Euler's reaction is rather sceptic:[br][i][i]. . .  Thus you see, most noble Sir, how this type of solution[br]bears little relationship to mathematics, and I do not understand why you[br]expect a mathematician to produce it, rather than anyone else, for the solution[br]is based on reason alone, and its discovery does not depend on any[br]mathematical principle.  Because of this, I do not know why even[br]questions which bear so little relationship to mathematics are solved more[br]quickly by mathematicians than by others.[/i][/i][br] 

[br]Although Euler thought it to be rather a trivial problem, it keeps intriguing him and he writes to Giovanni Marinoni, an Italian mathematician and engineer:[br][i]"[i]This question is so banal, but seemed to me worthy of attention in that [neither] geometry, nor algebra, [br]nor even the art of counting was sufficient to solve it.[/i]"[/i][br][br]Euler believes this problem was related to a topic that Leibniz had once discussed and longed to work with, something Leibniz referred to as [i]geometria situs[/i], or geometry of position. And how does a mathematician deal with such kind of problems? He makes a generalization of it and establishes a model, that will turn out to be the start of [i]graphing theory[/i] and of [i]topology[/i].

As mathematician Euler knows you'd better start by generalizing a problem. So you don't speak anymore about a town, islands and bridges using their proper names. Instead you say that the river devides the city in four parts A, B, C en D, connected by 7 links. If you cross a bridge, going from part A to B, you just note it as [b]AB[/b]. If you go from A to B and cross a second bridge to C and a third to D, you simply note it as [b]ABCD[/b]. Euler immediately sees that you need one letter more than the number of bridges to cross. In other words: to cross seven bridges you need 8 letters. Euler is the first one to examine a similar problem systematically. [br]More than 100 years later, James Joseph Sylvester introduces in 1878 a graphical representation of such systems. And so we end up with [b]graphs[/b]: a representation with points, connected by lines.

Now the problem of the bridges is turned into the question 'what are the properties of such graphs ?'