A Tangled Tale

A Tangled Tale is a collection of 10 brief humorous stories by Lewis Carroll (Charles Lutwidge Dodgson), published serially between April 1880 and March 1885 in The Monthly Packet magazine. Arthur B. Frost added illustrations when the series was printed in book form. The stories, or Knots as Carroll calls them, present mathematical problems. In a later issue, Carroll gives the solution to a Knot and discusses readers'' answers. The mathematical interpretations of the Knots are not always straightforward. The ribbing of readers answering wrongly - giving their names - was not always well received (see Knot VI below). In the December 1885 book preface Carroll writes: The writer''s intention was to embody in each Knot (like medicine so dexterously, but ineffectually, concealed in the jam of our early childhood) one or more mathematical questions - in Arithmetic, Algebra, or Geometry, as the case might be - for the amusement, and possible edification, of the fair readers of that magazine. Describing why he was ending the series, Carroll writes to his readers that the Knots were "but a lame attempt." Others were more receptive: In 1888 Stuart Dodgson Collingwood wrote, "With some people, this is the most popular of all his books; it is certainly the most successful attempt he ever made to combine mathematics and humour." They have more recently been described as having "all the charm and wit of his better-known works". Knot I, Excelsior. Two knights discuss the distance they will have travelled that day, uphill and downhill at different speeds. The older knight obscurely explains the mathematical problem. Carroll''s Solution: As with most of the Knots, the solution includes: a simplified restatement of the problem, a method to arrive at the solution, the solution, a discussion of readers'' solutions, then readers'' grades. In his discussion, Carroll relates that one reader accuses the senior knight of untruthfulness (this is rebutted by Carroll, using the knight''s tone). AuthorCharles Lutwidge Dodgson (27 January 1832 - 14 January 1898), better known by his pen name Lewis Carroll, was an English writer, mathematician, logician, Anglican deacon, and photographer. His most famous writings are Alice''s Adventures in Wonderland, its sequel Through the Looking-Glass, which includes the poem "Jabberwocky", and the poem The Hunting of the Snark - all examples of the genre of literary nonsense. He is noted for his facility at word play, logic and fantasy. There are societies in many parts of the world dedicated to the enjoyment and promotion of his works and the investigation of his life. Within the academic discipline of mathematics, Dodgson worked primarily in the fields of geometry, linear and matrix algebra, mathematical logic, and recreational mathematics, producing nearly a dozen books under his real name. Dodgson also developed new ideas in linear algebra (e.g., the first printed proof of the Kronecker-Capelli theorem), probability, and the study of elections (e.g., Dodgson''s method) and committees; some of this work was not published until well after his death. His occupation as Mathematical Lecturer at Christ Church gave him some financial security. His mathematical work attracted renewed interest in the late 20th century. Martin Gardner''s book on logic machines and diagrams and William Warren Bartley''s posthumous publication of the second part of Carroll''s symbolic logic book have sparked a reevaluation of Carroll''s contributions to symbolic logic. Robbins'' and Rumsey''s investigation of Dodgson condensation, a method of evaluating determinants, led them to the Alternating Sign Matrix conjecture, now a theorem. The algorithm known as Dodgson condensation is closely related to the Schur complement and the Desnanot-Jacobi identity. The discovery in the 1990s of additional ciphers that Carroll had constructed, in addition to his "Memoria Technica", showed that he had employed sophisticated mathematical ideas in their creation.