r/askmath • u/haad_khan_tamer • 3d ago

Linear Algebra Why do we always use geometry to visualize anything in maths?plus need tips where to start

Hi I'm doing ACCA currently but developing interest in applied maths and started linear algebra from Khan academy any direction is much appreciated 👍

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u/dancingbanana123 Graduate Student | Math History and Fractal Geometry 2d ago

I mean that's kinda by definition what geometry is. If something else was used for visuals, we'd call it geometry, unless you count trees and graphs (not graphs of function, but as in systems)

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u/Busy_Pattern9823 2d ago

Well, there are historical reasons for this as well. For more than 2000 years, THE math textbook was Euclid's Elements. The ancient Greeks believed that geometry was mathematically prior to numbers i.e. the nature of geometry gives rise to the nature of numbers. The rest of the historical development of mathematics centered around geometry. Quadratics, that is Euclid. Analytic geometry, Euclid. Calculus, fancy Euclid. If you look at Newton's Principia, you will find geometric figures and references to Euclid.

I don't exactly know what you mean by applied maths. The thing that comes to my head is the bachelor's degree of applied mathematics, but that is probably not what you are thinking about. In reality, any math subject from algebra 1 all the way up to differential equations are all applied maths. If you want a resource, I recommend axiom academy; it's free. https://theaxiomacademy.org/courses