The algebraic notations we use today are new inventions that have enabled us to discover many things. However, one could argue that by implementing these symbols, we have lost sight of the true mathematics. Many students leave high school math thinking that math only exists in the symbolic form, and that anything that is not explicitly stated via the symbols is not math. The invention of these symbols has helped, but they has also become a sort of false idol.
The invention of i as a solution to a quadratic that has no real solutions is a perfect example of how symbolic algebra has allowed us to leave the constraints of our reality to understand math at a deeper level. Symbols allow us to see past our plane of existence to what logically does exist. Our senses no longer dictate our understanding of math.
But we have swung too far on this pendulum. Students now do not value their senses to perform maths. Math exists in front of our eyes yet we do not look for it. Most math in history was done geometrically with physical objects. And even the modern theories we have today are often best described using visuals. Even imaginary numbers themselves are easily conveyed as 2D numbers. Just because a proof involves our physical senses, does not make it any less worthy.
It is up to us as educators to bring the perception of math back in harmony between our senses and our symbols.
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