George Peacock (1791–1858) was educated at Trinity College, Cambridge, became Lowndean professor there, and later, dean of Ely. His chief publications are his Algebra, 1830 and 1842,
and his Report on Recent Progress in Analysis, which was the first of several valuable summaries of scientific progress printed in the volumes of the British Association. He was one of the first to study seriously the fundamental principles of algebra, and to fully recognise its purely symbolic character. He advances, though somewhat imperfectly, the "principle of the permanence of equivalent forms." It assumes that the rules applying to the symbols of arithmetical algebra apply also in symbolical algebra. About this time D. F. Gregory wrote
a paper "on the real nature of symbolical algebra," which brought out clearly the commutative and distributive laws. These laws had been noticed years before by the inventors of symbolic methods in the calculus. It was Servois who
introduced the names commutative and distributive in 1813.
Peacock's investigations on the foundation of algebra were considerably advanced by De Morgan and Hankel.
James Ivory (1765–1842) was a Scotch mathematician who
for twelve years, beginning in 1804, held the mathematical chair in the Royal Military College at Marlow (now at Sandhurst). He was essentially a self-trained mathematician, and almost the only one in Great Britain previous to the organisation of the Analytical Society who was well versed in continental mathematics. Of importance is his memoir (Phil. Trans., 1809) in which the problem of the attraction of a homogeneous ellipsoid upon an external point is reduced to
the simpler problem of the attraction of a related ellipsoid upon a corresponding point interior to it. This is known as "Ivory's theorem." He criticised with undue severity Laplace's
solution of the method of least squares, and gave three proofs
of the principle without recourse to probability; but they are
far from being satisfactory.
The Origin of Modern Geometry
By the researches of Descartes and the invention of the calculus, the analytical treatment of geometry was brought into great prominence for over a century. Notwithstanding the efforts to revive synthetic methods made by Desargues, Pascal,
De Lahire, Newton, and Maclaurin, the analytical method
retained almost undisputed supremacy. It was reserved for the genius of Monge to bring synthetic geometry in the foreground, and to open up new avenues of progress. His Géométrie descriptive marks the beginning of a wonderful development of modern geometry.