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True beauty of mathematics

Author: Youngjin Kang

Date: 2022.10

Those who have studied mathematics from a perspective of contemplative immersion would agree with the statement: "Math is beautiful". When the exact origin of such an abstract sense of delight is concerned, however, there seems be a profound sense of dissonance.

On the one hand, a person may claim that mathematics is a fascinating subject because everything in it is deeply related to another. One could preach the charm of mathematical wonders by going on like this:

"There is a theorem here which is derived from the other theorem there, from which we can derive a special equation which reveals a pattern we are all familiar with when we plug in this special constant! And we can also use this same equation for solving any homogeneous differential equation of type 'A', where type 'A' refers to one of the special classes of equations defined in that other lemma I mentioned before. In that lemma, we can plug in the other formula from the previous theorem, and by doing so we will reveal yet another special variable, which is the same as the one we saw in the first theorem! And..."

Such a series of passionate exclamations, originating from a conviction that mathematical concepts are "beautiful" because there are so many ways in which one can somehow connect them with each another, are nothing but the tip of the iceberg. A jungle of technical rules, within which one may find a bucketful of resemblances, congruences, and other apparent patterns of synchronicity, do not represent math itself. Rather, they merely embody layers upon layers of abstract byproducts radiating from a stream of consciousness.

The true beauty of mathematics lies in its intrinsic implications inside the domain of metaphysics. Math is fundamentally philosophical in nature, meaning that it is an area of study which seeks to contemplate upon the essence of thoughts themselves in their purest form, rather than to build layers of meaningless abstraction on top of them.