Tait, Maxwell developed an interest in quaternions. (4) Tait was the main opponent of modern vector analysis -
Period: to
Publicacion del libro de quaterniones
A partir de 1857 su interés en los quaterniones continuó incrementándose por lo que sostuvo una gran correspondencia con Hamilton, aproximadamente se escribieron 50 cartas, una de las cuales constaba de 96 páginas. Se distinguió como un gran lector y escritor de libros científicos (22 libros fueron tanto total como parcialmente escritos por él) y como un productivo investigador científico. Publicó 365 documentos, de los cuales aproximadamente 70 fueron sobre los quaterniones. -
Period: to
AVERAGE PERIOD
It can be described as the time when some early period vector systems were discussed, tested and in some cases extended. This period was more a time of recognition than of discovery. So, for example, in this period scientists recognized the need for a vector method and specifying its characteristics within a vector system. -
PUBLICACION DE DOCUMENTOS DE ELECTRICIDAD DE MAXWELL
Maxwell presentó una interpretación histórica sobre lo que Thomson había descubierto. Esta interpretación la dio en dos documentos; el primero es un discurso a la "British Association" y el segundo es un documento titulado "On the Mathematical Classification of Physical Quantities" en el cual Maxwell se internó en una explicación del porque era importante una clasificación matemática de cantidades físicas, centrado en la clasificación de entidades físicas dentro de escalares y vectores. -
On the Mathematical Classification of Physical Quantities
Maxwell classified vectors into force vectors (which refer to units of length) and flux vectors (which refer to units of area). However, Maxwell in general disliked the quaternion method, for example he was upset by the non-homogeneity of quaternions, by the vector product and by the fact that the square of a vector was negative, the which in the case of the velocity vector made a negative kinetic energy. -
William Kingdon Clifford (1845-1879)
Clifford's significance for the history of vector analysis is seen in two ways.
(1) He was one of the few mathematicians of his time who knew both quaternion analysis and Grassmann's.
(2) he wrote a paper which is in a sense transitional from quaternion analysis to vector analysis. -
Elements of Dynamics
introduce los vectores; en su parte inicial, el trabajo explica sus ideas sobre la adición de vectores y en la parte media escribió una sección titulada "Product of Two Vectors" la cual parece ser una definición del producto escalar y vectorial moderno. puede considerarse como una figura de transición; sus escritos son posteriores al tiempo de Grassmann y Hamilton y antes de la creación del sistema moderno del análisis vectorial de Gibbs y Heaveside. -
James Clark Maxwell
This brilliant Scotsman was not only a figure in the history of vector analysis but also had important developments in the physical sciences of the 19th century. This was due to the growing need for an approach to solving physical problems. Maxwell presented his famous equation in the year 1860 written in component notation while in his "Treatise on Electricity and Magnetism" of 1873 he wrote it in both component and quaternion notation. -
CONTRIBUTION OF BENJAMIN PEIRCEN
He publishes a document "Linear Associative Algebra" in which he shows his great interest in quaternions and develops 162 algebras. This document is published in 1881 and helped to develop the theory of the aforementioned hyper-complexes. -
Period: to
VECTOR METHODS DISCUSSION
The Gibbs-Heaviside system was widely known, although in 1894 this system was not yet accepted by the scientific community. In the period from 1894 to 1910, vector analysis was accepted, which is established by the fact that a substantial number of important publications presented the system of vector analysis as something common. There were perhaps 1,000 articles published from 1894 to 1910 in which some form of vector analysis was discussed and used. -
MATHEMATICAL ANALYSIS
This need for rigorization makes mathematics stop being an idealization of nature; and they come to be considered as a creation of the human being. Its primary objective is no longer the description of nature, but the study of mathematical entities, which come to have an independent existence and on an equal footing with the other objects that make up reality. Thus they cease to be creations of the mind, to become real objects to be discovered and studied.