Lewis Carroll and maths

By Prakash Khare

QUEEN Victoria, after reading Alice’s Adventures in Wonderland, enquired if the author Lewis Carroll had other books also to his credit. The story goes that the next book the Queen received was The Elementary Treatise on Determinants, a mathematical work attributed to one Charles Lutwidge Dodgson. For Dodgson it was who had adopted Lewis Carroll as a pseudonym for the Alice story.

Today, a century after Carroll’s death, Alice’s Adventures continue to captivate the young and the old alike. However, very few of its readers are, perhaps, aware that Lewis Carroll had indeed authored a good many books on pure mathematics also, besides other assorted topics. It makes an enchanting study to peep into this lesser known aspect of his work.

Born in 1832, Dodgson went to Oxford in 1850 with a fellowship on the condition that he remained celibate and joined the holy order. He graduated in 1854 and went on to collect a master’s degree in mathematics. In 1857 he was appointed a lecturer at Christ Church College and was also ordained Deacon of the Church of England. His secluded life provided him ample opportunity for writing.

The complete bibliography of his published works lists 256 items and about three times that number was never published. Of the former, the books on mathematics and logic (which was Dodgson’s other diversion) number 58. He was concerned with the presentation of fundamental mathematical principles in the simplest possible form. Thus, of his works on mathematics, no fewer than 24 were texts for students in arithmetic, algebra, trigonometry, plane and analytical geometry.

Significantly his first published work itself was a book on mathematics — A Syllabus of Plane Analytical Geometry by Charles Lutwidge Dodgson, M.A., student and mathematical lecturer of Christ Church, Oxford (1860). The next year saw yet another book on geometry — The Formulae of Plane Geometry, Alice’s Adventures in Wonderland appeared only later in 1865, to be followed by An Elementary Treatise on Determinants, the book that gave birth to the famous story already mentioned. A few more minor writings, and then came Dodgson’s "most serious" work on geometry — Euclid and His Modern Rivals (1879). In it he projected his appreciation of the basic foundations on which Euclidean geometry is based, and he sought to defend that for their sheer invincible simplicity, Euclid’s axioms, definitions and methods could simply not be improved upon. He vehemently decried all attempts at "reforming". Euclid as "simply monstrous".

In Pillow Problems, one of his less serious efforts, he gives an interesting collection of puzzles which require application of algebra, geometry and trigonometry but which one is expected to solve in bed itself without the help of pencil or paper. A Tangled Tale is his other book of mathematical riddles.

To concede Dodgson due credit for his sharp mathematical acumen, it may be recalled that his most favourite puzzle "Where does the day begin?" was not satisfactorily answered until 24 years after it had been posed. If a man were to travel westward around the earth at the same speed at which the sun crosses the circles of longitude, he will find that though he started on Friday, he returns to the starting point on Saturday. "When did the date change?" Dodgson asked. He even carried on a protracted correspondence in the matter with the official authorities, international telephone companies, etc., without a satisfactory answer. The solution, of course, was available only in 1884 when the international dateline was first established.

Dodgson’s dabbling with mathematics produced writings on a great variety of topics. Among his last contributions was Curiosa Mathematica. Other assorted topics dealt with by him were remembering dates the easy way, cipher games, ready reckoner for postage, and so forth. He also wrote on social issues, advocated education for women and stoutly opposed vivisection. He also ranked as a pioneer of British amateur photography, especially child photography.

He passed away in 1898 at the age of 66. Finally how does Lewis Carroll measure up as a mathematician? He himself provides this unpretentious answer in his diary. " Tried a little mathematics unsuccessfully."