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NishMath
@phys.org
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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.
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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.
ImgSrc: scx2.b-cdn.net
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References :
- phys.org: Mathematician solves algebra's oldest problem using intriguing new number sequences
- www.sciencedaily.com: Mathematician solves algebra's oldest problem using intriguing new number sequences
- John Carlos Baez: Blog post on 2025/05/04 that contains a headline: Mathematician solves algebra’s oldest problem using intriguing new number sequences.
- www.eurekalert.org: Headline: "Mathematician solves algebra’s oldest problem using intriguing new number sequences." 😮 In the article: "So, when we assume ∛7 'exists' in a formula, we’re assuming that this infinite, never-ending decimal is somehow a complete object. This is why, Prof. Wildberger says, he “doesn’t believe in irrational numbers."
- www.techexplorist.com: Mathematician solves algebra’s oldest problem
- Tech Explorist: New approach using novel number sequence.
Classification:
- HashTags: #Mathematics #Algebra #PolynomialEquations
- Company: UNSW
- Target: Solution
- Product: Equations
- Feature: Algebra
- Type: Research
- Severity: Informative