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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 sp

by Qem 1y ago

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? [1] https://en.wikipedia.org/wiki/Galactic_algorithm https://en.wikipedia.org/wiki/Galactic_algorithm

mixedmath 1y ago
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.
- michelpp 1y ago
  > 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.
  - ogogmad 1y ago
    His channel is sometimes the best way of learning certain topics in classical geometry.
    - michelpp 1y ago
      Agreed, his videos on Tropical Algebra are also very good!
- Qem 1y ago
  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. [1] https://en.m.wikipedia.org/wiki/Hyperreal_number https://en.m.wikipedia.org/wiki/Hyperreal_number
ogogmad 1y ago
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. Journal article here: https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2460966#d1e754 https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2...

by Qem 1y ago

mixedmath 1y ago

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.

michelpp 1y ago
> 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.
- ogogmad 1y ago
  His channel is sometimes the best way of learning certain topics in classical geometry.
  - michelpp 1y ago
    Agreed, his videos on Tropical Algebra are also very good!
Qem 1y ago
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. [1] https://en.m.wikipedia.org/wiki/Hyperreal_number https://en.m.wikipedia.org/wiki/Hyperreal_number

ogogmad 1y ago

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. Journal article here: https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2460966#d1e754 https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2...