Polynomials to the fifth degree? No problem! Mathematician presents simple solution

A mathematician has found a way to solve an algebra problem that has been around for over two centuries. Solving polynomial equations that go beyond x to the power of four has remained impossible. But Mathematician Norman Wildberger, an Honorary Professor at Australia's University of New South Wales, and computer scientist Dean Rubine have figured out an innovative method to do it.

Polynomials are equations with a variable raised to powers. They have wide applications in Maths and Science and are used in computer programs and even space studies. However, "higher order" polynomial equations, where x is raised to the power of five or higher, have remained tricky.

Wildberger and Rubine provide a new approach to solving these problems using novel number sequences in The American Mathematical Monthly journal. 

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“Our solution reopens a previously closed book in mathematics history,” Wildberger said.

He suggests getting rid of irrational numbers and radicals. The radicals generally represent irrational numbers, which are decimals that extend to infinity. They never repeat and cannot be written as simple fractions. 

Prof. Wildberger says it is impossible to reach the real answer because "you would need an infinite amount of work and a hard drive larger than the universe."

Prof. Wildberger says he "doesn't believe in irrational numbers". He states that an infinite number of possibilities is the fundamental issue. So he has thrown out the entire concept.

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He used adding, multiplying, and squaring to solve the problem, using specific polynomial variants called "power series," which possess infinite terms within the powers of x. The method yielded results, and they tested it out on a 17th-century equation.

"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.

Babylonians were the first to conceive two-degree polynomials around 1800 BCE. It was only in the 16th century that the concept evolved to incorporate three- and four-degree variables using root numbers, also known as radicals. But solving the bigger examples remained impossible.

In 1832, French mathematician Évariste Galois showed why this could never be done. He demonstrated that the mathematical symmetry that was used to solve lower-order polynomials could not be applied while solving degree five and higher polynomials.