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Tom Bridges@blogs.surrey.ac.uk
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Recent mathematical explorations have focused on a variety of intriguing number patterns and historical mathematical context. One notable discovery comes from UNSW Sydney mathematician Norman Wildberger, who has revealed a new algebraic solution to higher polynomial equations, a problem considered unsolvable since the 19th century. Polynomials are equations with variables raised to powers, and while solutions for lower-degree polynomials are well-known, a general method for those of degree five or higher has remained elusive. Wildberger's method, detailed in a publication with computer scientist Dr. Dean Rubine in The American Mathematical Monthly, uses novel number sequences to "reopen a previously closed book in mathematics history."
Wildberger's approach challenges the traditional use of radicals, which often involve irrational numbers. Irrational numbers, with their infinite, non-repeating decimal expansions, are seen by Wildberger as problematic. He argues that assuming their existence in formulas implies treating infinite decimals as complete objects, an assumption he rejects. His solution involves discarding irrational numbers, a move that may redefine how certain algebraic problems are approached. Critics may find the claims overstated, as one commentary notes the article never specifies what "algebra's oldest problem" actually is, but indicates that solving it requires discarding irrational numbers.
In addition to advancements in solving polynomial equations, mathematicians continue to explore other number sequences, such as Recamán’s sequence, a favorite of N. J. A. Sloane, founder of the Online Encyclopedia of Integer Sequences. The sequence starts at 0, and each subsequent number is derived by moving forward or backward a specific number of steps from the previous number, based on certain conditions. Recamán’s sequence can be visualized using circular arcs and even represented as music, associating each number with a note on the chromatic scale, showcasing the diverse ways in which mathematical concepts can be explored and interpreted.
References :
Wildberger's approach challenges the traditional use of radicals, which often involve irrational numbers. Irrational numbers, with their infinite, non-repeating decimal expansions, are seen by Wildberger as problematic. He argues that assuming their existence in formulas implies treating infinite decimals as complete objects, an assumption he rejects. His solution involves discarding irrational numbers, a move that may redefine how certain algebraic problems are approached. Critics may find the claims overstated, as one commentary notes the article never specifies what "algebra's oldest problem" actually is, but indicates that solving it requires discarding irrational numbers.
In addition to advancements in solving polynomial equations, mathematicians continue to explore other number sequences, such as Recamán’s sequence, a favorite of N. J. A. Sloane, founder of the Online Encyclopedia of Integer Sequences. The sequence starts at 0, and each subsequent number is derived by moving forward or backward a specific number of steps from the previous number, based on certain conditions. Recamán’s sequence can be visualized using circular arcs and even represented as music, associating each number with a note on the chromatic scale, showcasing the diverse ways in which mathematical concepts can be explored and interpreted.
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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
Classification:
- HashTags: #Mathematics #NumberTheory #History
- Company: Ballew
- Target: Knowledge
- Product: Numbers
- Feature: Exploration
- Type: Research
- Severity: High