The Universal Beauty of Mathematics

When I hear someone say, “I hate math” or “I’m bad at math“, I cringe slightly, and respond almost embarrassed, “I like math, it’s quite beautiful“.

I sometimes go on to defend my belief that there is no useful difference between art, math, and science — none. I’ve had this conversation many times with many people.

Is math beautiful?

Most people seem to agree in theory — and I hear (all too common) stories involving painful memories of math classes. As if the beauty in mathematics is out of their reach, perhaps only beautiful to some nerd minority.

I remember my own math classes when I was young, and I cringe again.

The teaching of Mathematics, a language to express the ineffable beauty of existence, is reduced in classrooms everywhere to a painful Pavlovian conditioning of forced computation.

Imagine for a moment, that instead of teaching children to read and write, that we instead forced them to copy (like little drawing machines) printed books but only one letter of the alphabet at a time. Never learning to read, just forcing them to copy all the A’s on page, and then to copy all the B’s, and so on.

So a young student begins with the letter A and painfully fills in A’s on a blank sheet of paper attempting to match them to the A’s they see in a printed book.

Teachers hold up answer sheets to make sure the young students copied all the A’s and copied them to all the right places on their practice page.

This is a very good copy of the A’s,” the teacher will say.

And then as they get older they copy more and more letters, A’s, B’s, C’s and onward. We do not tell them why they are doing this, we do not tell them that these letters have any relation to their spoken language. And whenever a student asks why they have to do this, we tell them, “because I said so“.

Eventually, years later, a student has copied all the way to Z and finally copies entire pages of printed books. This student can now graduate.

As this student graduates she expresses in angst, “I will never need to do this again, I hate letters“. And she is illiterate, and so is most of this imagined society that forces children to copy letters without ever telling them why.

But perhaps this student goes to college, and while in college she decides to learn more about these letters. She takes an advanced class in letter writing.

She wonders if there are more letters to write, maybe new letters that she has never seen before. She has heard that these letters contain beauty, but she cannot possibly understand how.

The class she takes is called “Letter Theory”, and the teacher begins by asking a simple question,

What is a letter?”

How absurd, the student thinks, obviously a letter is what she’s been copying her entire life!

The teacher goes on, “when we put these letters together they form words, like the ones I am speaking now

Shocked, the student exclaims, “certainly not all words are made of letters, there are so few letters and so many words that we speak

The teacher smiles and replies, “all words, all the ideas you have ever heard with your ears, every lecture, every song, all of it, can be expressed using combinations of letters

Years later, the student has learned about grammar, semantics, composition, literature, poetry — and now she finds beauty in the letters that she never understood before.

Letters are amazing, just as numbers are amazing.

Mathematics is the study of beauty, and it is expressed in numbers.

You need not be a great writer to understand and experience beautiful writing, and you need not be a professional scientist or engineer to understand and experience the beauty of numbers.

Imagine if only professional writers learned how to read, that is our current world concerning mathematics.

If you have never experienced the beauty of numbers, understand that your entire education has failed you, and you are mathematically illiterate. Most likely, you have learned only drilled computation, and perhaps touched upon Algebra or Calculus without any explanation of what you were actually doing and, most importantly, why.

If you believe you are bad at the computation that was drilled into you at a young age, you are not alone; if you believe you were good at those computational drills, you are wrong — all humans are bad at computation. All of us. Our greatest computational geniuses are slower and stupider than even the cheapest pocket calculator. We don’t hire humans to be computers, and we don’t hire humans to be printers — fortunately, we are not training humans to be printers, but we are training children to be computers (really slow error prone computers), and we are robbing them of mathematic literacy.

And if you are mathematically illiterate, you are also (necessarily) scientifically illiterate.

This failure to teach math results in widespread illiteracy, and an inability for many people to read and express the beauty of existence, a poetry in numbers that opens our eyes to the infinite beauty of life.

When we stare at the stars and express their beauty in words, we have religious mythologies — and when we stare at the stars and express their beauty in numbers, we have a scientific revolution. For tens of thousands of years humans have had scientifically illiterate explanations for the stars (pinholes in a celestial blanket), but with the language of mathematics those stars became far grander and far more beautiful than anything we could possibly have imagined.

It is in that moment where science, math, and art converge into a unified inquiry — the study of existence, the study of infinite beauty.