Mathematician Heikkilä illustrates problems in his field with the help of knitwear

Lay Fortunately the mathematician Susanna Heikkilä Hobbies knitting.

With the help of a knit, he can try to shed light on us how he solved a tough mathematical problem. Mathematicians in a particular industry have been plagued by more than 40 years.

He describes a difficult thing with a regular knit. It was completed last summer at a dissertation, where Heikkilä also wanted to tell his difficulty in general.

Mathematician Heikkilä studies topology in mathematics. For the layman, it is described as a single geometric area that explores surfaces and their properties.

For example, according to Wikipedia, topology is “math branch that applies to the characteristics of space”.

One example is Donits’ topology. Topologically it can be formed by taking a square. Its top and bottom edge are glued together, and also the right and left edge of the square.

Topological spaces They are the simplest mathematical structures that can define concepts such as openness continuity and unity.

Heikkilän Knit Knit depicts a transition from a flat surface to the ball surface, says the University of Helsinki Bulletin.

This transition is known in topology as Alexander.

Heikkilä has weaved patches of different colors in the sample. He compiled a scab -like grid with nine screens. There are different colored squares at the corners.

In addition, Heikkilä needs a ball for his presentation, whose halves are knit with different colors.

Heikkilä puts his grid around the ball so that the colored corners attach to each other. There is an opening between the edges of the screen.

Knitwear can now be stretched so that the openings are closed. In this stretch, the subject of Heikkilä’s summer dissertation condenses: quas idea.

Heikkilä resolved his director professor Pekka’s bank with the mathematical problem associated with it. So it bothered mathematicians for at least two generations.

The mathematician asks the problem of what kind of square -dimensional shapes can be presented by the geometry of square euclideic space.

We live in a three -dimensional world. Thus, square thinking requires a little effort.

For a mathematician, three more dimensions are not a major problem. They can be calculated and solved with mathematics.

Russian-French award-winning mathematician Misha Gromov asked in 1981 whether there was an obstacle to the existence of a kvas -regulating description that is not related to the gaps measured by the base group.

He specified: If the paint side of the description is one uniform, is the existence of the description guaranteed?

The answer to the question was open until 2019. Then a mathematician Eden prywes offered a four -dimensional counter -example.

“My dissertation will complement Gromov’s question,” Heikkilä says.

Main result One can classify four -dimensional single songs that have a quasi -ruled description of Euchlide space, says Heikkilä.

Now the layman can ask the familiar question: How does this discovery affect the life and everyday life of an ordinary person? So are there any applications?

Heikkilä’s answer is slightly distant.

“At least at the moment, I can’t tell the way the finding would touch the layman and everyday things.”

“The finding is covered by pure mathematics. Its applications are internal in mathematics. ”

So. But science and basic mutation often offer surprises later.

Perhaps the best examples of this are these days search engines and artificial intelligence. Their base is in pure mathematics and statistics.

So, something can sometimes be overwhelmed by a casual door that requires Heikkilä’s solution and topology.

So let’s wait, maybe another 40 years.

In the meantime, Heikkilä’s research continues.

“The research seems meaningful when there is a supportive instructor and colleagues. The spouse was found in the same field, even though there is no math at home in the evenings, ”he says.

At the beginning of 2025, Heikkilä started as a postdoctoral researcher at the University of Jyväskylä.