How does new math get invented/discovered?
In: Mathematics
People come across a problem they can’t solve. They then explain that problem to others. Somebody discovers a solution for it. From that solution they create a step by step guide. Now the real test of whether or not that is a correct solution or just something that happened to work is whether or not the same result under the same rules are achieved regardless of the number applied.
So a² x b² = c² would have come about in a similar fashion to someone noticing that there always seemed to be a size relation between the longest end of a triangle and the other two shorter ends. Then Pythagorean comes around and declares that his formula explains this ratio for non-right triangles. In the entire time since his claim, not one person has ever been able to produce a non-right triangle that doesn’t follow that this formula.
Nothing changed. We’ve just evolved from trying to explain triangles to trying to understand the nature of black matter. Same thing though. It’s all just seeking a solution to explain a problem.
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