When was topology invented

This page also credits Euler with creating the concept of topology, using it to solve the Seven Bridges problem. One of these areas is the topology of networks, first developed by Leonhard Euler in His work in this field was inspired by the following problem: The Seven Bridges of Konigsberg. Here we find an interesting PDF on the development of algebraic topology. Some topological problems were considered long ago, for example by Euler see the previous answer.

Some ideas about topology were even earlier proposed by Leibniz. The famous kindergarten problem about three houses and three wells belongs to this class. Originally it was known as Analysis Situs, the term which existed until the beginning of 20th century. The term "Analysis Situs" was introduced by Leibniz! The word topology was used by the Germans and since the beginning of the 20th century it is accepted. Poincare, Analysis situs, J. Ecole Polyutechnique , 1, All this concerns what is called today "Algebraic topology".

A different part of mathematics, called "General topology", has a different origin: in real analysis Cantor. The formula is nowadays called Euler's formula yet again, Euler! I say "to attempt" because his proof was "almost" correct. But exactly in this almost layed the interesting part.

In the nineteenth century various mathematicians proposed example of "polyhedra" that were not satisfying the formula: a cube with inside a cubic cavity, a smaller cube sitting on the side of a larger cube which satisfies or not the formula dependind on how you count faces and so on. I wrote "polyhedra" because the usual objection to such examples was to refine the notion of polyhedra as to exclude them.

When it turned out the the definition of polyhedra became so complicated to counter intuition, it solwly became clear that such anomalies could in fact bring in new informations A discover which sits at the core of further developments of homotopy thoery and later on homology theory.

Combinatorial topology considers the global properties of spaces, built up from a network of vertices, edges, and faces. This is the oldest branch of topology, and dates back to Euler.

It has been shown that topologically equivalent spaces have the same numerical invariant, which we now call the Euler characteristic. Algebraic Topology. Algebraic topology also considers the global properties of spaces, and uses algebraic objects such as groups and rings to answer topological questions.

Algebraic topology converts a topological problem into an algebraic problem that is hopefully easier to solve. For example, a group called a homology group can be associated to each space, and the torus and the Klein bottle can be distinguished from each other because they have different homology groups.

Torus Klein Bottle Algebraic topology sometimes uses the combinatorial structure of a space to calculate the various groups associated to that space. Differential Topology. Differential topology considers spaces with some kind of smoothness associated to each point.

In this case, the square and the circle would not be smoothly or differentiably equivalent to each other. Differential topology is useful for studying properties of vector fields, such as a magnetic or electric fields. University of Waterloo. Log in. Perhaps the first work which deserves to be considered as the beginnings of topology is due to Euler.

The title itself indicates that Euler was aware that he was dealing with a different type of geometry where distance was not relevant. The next step in freeing mathematics from being a subject about measurement was also due to Euler. References show.