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enigmatologist noun [C]
someone who studies and writes mathematical, word or logic puzzles
enigmatology also enigmatography noun [U]

‘The annual war with words was spawned a quarter-century ago by enigmatologist Will Shortz, current puzzle editor of The New York Times.’
(Dallas Morning News, 9th March 2003)

The creation of a word for referring to the science of puzzle construction doesn’t seem unreasonable, given the existence of many other, rather more obscure ‘-ologies’ which have existed in the English language for centuries (e.g. algology, the science or study of seaweeds, dating from 1849 according to the Shorter Oxford Dictionary).

The term enigmatology is a relatively recent coining however, originating around thirty years ago with the American Will Shortz, the only academically accredited enigmatologist in the world. Shortz earned a degree in Enigmatology from Indiana University in 1974, and after spending many years as editor of the American magazine Games, is currently crossword editor of The New York Times. Shortz’s use of enigmatologist is as a generic term for someone involved in the science of puzzles of any kind, be they mathematical, word or logic oriented.

Someone who has a specific interest in crossword puzzles however, should strictly speaking be described as a cruciverbalist. The noun cruciverbalist is also a relatively recent coining, first appearing in English in the early eighties as a means of describing someone who compiles or solves crosswords. The word is a modern invention, made to look more established by being based on a Latin translation of crossword (i.e. Latin cruce is ‘cross’ and verbum is ‘word’). Bizarrely, a very common use of the word is as a crossword solution to a clue such as: ‘crossword puzzle fan (14 [letters])’. There is also evidence for a derived noun cruciverbalism for the science of crossword compilation or solving, and an adjective cruciverbal, though these are much rarer. There is even a website called cruciverb.com which is devoted to the construction of crossword puzzles.

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