Top Mathematics discussions
NishMath - #Equations
|
@phys.org
//
A mathematician from UNSW Sydney has made a significant breakthrough in addressing a longstanding problem in algebra: solving higher polynomial equations. Honorary Professor Norman Wildberger has developed a novel method that utilizes intriguing number sequences to tackle equations where variables are raised to the power of five or higher, a challenge that has eluded mathematicians for centuries. The findings are outlined in a recent publication co-authored with computer scientist Dr. Dean Rubine, and could lead to advancements in various mathematical disciplines. This new approach has the potential to reshape mathematical problem-solving techniques.
Professor Wildberger's approach challenges traditional methods that rely on radicals, which often represent irrational numbers—decimals that extend infinitely without repeating. He argues that these irrational numbers introduce imprecision, and that a real answer to a polynomial equation can never be completely calculated because it would need an infinite amount of work. The mathematician suggests this solution "reopens a previously closed book in mathematics history." Prior to this discovery, French mathematician Évariste Galois demonstrated in 1832 that it's impossible to resolve higher polynomial equations with a general formula, such as the quadratic formula. Approximate solutions for higher-degree polynomials have been used, but are not pure algebra. Wildberger's radical rejection has lead to a new method for solving this decades old problem.
Share:
References :
Classification:
@ncatlab.org
//
Jarmo Hietarinta's work on the constant quantum Yang-Baxter equation is a significant contribution to mathematical physics. His research focuses on finding and analyzing solutions to this equation, particularly in two dimensions. Hietarinta has identified a complete set of solutions for the constant quantum Yang-Baxter equation in two dimensions, totaling 96 solutions that fall into 23 distinct classes.
His findings were presented at the 19th International Colloquium on Group-theoretical Methods in Physics, where he delivered a talk detailing the complete solution. His work is documented in publications such as "All solutions to the constant quantum Yang-Baxter equation in two dimensions," published in Physics Letters A. Hietarinta's research offers insights into the mathematical structures that underlie various physical phenomena.
Share:
References :
Classification: |
Blogs
|