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Yes, 'imaginary' numbers are invented syntax. I think imaginary numbers are just an additional tool tacked on to our existing tools in order to explore new are

Yes, 'imaginary' numbers are invented syntax. I think imaginary numbers are just an additional tool tacked on to our existing tools in order to explore new areas. They are a patch written to cover some cases our previous tools failed to cover. > The idea that mathematics is "the language of the universe" that can be precisely "discovered" by brilliant minds is a ridiculous notion that only serves the status of the mathematical elite. Mathematics is fundamentally about designing models and abstractions that help us reason about real phenomena with minimal cognitive resources. Yes, creating abstractions and designing models are aspects of math, but I believe the modern definition of mathematics has expanded to include the study of abstract objects. Abstractions can describe concepts (concepts that exist in many different places) but are not the same as the concepts. I believe these concepts are discoverable and independent of any notations/models/abstractions we create. So in that sense, I believe mathematics can be discovered. e.g. exponential growth/decay (the spread of COVID in an unvaccinated population, bacterial growth, etc.) - invented or discovered? (https://en.wikipedia.org/wiki/Exponential_growth#Examples https://en.wikipedia.org/wiki/Exponential_growth#Examples) fractals (pattern of rivers, trees, blood vessels, etc.) - invented or discovered? I can describe the details of these with tools like 'geometric progression', and 'the Mandelbrot set'. Those are tools aiding my understanding of these concepts, but the concepts themselves certainly seem like they were discovered.

ncmncm 5y ago
All of mathematics is invented syntax. For every bit of mathematics that is taught, there are a thousand bits somebody explored and, maybe, published, but it wasn't considered beautiful enough to teach. So, the maths that are taught are the bits enough mathematicians liked. Some that are taught were considered ugly by older mathematicians, but were embraced by their students. The really ugly stuff has either fallen away or just not been adopted into canon yet. Physicists have pushed mathematics in directions mathematicians hated to go, but those directions have borne surprising fruit, so mathematicians are beginning to accept them. Mathematics is a tapestry being woven by living mathematicians guided by what they like.

ncmncm 5y ago

All of mathematics is invented syntax. For every bit of mathematics that is taught, there are a thousand bits somebody explored and, maybe, published, but it wasn't considered beautiful enough to teach. So, the maths that are taught are the bits enough mathematicians liked. Some that are taught were considered ugly by older mathematicians, but were embraced by their students. The really ugly stuff has either fallen away or just not been adopted into canon yet. Physicists have pushed mathematics in directions mathematicians hated to go, but those directions have borne surprising fruit, so mathematicians are beginning to accept them. Mathematics is a tapestry being woven by living mathematicians guided by what they like.