George Peacock FRS (9 April 1791 – 8 November 1858) was an English mathematician and Anglican cleric.

Peacock was born on 9 April 1791 at Thornton Hall, Denton, near Darlington, County Durham.

[1] His father, Thomas Peacock, was a priest of the Church of England, incumbent and for 50 years curate of the parish of Denton, where he also kept a school.

At this school he distinguished himself greatly both in classics and in the rather elementary mathematics then required for entrance at Cambridge.

Two years later, he became a candidate for a fellowship in his college and won it immediately, partly by means of his extensive and accurate knowledge of the classics.

Peacock, in common with many other students of his own standing, was profoundly impressed with the need of reforming Cambridge's position ignoring the differential notation for calculus, and while still an undergraduate formed a league with Babbage and Herschel to adopt measures to bring it about.

In 1815 they formed what they called the Analytical Society, the object of which was stated to be to advocate the d 'ism of the Continent versus the dot-age of the university.

The first movement on the part of the Analytical Society was to translate from the French the smaller work of Lacroix on the differential and integral calculus; it was published in 1816.

Peacock followed up the translation with a volume containing a copious Collection of Examples of the Application of the Differential and Integral Calculus, which was published in 1820.

Peacock was appointed an examiner in 1817, and he did not fail to make use of the position as a powerful lever to advance the cause of reform.

In his questions set for the examination the differential notation was for the first time officially employed in Cambridge.

The innovation did not escape censure, but he wrote to a friend as follows: "I assure you that I shall never cease to exert myself to the utmost in the cause of reform, and that I will never decline any office which may increase my power to effect it.

I am nearly certain of being nominated to the office of Moderator in the year 1818-1819, and as I am an examiner in virtue of my office, for the next year I shall pursue a course even more decided than hitherto, since I shall feel that men have been prepared for the change, and will then be enabled to have acquired a better system by the publication of improved elementary books.

It is by silent perseverance only, that we can hope to reduce the many-headed monster of prejudice and make the University answer her character as the loving mother of good learning and science."

These few sentences give an insight into the character of Peacock: he was an ardent reformer and a few years brought success to the cause of the Analytical Society.

One of the first resolutions adopted was to procure reports on the state and progress of particular sciences, to be drawn up from time to time by competent persons for the information of the annual meetings, and the first to be placed on the list was a report on the progress of mathematical science.

An object of reform was the statutes of the university; he worked hard at it and was made a member of a commission appointed by the Government for the purpose.

[8] In 1839 he was appointed Dean of Ely cathedral, Cambridgeshire, a position he held for the rest of his life, some 20 years.

Together with the architect George Gilbert Scott he undertook a major restoration of the cathedral building.

Peacock's main contribution to mathematical analysis is his attempt to place algebra on a strictly logical basis.

He founded what has been called the British algebra of logic; to which Gregory, De Morgan and Boole belonged.

denote the operations of addition and subtraction in their ordinary meaning only, and those operations are considered as impossible in all cases where the symbols subjected to them possess values which would render them so in case they were replaced by digital numbers; thus in expressions such as

we must suppose the multiplier and divisor to be abstract numbers; all results whatsoever, including negative quantities, which are not strictly deducible as legitimate conclusions from the definitions of the several operations must be rejected as impossible, or as foreign to the science."

Peacock's principle may be stated thus: the elementary symbol of arithmetical algebra denotes a digital, i.e., an integer number; and every combination of elementary symbols must reduce to a digital number, otherwise it is impossible or foreign to the science.

must be held to be an impossible expression in general, or else the meaning of the fundamental symbol of algebra must be extended so as to include rational fractions.

One of the earliest English writers on arithmetic is Robert Recorde, who dedicated his work to King Edward VI.

Suppose, however, that we pass over this objection; how does Peacock lay the foundation for general algebra?

is any whole number, if it be exhibited in a general form, without reference to a final term, may be shown upon the same principle to the equivalent series for

But the antecedent is still too narrow; the true scientific problem consists in specifying the meaning of the symbols, which, and only which, will admit of the forms being equal.

Let us examine some other cases; we shall find that Peacock's principle is not a solution of the difficulty; the great logical process of generalization cannot be reduced to any such easy and arbitrary procedure.