TECH

The puzzle solved 300 years ago by the mathematician Leonard Euler and that today allows us to surf the internet

The annual mathematical challenge presented by the Academy of Sciences in Paris in 1727 was this: "What is the best way to organize masts in a boat?"At first glance, it's a very practical problem, but the young Swiss mathematician Leonhard Euler approached it as a purely mathematical puzzle.Although he had never set foot on a boat, he felt perfectly qualified to calculate the best layout of the masts.
"It did not seem necessary to confirm this theory with practical experiments because it derives from the most secure principles of mathematics. There is no doubt about its validity and practical functioning," he said.Leonhard Euler had absolute faith in mathematics. He lent his name to various formulas and principles and, 50 years after his death, his work is still published.Euler has reformulated almost every area of ​​mathematics. As a hobby, he solved the problem of the seven bridges of Königsberg, a popular 18th-century conundrum."For Euler, solving the problem was a form of entertainment. It was kind of cool for him," technology expert Bill Thompson told the BBC."Of course he had no idea how much we would take advantage of his work, how we would build on his ideas, or even use them to create a search platform that would change the world completely."

'Calculating was like breathing'
From childhood. Leonhard Euler did calculations without any apparent effort. He did it as men breathe, or as eagles hang in the air, said the French mathematician Francois Arago.I tested theorems for fun, just as you and I could do the Sudoku. But Euler's father, who was a priest, wanted his son to follow in his footsteps."I had to enroll in theology faculty and strive to learn the Greek and Hebrew languages, but I did not make much progress because I spent most of my time studying mathematics. To my delight, Johann Bernoulli's visits on Saturdays continued, "wrote the mathematician.Johann Bernoulli was a leading mathematician from Basle, Euler's hometown. Bernoulli's family "produced" eight successful mathematicians in just four generations.Johann was tutor to Euler and convinced his father to allow him to study mathematics instead of theology.And it was the son of Johann, Daniel, a good friend of Euler, who obtained for him the first job in the Academy of Saint Petersburg, where he worked.Euler assumed a role in the medical field, which was not ideal. Dedicated, before going to Russia, the mathematician read everything he could about medicine. He succeeded in converting ear physiology into a mathematical problem.On the day Euler arrived in St. Petersburg, Tsarina Catherine 1st of Russia, great patron of the Academy of St. Petersburg, died.In the midst of the confusion, Euler discreetly transferred from the medical department to the math department.

While working in St. Petersburg, the Swiss mathematician became aware of the enigma of the seven bridges of Königsberg.
The Prussian city of Königsberg was divided into four different regions bathed by the river Pregel. Seven bridges connected these four areas, and in Euler's time a common hobby among residents was to try to find a way to cross all the bridges only once and get back to their starting point.
Euler wrote a letter to the Vienna court astronomer in 1736, describing what he thought about the problem:

"This question is so trivial, but it seemed to me worthy of attention because neither geometry nor algebra nor even the art of making accounts was enough to answer it." It occurred to me to ask whether the answer would be in position geometry So after a bit of deliberation, I got a simple rule, with the help of which I was able to decide immediately whether this round trip is possible. "
Instead of walking endlessly through the city, testing different routes, Euler created a new "position geometry", by which measures such as longitude and angle are irrelevant. What matters is to see how things are connected.
Euler decided to think of the different land regions separated by the river as points, and the bridges that connect them, like lines connecting points.

You have discovered the following: For a round trip (without returning to the same path) to be possible, each point - with the exception of the starting point and end point - must have an even number of lines going in and out.
The advantage of Euler's rule is that it works for any situation.
When he analyzed the map of the seven bridges of Königsberg in this way, the mathematician discovered that every point - or piece of land - had an odd number of lines or bridges emerging from them.
So, without having to walk through the city, Euler mathematically discovered that it was not impossible to walk all over town crossing each bridge only once.

From the 18th to the 21st century
Euler's rule is easy to apply. And it does not take a mathematician to realize that it is useful in different situations.
The mathematical solution to the Königsberg riddle now drives one of the most important networks of the 21st century: the internet, which connects millions of computers worldwide and moves digital data between them at incredible speed.
"If I have my computer at home and want to get into a site, I need to make a connection between my computer and the web site, which can be anywhere," says Bill Thomson.

"I can make this connection because my computer is programmed by the rules based on the work that Euler developed in the 18th century, when solving the enigma of the Königsberg bridges," explains the technology expert.
The Königsberg enigma was far from an urgent problem at the time - it was more of a curiosity - but its solution lasted and revolutionized the information age of the 21st century.
What for Euler was just a hobby played a decisive role in the world we live in today.

bbc.com