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Why do mathematics?

Of course, mathematics can be a means to an end. Perhaps you like physics or chemistry, and you wish to expand your knowledge in those fields. The further you go, the more math you need to help explain the subject matter at hand, and the more math you need, the more time you need to spend doing boring and tedious exercises or reading tutorials off of google.

Doing mathematics for fun though? For the sake of doing it? "Psh! That's for the recluse---for the eccentric!" you cry! "I don't have the patience or the time for that!"

However, I would be inclined to point out that a response like that is not truly concerning doing mathematics, but doing what you were taught was "mathematics". Indeed, the mathematics curriculum is completely bonkers and there is no doubt about that! What one gets taught in grade school about mathematics is about as representative of mathematics as a paint-by-number is representative of art.

Borrowing from Paul Lockhart, physical reality is a mess. A complete, utter, and absolute mess. Everything that can be over-complicated is indeed over-complicated. Atoms spontaneously break apart, particles fly every-which-way, and when you zoom in close enough, everything goes wonky. But this is not the only reality. There exists a "mathematical reality"---an imaginary one that only exists within you.

It is in this reality that things are as simple and pretty as you want them to be. Where mysterious patterns leave you in awe and wonder, keeping you up late at night as you lie awake wondering what happens next. However beautiful, this reality is not for those looking for a slip and slide. This is mathematics. But these wonders will not come without effort, as Paul Lockhart puts it:

But I won't lie to you: this is going to be very hard work. Mathematical reality is an infinite jungle full of enchanting mysteries, but the jungle does not give up its secrets easily. Be prepared to struggle, both intellectually and creatively. The truth is, I don't know of any human activity as demanding of one's imagination, intuition, and ingenuity. But I do it anyway. I do it because I love it and because I can't help it. Once you've been to the jungle, you can never really leave. It haunts your waking dreams. ("Measurement", pg. 2)

So what are you waiting for? Are you ready to enter the jungle? Are you prepared to stretch your imagination, intuition, and to discover the truly infinite possibilities of mathematical realty?