George Peacock – Mathematical Genius

George Thomas Peacock

Many mathematicians have graced the green earth, but few have left a mark as deep as the one left by George Peacock. This mathematical genius dedicated his life to understanding the logic of symbolic algebra. He also worked alongside celebrated mathematicians like Charles Babbage and John Herschel to make the world wiser than they found it.

History

Born in April 1791 in Thornton Hall, Denton, near County Durham, George Peacock was a renowned English mathematician. Peacock had a very humble and average beginning. In his early life, he did not show any signs of exceptional genius. However, he was as remarkable in his adventures of climbing as in any special attachment to academics.

George Peacock got his elementary education from his father, Thomas Peacock, who was also a priest in the Church of England. He held the office as the curate of the parish of Denton for 50 years. Thomas also kept a school here. After his initial education, George went to the Sedbergh School.

When George was 17 years old, under the supervision of James Tate, he went to Richmond School. James Tate was a Cambridge University graduate. It was in this school where George began to distinguish himself significantly in elementary and classic mathematics, and this was more than what he needed for entrance to Cambridge. That’s how he became the student of Trinity College in Cambridge.

In 1812, George Peacock scored the second-highest in his university and received the title of the second wrangler. This means in just the third year, he gained first-class honors in his undergraduate degree in mathematics.

During 1812 and 1813, he also won the Smith’s Prize for his examination performance along with the senior wrangler, John Herschel. At the time, the value of this prize was £25.

Two years after that, he applied for a fellowship at his college. He won the fellowship almost immediately partly because of his accurate and extensive knowledge of the classics of mathematics. At that time, this fellowship was worth £200 per year and would continue for seven years under the condition that the fellow remained unmarried during this period. The fellowship was also extendable under the condition that the fellow took clerical orders.

In 1819, Peacock extended his fellowship, meeting all the terms and conditions.

Biography

George Peacock’s history started as soon as he took the fellowship. Just a year after accepting the fellowship, Peacock received the appointment of lecturer and tutor in his college. He continued to hold this position for many years.

Peacock was profoundly impressed and saw the need to reform Cambridge’s position of ignoring calculus differential notation. Therefore, while he was still an undergraduate, he got together with some students of his own standing like Charles Babbage and John Herschel. Together, they worked on and brought about the change they envisioned. Mainly, they wanted to leave the world wiser than they found it.

In 1815, Peacock, with the help of Babbage and Herschel, was able to form the later infamous The Analytical Society. This society was to advocate the Continent’s d’ism over the dot-age of the University. In other words, the purpose of this movement was to adopt the continental methods of mathematical analysis.

The Analytical Society

Immediately after initiation, the society got to work with their first task, which was to translate the smaller work of Lacroix from French to English. In 1816, their translated work on Lacroix’s integral and differential calculus went public. After this work, there were more translations since, at that time, the best manuals and the most significant works in mathematics were written in French. In 1820, the Society published an extensive collection of translations which contained examples of the application of the integral and differential calculus.

Not only did the books sell very rapidly, but they also contributed significantly to furthering the Society’s objective.

After an estimated three years, George Peacock became the examiner in 1817. As an examiner of the mathematical tripos, he used the powerful leverage of his new position to further advance the message of his reform. He did that by adding the differential notation to the question set of the examination for the very first time since he was an official employee of Cambridge. This innovation met with severe disapproval.

This gives us quite an insight into the traits and character of George Peacock. He was a passionate and enthusiastic reformer. It was his ardency with the movement which brought success to the objective of The Analytical Society in just a few years.

Elected In 1818, George Peacock was a fellow of the Royal Society. The judges of London’s Royal Society would grant this award to individuals who had made a substantial contribution to the improvement of natural knowledge like mathematics, medical science, and engineering science.

Astrological and Philosophical Side

The Astronomical Society of London took shape to elevate astronomical science. The three prime movers of the reform were, again, Peacock, Babbage, and Herschel. George Peacock was also an ardent promoter of an astronomical observatory at Cambridge. He helped establish Cambridge’s Philosophical Society.

George Peacock and Algebra

Besides all the reforms he was passionately involved in, one remained constant, i.e., his teaching of algebra. In 1830, he published a formal and systematically written work on algebra. His work had no storage of depth and was primarily concerned with exposing and investigating the principle of algebra. The objective of the Treatise was to place algebra on a truly scientific base and make it adequate for development. Whatever development continental mathematicians were able to make on algebra had its roots in this.

In 1833, Peacock presented a comprehensive report on algebra, trigonometry, and the arithmetic of sines at the British Association for the Advancement of Science’s third meeting, held two years after its formation. This was a prototype association of the American, French, and Australian associations, which held its first meeting in the ancient city of York.

The report presented by Peacock is one of the most valuable reports the association has prepared and printed.

In 1837, Peacock received the Lowndean Chair of Astronomy professorship at Cambridge University. Everything he did helped further the object of his reform to improve the status of the university. Each role and responsibility he undertook, he worked hard on it. This is why he became a member of the commission and was appointed by the government.

In 1839, George Peacock got appointed Ely Cathedral’s Dean in Cambridgeshire. He held this position until the very end of his life, which was approximately 20 years. While in this position, Peacock undertook remarkable accomplishments like major restorations on the cathedral building, installation of the boarded ceiling, and writing two volumes of a textbook. He dedicated the book to algebra with one volume named Arithmetical Algebra and the other volume named Symbolical Algebra.

In 1847, Peacock got married at the age of 56 to Ms. Frances Elizabeth Selwyn. They had no children. His health started to deteriorate around this time.

In 1858, Peacock departed from this world in Ely at the age of 68. Before his death, he attended the University Reform Commission’s meeting as his last public act.

A Summary of George Peacock Timeline

Year 

George Peacock 

1791

Was born

1809

Became a student at Trinity College, Cambridge

1812

Won second wrangler award at Cambridge

1812

Won second Smith’s prize at Cambridge

1814

Was immediately selected for the fellowship

1815

Was appointed as a tutor and a lecturer in his colleges

1815

Founded Analytical Society with Charles Babbage and John Herschel

1816

Analytical Society’s first publication which was the translation of Lacroix’s Differential Calculus

1817

Got appointed as an examiner at Cambridge

1818

Was elected Fellow of The Royal Society

1819

Extended his fellowship

1819

Was ordained as a deacon

1822

Was ordained as a priest

1826-35

Was appointed Vicar of Wymeswold, Leicestershire

1830

Published Treatise on Algebra

1833

Report to the British Association for the Advancement of Science

1837

Received Chair of Lowndean Professor of Astronomy

1839-58

Was appointed Dean of Ely Cathedral, Cambridgeshire

1842-45

Wrote an updated edition of Treatise on Algebra in two volumes

1847

Married Frances Elizabeth Selwyn

1858

Died

George Peacock Accomplishments

Few people can claim to have lived a life like George Peacock. Although his life had both small and astronomically large achievements, he is most renowned for his achievements in the field of Mathematics, Algebra, to be specific.

Today, we have a varying view on George Peacock. While some consider him as the person who invented symbolic algebra, others explain his work as an aspiration to dismantle an existing area of mathematics. Regardless, the main contribution of Peacock remains his attempt to place algebra on a strictly logical basis.

He extended the scope of algebra beyond the ordinary systems of numbers. He was the first to recognize the possibility of having a part of algebra that was non-arithmetical and helped further build on the arithmetical part. His work is the stepping stone for many future mathematicians to expand on it to form more of the abstract algebra.

In his updated edition of Treatise on Algebra, he explained that the science of algebra had two parts. One was arithmetical, while the other was symbolical. He also explained that they both made mistakes in restricting the science to the algorithm part.

If we were to think like George Peacock in terms of mathematical algebra, we would begin by thinking of the symbols as a representation of numbers. These symbols or numbers will go into operation in the same definition as you would in standard arithmetic. That means the signs + and – would still perform the functions of addition and subtraction.

Therefore, George Peacock’s principle about algebra theory states that arithmetic algebra’s elementary symbols denote digital numbers, most likely integers. According to him, the rules of arithmetical algebra still apply to the symbolic algebra but without the restrictions. In other words, all the rules and results of general mathematical algebraic expression also hold for the general symbolic algebraic expression. Peacock explains this in great detail with examples on page 50 of his book The Symbolic Algebra.

Another most notable accomplishment of this 19^th-century Englishman is that he founded the symbolic or philosophical school of mathematicians. This school later housed some of history’s most renowned and celebrated brains, including George Boole, Augustus De Morgan, and Duncan F. Gregory.

In a letter to a friend, he expressed his utmost dedication to the cause. He also expressed his desire never to decline any position or office which would put him in power or increase this influence so that he could positively affect the cause of the reform. This reform was happening around the time he was certain of nomination as a moderator for the year 1818 to 1819. He also vowed not to neglect his role and influence as a lecturer.