The birth of topology │ The History of Mathematics with Luc de Brabandère
Why was Swiss mathematician Leonhard Euler so obsessed with the bridges in his hometown of Königsberg?
How did it lead him to discover the discipline of topology?
Join Luc de Brabandère, in the latest episode of his remarkable series The History of Maths, to discover more about this incredible man and his erratic city walks.
Find out more:
Leonhard Euler thought about crossing all of his home city's seven bridges in one single walk. His failed attempts led to the birth of topology.
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When you ask a mathematician: ‘Which are the five most important constants in his field?’ he will probably answer ‘Pi’, as we have seen in video number 10; ‘e’, as we have seen in video number 8. The definition is the limit of (1+1)/n^n ; ‘i’, and ‘i’ is defined as i^2 = -1. And also ‘0 ‘and ‘1’. Those are definitely the five most important constants in mathematics.
You know what? One day, somebody connected all those five constants in one single formula. The formula is known as Euler's formula. Indeed, Swiss mathematician Euler connected the five numbers into one single formula. Probably the most remarkable formula in mathematics. Euler again was a genius; he opened many new fields.
One of them is particularly interesting now in the 21st century. It's topology and networks. How did it happen? Euler by coincidence was living in a city called Königsberg. The city has a river crossing the city, and the river surrounds two islands. The islands were connected to the city through seven bridges.
So, Euler, as a great mathematician, one day came up with a new question. You know, mathematics is sometimes about new answers, but also sometimes about new questions. He said: ‘OK I'm gonna walk the 7 bridges in 1 single walk, crossing each bridge only once.’
Then he tried, and tried again, and he realised this was impossible. ‘I cannot do my walk only with 1 cross of each bridge.’ Then he started thinking, and he opened a new field which is called topology.
The first thing he did was to map the city into a graph. You can see on the drawing how the city suddenly became the graph. Then he came up with a conclusion: this kind of walk is possible if only two knots are connected to an odd number of connections. This is probably the birth of this discipline, topology.
Today it's more famous. You can see it everywhere.
George Boole invented the world of zeros and ones, a century before the first computer.
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