A Canadian university professor has solved an equation that gave mathematicians for almost 200 years.
Norman Wildberger/PHOTO: UNSW Sydney
Norman Widlberg, born in Canada, collaborated with computer scientist Dean Rubine on this project, which details how these equations could be resolved involving extremely complex calculations, writes Science Alert.
Widlberg is currently honorary professor at the University of New South Wales (UNSW).
Wildberger’s discovery could have significant implications. Higher polynomial equations play a fundamental role in both mathematics and science, helping with anything, from writing computer programs to description of the planet movement.
“Our solution reopens a previously closed book in the history of mathematics“Wildberger said, according to Newsweek.
Mathematicians discovered how to solve the lower -degree polynomial equations. For a long time, it was believed that the systematic resolution of the upper degree is impossible.
Before Wilberger’s study and rubies, mathematicians were based on approximations.
The two resorted to a new approach to the problem, which is based on the Catalan numbers. These are used, among others, to count the ways in which polygons can be divided into triangles.
By extending the idea of Catalan numbers, the researchers have managed to demonstrate that they can be used as a basis to solve polynomial equations of any degree. Establishing the resolution method involved in extending the counting of polygons to other forms, in addition to triangles.
This represents a deviation from the traditional method of using radical expressions (such as square roots and cubic roots) to solve such equations. Instead, the new method resorts to advanced combinatoria.
The researchers checked their new method with some well-known polynomial equations, including a famous cubic equation studied by John Wallis. The results validated the new approach.
Wildberger and ruby did not stop here. They have discovered a new mathematical structure called geoda, which binds to the Catalan numbers and seems to act as a foundation for them. Geoda could be the basis of many other future studies and discoveries, they estimate.
Because their approach is clearly different from the previous ones, there is the potential to rethink many key ideas that mathematicians have based a long time for computer algorithms, data structuring and game theory.
The discovery could have applications including in biology, for example, to count the folding of the RNA molecular chains.
