Between 1830 and 1930, some 40 million people emigrated to the US from Europe, more than nine million of them leaving from Liverpool hoping that the new world held a fortune.

The dream of Arthur Wynne, son of the editor of the Liverpool Mercury, was journalism. Wynne's destiny was indeed print. But on the pages of reportage and editorial, he left no mark worthy of note. He had a higher calling: as the inventor of the crossword puzzle.

Wynne found himself in charge of the puzzle pages of the New York World, a daily which mixed sensation with investigation. For the Christmas edition of 1913, he had the idea of providing a diamond grid and an instruction to solvers – though they weren't yet known as such – to "fill in the small squares with words which agree with the following definitions".

Space filled. And barely a newspaper has failed to follow suit in the century since.

The crossword would be among the hottest rages of that faddiest of decades, the 1920s.

There were crossword-themed cigars and biscuits, collar pins and dresses and a Broadway revue, Puzzles of 1925, which featured a scene in a crossword puzzle sanatorium filled with Americans driven to madness by puzzle fever.In the same decade, the crossword started appearing around the world, even in languages that don't use letters – Japanese grids, for example, take one syllable in each square. Anyone that has ever attempted a crossword in a language other than English will have noticed that there's a lot more description and a lot less ingenious invention.

Setters working in German or in Greek have fewer words to play with. English, by contrast, has far more words than it needs: centuries of trade and empire have given it hundreds of new pieces of vocabulary – crucial, that is, if you like word games.

It means that for any answer in a crossword grid, there are likely to be many quasi-synonymous words. So while English-language quick crosswords can be based around pleasurable ambiguity, the rest of the world’s are more prone to asking for names of far-off rivers and the obscure fishes within them.

English is also the best language for the cryptic crossword, where the apparent meaning of the clue is not immediately apparent.

Here is a form of puzzle in which the “flower” is more likely to be a river than a piece of fauna, where “wicked things” are candles and “number of people in a theatre” is an anaesthetist.

The cryptic was developed in the 1930s by various British men for publications which wanted to offer a stiffer challenge than the definitional puzzles in the mould of Wynne.

Derek Crozier started setting for The Irish Times in 1943 as Crosaire, his nom de guerre inspired by the affinity his surname had with road signs indicating crossroads.

From 1948, Crozier sent his typewritten puzzles from Zimbabwe, where he was trying to make a living as a tobacco farmer.

In most cryptics, from Australia to Canada, South Africa to India, the form of the clue is the same: there is a definition at the beginning or at the end and the rest is “wordplay” – a more allusive route to the answer. Crozier was never one to let such rules stand in the way of a laugh or an engaging turn of phrase, so “What a fat ram! (6)” is his way of indicating some butter, with the definition in the middle, and while “It’s quite right all rite (7)” definitely clues the answer, literal, I’d be at a loss to tell you why – and somehow, it doesn’t seem to matter.

So he went on until his death in 2010, and had stockpiled enough Crosaire crosswords to run until October 2011 (Crosaire by Mac an Iarla followed until June 2011 and was succeeded by the current Crosaire by Crossheir), saying one thing while meaning quite anothe – and that, really, is the essence of the cryptic crossword, and the reason why these puzzles are so compulsive. There’s a lift in the brain when the penny drops and the solver realises that a “die of cold” is an ice cube, or that “spoils of war” is indicating Mars.

There was a thin-lipped response among British setters and solvers in 1998 when the Daily Telegraph announced that its puzzles would be set by computers. Individual clues would still be created, at least for a while, by human beings – but they would be entered in to a database from which any day's puzzle might be assembled.

One setter, who operates under the name Rufus, declared that any crosswords assembled in this way would be “like combining the musical styles of Beethoven and Mozart in the same musical movement”.

The setters refused to set. The solvers wrinkled their noses at both the idea of automated puzzles and the breach of fair play. Boris Johnson, then the Telegraph's deputy editor, gave in to the inevitable, conceding that "in spite of the advantages the computer possesses, the machine has been condemned for a fatal lack of soul".

So we won’t have robots setting our crosswords. But can they solve them? It might alarm you to hear that they are making great strides.

Those who work in artificial intelligence have long been interested in the extent to which computer programs can do things that we might assume are ineffably human.

Equip an algorithm with a nice fat corpus of words and what they mean, explain to it the limited number of devices – anagrams, acrostics and so on – that make up the vast majority of cryptic clues and the results are humblingly similar to the way that we flesh-and-blood solvers go about solving.

The only area where we have the edge is when the clues are their most playful. A robo-solver developed at Duke University was invited to compete in the American Crossword Puzzle Tournament. It did well, except on one in which all the clues had been garbled as if by the Reverend Spooner: “Spate of studs”, say, instead of “State of spuds” – for the answer Idaho.

So while it might seem creepy that the machines are even threatening to do our hobbies better than us, perhaps the spirit of Crosaire, with his relentlessly incorrigible illogic, is our final bulwark against complete digitalisation?The most powerful effect of technology on the crossword, though, is the threat posed by digital media to the puzzle’s very existence.

For a century, people have been buying a crossword every day without necessarily intending to: a newspaper has been a trivial purchase, and the puzzle has been waiting there to convert newcomers any day that they can’t bear the realities of the news pages.

In its second century, the puzzle may need to make some adjustments as its home moves from dead-tree to touchscreen and it becomes merely one among millions of diversions, rather than the only fun in the newspaper.

I just hope that someone is working on a way of making tapping and swiping as physically satisfying as pencilling the correct answer into a newsprint grid.

Alan Connor is the author of Two Girls, One On Each Knee: the Puzzling Past of the Cryptic Crossword on its 100th Birthday