The man who invented Sudoku

When Leonhard Euler came up with a numbers puzzle, he could not have known it would one day obsess the British public. But is he remembered in his homeland? Cahal Milmo reports from Basle

Saturday 14 May 2005 00:00 BST

Andreas Conrad scratched his head as he stared once more at the grid dotted with random figures and then let out a long sigh of exasperation. He said: "It is some kind of fiendish torture. I don't know how anyone could enjoy such a thing. It looks like something they would invent in the Far East. You know - by a wise man sat in a temple on a mountain trying to keep himself amused." For seven very long minutes yesterday, Mr Conrad, a 28-year-old harpsichordist, joined the frowning multitudes caught in the grip of Sudoku.

Andreas Conrad scratched his head as he stared once more at the grid dotted with random figures and then let out a long sigh of exasperation. He said: "It is some kind of fiendish torture. I don't know how anyone could enjoy such a thing. It looks like something they would invent in the Far East. You know - by a wise man sat in a temple on a mountain trying to keep himself amused." For seven very long minutes yesterday, Mr Conrad, a 28-year-old harpsichordist, joined the frowning multitudes caught in the grip of Sudoku.

Stood on the corner of a handsome street of 18th century townhouses in this city which prides itself as the home of a string of intellectual heavyweights from Erasmus to Nietzsche, he wrestled with the mind-numbing number puzzle that every day is sending thousands of Britons into an addictive world of logic and worried scribbling.

But in the fraught universe of Sudoku, this was no ordinary thoroughfare. It was Eulerstrasse, the hitherto unrecognised spiritual home of Sudoku sufferers the world over. The street is named after Leonhard Euler, a prolific mathematical genius and native of Basle who died in 1783 - the same year that he invented his "carrés magiques" or magic squares, a diabolical 81-square grid that can be filled with almost infinite variety so that every row and every column contains the digits one to nine.

To any Sudoku player, it is a formula that will sound worryingly familiar. Yes, far from being the brainchild of an Oriental hermit, the game was invented 222 years ago by a Swiss mathematician who fathered 13 children and still found time to transform understanding of subjects from shipbuilding to lunar cycles with his formulae.

To that tally of achievements can now be added the fact of causing British commuters to miss their stops and housewives to spurn daytime television as they seek their daily fix from newspapers offering a range of Sudokus from "hand-generated" versions to The Independent's super-sized mind-scrambler, with its 256 spaces.

In the name of cross-cultural understanding (not to mention revenge), The Independent repatriated Sudoku yesterday to the people of Basle on Eulerstrasse, less than 300 metres from the Gothic church where the infant Leonhard was baptised, by leaving a series of passers-by to work with the puzzle for a few minutes.

Mr Conrad, who struggled manfully to fill a row and two boxes of the intermediate-level game before admitting defeat after nine minutes, received with equanimity the news that he had been briefly bamboozled by a compatriot.

He said: "Really, it was invented by Euler? Well, I'm not too surprised actually. The Swiss love to get very deeply into something, to be obsessed with one particular task. But it is not really my idea of fun - it looks like you might spend many hours doing this and if you get one number wrong the whole thing collapses. You could go a bit mad."

They are sentiments with which those who have completed one of the puzzles - only to scream as they find two eights in the same row - will identify.

David Bebera, 29, a youth worker at Basle's 19th century synagogue, on Eulerstrasse, lasted 90 seconds on the elementary-level Sudoku before adding: "In Basle, people are very rational, so it makes sense that this game was invented here. But it does not strike me as a form of relaxation. Maybe they saw things differently in the 18th century. Perhaps such things were what kept people amused."

Certainly, "such things" as the interplay between mathematics and the physical world were what filled the mind of Leonhard Euler as he wandered the streets of Basle as a young man. He studied at the city's university, which was founded in 1459 and is the oldest in Switzerland. Born in 1707 the son of a Calvinist minister, the intention had always been that young Leonhard would follow in his father's footsteps. Up until the age of 14 he received no formal lessons in mathematics and arrived at university to study theology, Hebrew and Greek.

But, under the part-time tutelage of Johann Bernoulli, the first in a succession of mathematical prodigies produced by the university, Euler's natural talent was identified and his father was persuaded to let his son pursue the world of formulae rather than prayers.

The result was the unleashing of a mind almost feverish in its mathematical creativity. Bernoulli, himself a giant of Enlightenment thinking, declared his star pupil to be "princeps mathematicorum" - the Prince of Maths. By the time of his death at the age of 76, Euler had written more than 1,100 books and papers.

In a career which saw him occupy some of the most eminent academic seats in Europe, the mathematician, who for the last 12 years of his life was completely blind but still produced 300 texts, plunged himself into a bewildering range of subject areas.

While heading the newly founded Berlin Academy in 1744, a colleague described his activities: "He supervised the observatory and the botanical gardens; selected the personnel; oversaw various financial matters, and, in particular, managed the publication of various calendars and geographical maps." His professional life, which saw him leave Basle at the age of 19 to take up his first professorship in St Petersburg at the invitation of Catherine the Great, was underpinned by his role as a God-fearing family man.

He married Katharina Gsell, the daughter of a Swiss painter whom he met seven years after he arrived in Russia. Of their 13 children, only five survived beyond infancy, but Euler said he was never happier - or inspired - than when fulfilling his paternal role. He wrote: "I made some of my most important discoveries while holding a baby in my arms with other children playing around my feet."

At the core of the activities of this 18th century Renaissance man lay what Euler thought was the foundation of all thinking - maths. As one colleague put it: "Euler calculated without apparent effort - as men breathe." He was credited with revolutionising thinking on flow dynamics and the study of movement in liquids, as well as calculus. He also invented the notation used for key numbers such as Pi - the ratio of a circle's circumference to its radius.

A poll of the world's leading scientists conducted three years ago named one of Euler's formulae as the most "beautiful" ever as it combines the five most important numbers. For those who understand such things, the formula shows that when one is added to the transcendental number "e" (2.71828...) raised to the power of Pi (3.14159...) and then multiplied by the square-root of minus one, the result is zero, precisely.

According to another legend surrounding the professor, he used maths - or a pastiche of it - to prove the existence of God, in a public debate with the French philosopher Diderot ordered by Catherine the Great. Euler opened proceedings by stating: "Sir, (a + b^n)/n = x, hence God exists; reply". His learned adversary, whose mathematical knowledge was unfortunately slight, was unable to respond and lost the debate.

This desire for precision led Euler to the discovery of his magic squares which, apart from the addition of four lines dividing the grid into nine squares, perfectly mimic the Sudoku square. But he considered his carrés magiques to be a curiosity rather than a means to a publishing fortune. Little did he know.

The Japanese name of the puzzle, Su doku, roughly translating as "solitary number", originates from the Tokyo-based publisher which first spotted an American version of the game in 1984 and started producing its own Sudoku magazine. The brain teaser became a rapid hit and now five monthly Sudoku magazines in Japan have a combined circulation of 600,000.

Although it has also existed in Britain in specialist puzzle circles since the early 1980s, the game only reached the mainstream last November, when the Daily Mail started publishing a version and competitors began to follow suit. Versions for mobile phones are expected to be launched next month while the internet is crowded with websites offering tips on how to conquer the puzzle.

It is a legacy of which Leonhard Euler would no doubt be proud and maybe bemused, alongside modernday compatriots. Despite his background in Basle and the nearby village of Riehen, where he grew up, Switzerland's most famous mathematician never returned to his native country after leaving for St Petersburg at the age of 19. Now his native town is determined to claim him for its own and is organising a series of events to commemorate the 300th anniversary of his death in 2007.

Dr Fritz Nagel, a curator of maths history at the University of Basle, said: "He prided himself on the breadth and creativity of his thinking, so I think he would be happy to see lots of people in Britain working on one of his ideas day after day."

It is a privilege which seems unlikely to be extended to the people of Basle itself any time soon. Both of the city's daily newspapers, Basler Zeitung and Baslerslab, said they had no plans to start offering Sudoku to readers.

All of which was a relief to passers-by on Eulerstrasse. Sarah Haessig, 25, a pianist, spent six minutes staring at the elementary puzzle before handing back a blank sheet. She said dismissively: "I am sorry but it is possibly a wasted journey to come here to generate interest in this game. I don't know how it is in Britain, but there are other things to do on the bus."

As the Sudoku craze continues its upward spiral, however, Britain's growing tribe of magic-square junkies should bear in mind one last pearl of wisdom from its inventor. After losing the sight in his second eye as a result of a house fire in 1771, Euler insisted it would improve his powers of logic. He said: "Now I will have less distraction."

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