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Mathematician solves algebra's oldest problem using intriguing new number sequences [View all]
Is anyone familiar with Prof Norman Wildberger? He is a UNSW Honorary Professor. He used to produce math videos for the internet, for example, his History of Mathematics. Wildberger was well-known for his opposition to the use of infinity in mathematics. This paper is written by him and Dr Dean Rubine.
The problem is the solution of higher order polynomials.
An excerpt from phys.org
...
Prof. Wildberger's rejection of radicals inspired his best-known contributions to mathematics, rational trigonometry and universal hyperbolic geometry. Both approaches rely on mathematical functions like squaring, adding, or multiplying, rather than irrational numbers, radicals, or functions like sine and cosine.
His new method to solve polynomials also avoids radicals and irrational numbers, relying instead on special extensions of polynomials called "power series," which can have an infinite number of terms with the powers of x.
By truncating the power series, Prof. Wildberger says they were able to extract approximate numerical answers to check that the method worked.
"One of the equations we tested was a famous cubic equation used by Wallis in the 17th century to demonstrate Newton's method. Our solution worked beautifully," he said.
more ...
The full paper is open source and available here
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