Unsolved Mathematics Problem Since 1990 Has Been Solved!

Two Danish computer scientists have solved the unsolvable math problem since 1990. The subject of this abstract problem is about graph theory. The point that cannot be solved is the inability to find an algorithm to solve the flatness of a dynamic graph. This may sound a bit scary. If you have insufficient knowledge of graph theories, we can think in a more fun way. When we went back to 1913, there were 3 utility problems for math riddles. Let’s put it simply. Draw 3 houses on a piece of paper, and there are 3 public utilities, electricity, water and natural gas under these houses. Now we have to connect these public services to every home, but the challenge here is; none of the lines should cross each other.

Can we do that? Unfortunately, it is not possible, all of these houses cannot get the connections before they meet, at least on a 2D paper. But this is not a problem to be solved anyway. Just an example of how graphical networks are not planar. Graphs also have corners and intersections just like these houses.

When dealing with more complex graphs with more vertices, mathematicians would use Kuratowski’s theorem to determine if graphs were planar, and they had been trying to develop algorithms to do the same faster since the 1970s. After all, some progress was made in this regard in the 1990s. It was one of the most important developments in recent years, at least for solving dynamic graphics. When we looked last year, computer scientists Jacop Holm from the University of Copenhagen and Eva Rotenberg from Denmark Technical University were working on this issue.

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“We almost stopped doing the finishing and solving this riddle because we thought at best there should be another 5 years of work,” says Holm.

At that point they realized, almost by accident, that they had solved most of the problem in another study. The aforementioned research is a research on planar concepts for which its preliminary study was published online in 2019. The two researchers then blended their research with the secret solution that had already been published and officially announced that they had made improvements to the graphics algorithm, which had not made any progress since the 1990s.

“We worked on the article for 5-6 weeks without stopping, we created an 80-page article,” says Rotenberg.

The algorithm offers us the following in its final form; Can the vertices in a dynamic graph and the lines connecting them but intersect be deleted, can these lines be added or can this graph be placed planar .. In a simpler statement; Are houses and utilities drawn on paper? If it is drawn, will the lines cross? And it does this in the least computing time.

This is a big progress, because in the example we gave here, there were only 3 lines. However, the situation is getting more complicated in areas that have much more corners than 3 houses and 3 utilities, such as microchip design or road planning.

“We came to the following conclusion for dynamic graph problems. It turns out that after every change you make to the graph, some data structures are possible that can be used to compute much faster than calculating from scratch ”.