Is this something with potential to change mathematics as taught in schoolbooks, or just some sort of galactic algorithm[1] or research niche that will never spread beyond the expertise domain of half a dozen research groups across the whole world?
This will not be taught in textbooks. Wildberger works in a math world where "infinity" or even "really really big numbers" don't exist. There is nothing mathematically wrong about that world, but others (like me) do not find this problem context to be a useful framework to work in.
Interesting. So sort of a polar opposite to hyperreal numbers[1]. Instead of postulating de existence of numbers to the infinite and beyond, postulating there is no infinite.
> There is nothing mathematically wrong about that world
Thank you for acknowledging this. Every time Norm's work comes up on HN there is a subcurrent of comments about how his philosophy of math is wrong or dumb whose are arguments can be summed up as "Lol no infinity wtf".
Do I personally agree with his philosophy? No. But I still watched all his videos because they are entertaining, thoughtful, and his is rigorous in his definitions and examples.
Note that their solution is a formal power series solution, which will be divergent for some polynomial equations. Divergence is unavoidable because of the multiplicity of solutions.
[1] https://en.wikipedia.org/wiki/Galactic_algorithm