William Whewell


Born: 24 May 1794 in Lancaster, Lancashire, England
Died: 6 March 1866 in Cambridge, England

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William Whewell's parents were John Whewell, a master carpenter, and Elizabeth Bennison. It was a large family, and William was the eldest of his parents' seven children. He attended Blue School in Lancaster and his father intended that his son should proceed from there to become an apprentice carpenter. However, the Revd Joseph Rowley, headmaster of Lancaster grammar school and the parish priest, recognised William's talents and offered free education for him at Lancaster grammar school. Several years later he persuaded John to let William attend Heversham Grammar School in Westmorland, about 20 kilometres north of his native town, where he would receive instruction to allow him to compete for a scholarship at Trinity College, Cambridge. In 1810 William went to Heversham where he spent two years. He also received some private coaching in mathematics from John Gough, a blind mathematician from Kendal, in:-

... conic sections, fluxions, and mechanics.

He won an exhibition to Trinity College, but this was not sufficient to support him during his studies so further funds to support him were raised by private subscription.

Whewell entered Cambridge in October 1812, but by this time the family had suffered a series of tragedies with his mother dying in 1807 and three of his younger brothers dying before William began his university studies. His own health had been poor but a month after starting his studies at Cambridge he wrote to his father:-

I have enjoyed very good health since I left Lancaster.

His mother had been a poet who had published poems in local papers and Whewell must have inherited his mother's poetic gifts since, in 1814, he won the Chancellor's prize for an epic poem he wrote entitled Boadicea. He began to fit into the university life although given his background this did not come easily. He described his social activities in 1815 as [1]:-

... shooting swallows, bathing by half dozens, sailing to Chesterton, dancing at country fairs, playing billiards, turning beakers into musical glasses, making rockets, riding out in bodies ...

He also excelled in the Mathematical Tripos graduating as second wrangler in January 1816 and then becoming second Smith's Prizeman. It was the first time that Whewell had not achieved the top place in a class but he took it in good part explaining in a letter to his family that he had not been able to write quickly enough. In July 1816 his father died before his son had graduated. In October 1817 he was elected to a fellowship at Trinity and wrote to his sisters saying that he had received [1]:-

... the most substantial benefit at which you ever had to rejoice with me. It secures me a comfortable establishment for life at least so long as my life is a simple one.

We should note at this stage that Whewell had made a number of friends among top academics during his undergraduate years at Cambridge including John Herschel, Charles Babbage, George Peacock and other members of the Analytical Society. Whewell was appointed as a mathematics lecturer and assistant tutor at Cambridge in 1818. He was one of the founder members of the Cambridge Philosophical Society in 1819.

At a time when Cambridge was still finding acceptance of the superior Continental approach to mathematics, Whewell played a major role in modernising their approach with his textbooks An Elementary Treatise on Mechanics (1819) and A Treatise on Dynamics (1823). His 1819 text was the first applied mathematics work in English to adopt continental mathematical symbolism, while his second work was a beautiful text using French analytic techniques. His achievements were quickly recognised with election to the Royal Society of London in 1820. He was by now making friends with younger Cambridge men such as Augustus De Morgan and William Rowan Hamilton. Although he showed himself a great enthusiast for the French analytical methods in the first editions of the above two works, we should say that over the years Whewell became worried that the lack of geometric methods would damage students' intuitive understanding and as a result he reduced the analytical tools, increasing the geometrical methods in the later editions of his books. He also published The Mechanical Euclid, containing the Elements of Mechanics and Hydrostatics demonstrated after the Manner of the Elements of Geometry (1837) where he took a completely geometrical approach.

Up to the mid 1820s Whewell had taught, written and researched mathematics. However this changed and he moved towards broader scientific interests with publications of books such as Essay on Mineralogical Classification and Nomenclature (1828), Architectural Notes on German Churches, with Remarks on the Origin of Gothic Architecture (1830), Astronomy and General Physics (1833), History of the Inductive Sciences (3 vols.) (1837), and The Philosophy of the Inductive Sciences (2 vols.) (1840). As one might expect this led to his role changing at Cambridge and he was appointed professor of Mineralogy in 1828, then professor of Moral Philosophy in 1838. In June 1841 he became engaged to be married to Cordelia Marshall and they married on 12 October 1841 in Cumberland. Five days later Whewell received a letter from Sir Robert Peel, the prime minister, saying that the Queen had accepted his recommendation that Whewell should be appointed master of Trinity. He was Vice-Chancellor of Cambridge University in 1842 and again in 1855, the year in which his wife Cordelia died.

The breadth of Whewell's contributions are listed in [3]:-

Along with his role in educational reform, Whewell also proved a zealous and prolific researcher. He published significant works in experimental physics, crystallography, mineralogy, physical astronomy, science education, architecture, poetry, and religion, along with a bewildering number of more popular reviews, lectures, and sermons. He is the inventor of the self-registering anemometer, and the originator of many new scientific terms, including "ion," "cathode," "Eocene," "Miocene," "physicist," and "scientist."

In fact many of these words were coined by Whewell at the request of friends, for example terms "anode", "cathode" and "ion" were for Faraday, while "scientist" was produced at the request of the poet Samuel Taylor Coleridge. One should not get the impression that Whewell moved away from applied mathematics, however, rather he included many other areas in his wide range of interests while continuing to research applied mathematical fields. For example he published fourteen major papers on the study of the tides between 1833 and 1850. In fact he won the Royal Medal from the Royal Society for this outstanding work on tides.

Another important contribution was his support of, and work for, the British Association for the Advancement of Science. He strongly supported the founding of the Association in 1831 and, although he did not attend the first meeting of the Association in York in that year, it was his suggestion that they seek annual reports on the various sciences. He wrote the report on mineralogy for the meeting in 1832 and that on electricity and magnetism for the meeting of 1835. He served the British Association as vice-president at the Oxford meeting in 1832 and again at Dublin in 1835, he was the local secretary in 1833 when the Association met in Cambridge, then he was president at Plymouth in 1841. In fact it was in his address to the 1833 British Association meeting that he used the word 'scientist' for the first time, explaining that he coined the word in analogy to 'artist'. He later wrote [10]:-

... as an Artist is a Musician, Painter, or Poet, a Scientist is a Mathematician, Physicist, or Naturalist.

Note that the word 'Physicist' used in this quote by Whewell is also a word coined by him.

The areas for which Whewell is most famous today are philosophy of science, history of science, and moral philosophy. He examined 'knowledge' and claimed that [10]:-

... in every act of knowledge ... there are two opposite elements, which we may call Ideas and Perceptions.

He claimed that Fundamental Ideas were [10]:-

... not a consequence of experience, but a result of the particular constitution and activity of the mind, which is independent of all experience in its origin, though constantly combined with experience in its exercise.

As examples of Fundamental Ideas he gave time, number, cause, substance, and likeness. He wrote [10]:-

We cannot see one object without the idea of space; we cannot see two without the idea of resemblance or difference.

He developed a theory of induction, attempting to explain how physical laws are discovered. He argued that as well as the process of examining instances of a law [10]:-

... there is a New Element added to the combination [of instances] by the very act of thought by which they were combined.

After a law is produced by induction, Whewell argued that next is required a confirmation stage. He also argued for a concept he called Necessary Truth. He gave as an example the truth 7 + 8 = 15 [10]:-

... we refer to our conceptions of seven, of eight, and of addition, and as soon as we possess the conceptions distinctly, we see that the sum must be 15. That is, merely by knowing the meanings of "seven," and "eight," and "addition," we see that it follows necessarily that "7 + 8 = 15".

For Whewell his work on the history of science was an integral part of that on the philosophy of science, both contributing to knowledge. He felt that the history of science was extremely important [10]:-

... the present generation finds itself the heir of a vast patrimony of science; and it must needs concern us to know the steps by which these possessions were acquired, and the documents by which they are secured to us and our heirs for ever.

The last years of Whewell's life were filled with sadness. His wife Cordelia died on 18 December 1855 after a long illness. He then married Lady Everina Frances Affleck, widow of Sir Gilbert Affleck, on 1 July 1858. She died on 1 April 1865. On 24 February 1866 Whewell fell from his horse while riding outside Cambridge after the animal bolted. He was brought back to Trinity in a carriage but found to be paralysed. He died in his room in Trinity on 6 March, his last request being that the curtains be drawn back so that he could look at the great court of Trinity for the last time.

As to his character Leslie Stephen in his 1899 biography writes [24]:-

He loved an argument, and his position as a great man in a small circle tended to make argument one-sided. He was popular as a tutor; but for some time he provoked a good deal of hostility as master. In early days he had little chance of acquiring social refinement; and, though he was anxious to be hospitable, his sense of the dignity of his position led to a formality which made the drawing-room of the lodge anything but a place of easy sociability. In later years age and sorrow made him conspicuously milder, and the object not only of the pride but of the warm affection of the university. Though rough at times, he was from the first magnanimous; he never cherished resentment and admitted defeat frankly, and received the opinions of young and insignificant persons with remarkable courtesy. Few men, too, have had more friends or retained their friendships more carefully. He had many controversies, but no personal quarrels.

With so many achievements in so many different areas it is clear that we must have failed to mention many important aspects of his contributions in this article. Perhaps we should mention one final fact which we have failed to mention until now, namely his role as a priest. He was ordained a priest on Trinity Sunday 1825, which was a requirement of Fellows of Trinity, then ordained as a deacon in the following year. He preached in the university on a regular basis, in particular he preached four sermons On the Foundation of Morals in 1837 which were published in that year. Ten years later he published Sermons preached in the Chapel of Trinity College, Cambridge containing twenty-two of his sermons.

Let us end this biography of Whewell by quoting John Herschel, his friend for many years [3]:-

... a more wonderful variety and amount of knowledge in almost every department of human inquiry was perhaps never in the same interval of time accumulated by any man.

Article by: J J O'Connor and E F Robertson


List of References (26 books/articles)

A Quotation

A Poster of William Whewell

Mathematicians born in the same country


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  1. Mathematical Genealogy Project

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