Mathematician solves algebra's oldest problem using intriguing new number sequences
A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations.
by University of New South Wales
https://phys.org/news/2025-05-mathematician-algebra-oldest-problem-intriguing.html
More information:
https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2460966#abstract
»This is why, Prof. Wildberger says he "doesn't believe in irrational numbers."«
OK, this actually pretty bold.
Whilst possibly being a fruitful approach, as far as I see it, he hasn't come up yet with a method for effectively solving polynomials with a degree higher than five.
Or am I wrong?
@mina the article leaves out a key element of Galois theory: it doesn't state that "there are no solutions", just that the solutions can't be expressed using roots alone.
And "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." .
is weird because of course you can express a radical using a power series 
@mina @gutenberg_org
Well, irrational numbers don't constitute a belief system but are simply a definition¹ for a specific kind of a two-dimensional space. If you follow the definition you will get formal results. You can decide not to use this, but this has nothing more to do with belief than Kronecker's: “Natural numbers were created by God, everything else is the work of men.”
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¹or some axioms depending on how you approach it