So, I've been over fixated on negative numbers lately. I'm coming to the conclusion that, mathematics is usually progressed if it is "useful". The more "useful" a mathematical object is generally the more it appears in study and practice. Arguably the most useful mathematical object a natural number, has the most wide array of applications in the world.

Another example of this, is for example, there might be some kind of scenario where 2+2 = 10, and constructing a mathematical system with that as a theorm, but it would be a pretty specific / useless one and not studied very much / broadly.

The thing that I think was hard about accepting negative numbers, is firstly the conceptual problem when trying to understand a subtraction from 0 with a lack of context, and also a lack of geometric understanding (with respect to lengths and so forth).

I've observed throughout history, the most natural analogy mathematicians use for negative numbers is debt. In the this setting, it's natural that if your relieved of a debt you gain credit. This is probably the most common justification for the rule of signs I've observed, even from Euler himself.

So TLDR i'm looking for Euler's writings about negative numbers, and maybe any kind of paper that examines the relationship with usefulness and mathematical study.



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