Educators often stress how important math is. “Math will benefit you later in life.” they say. “If you look around, math is everywhere!” And, they are correct—math is, indeed, important.

Schools therefore come to the conclusion that they need to do whatever they can to make sure that students will memorize math concepts. “2πr2\pi r equals the circumference of a circle… a2+b2=c2a^2 +b^2=c^2 is the Pythagorean theorem…”—and, again, they are right. These concepts are important.

But as necessary as all of this is, we should realize that math is not just that. Though many students think that math is all about equations and formulas and whatnot, there is much, much more to math. Math in itself is actually full of creativity and imagination; you can play around with it as you might with any other toy. Simply put, math is an art.

“…there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depend heavily on properties of the physical universe),” Paul Lockhart writes in his paper, A Mathematician’s Lament. “Mathematics is the purest of the arts, as well as the most misunderstood…”

Lockhart is further explaining how math is an art, and hints at the fact that mathematics, like any other art, can be appreciated after truly experiencing it. We can tell with his last sentence, though, that not many really understand this. We as a culture are still not fully aware about this other side of math.

But, how is mathematics creative at all? Math and expression—those two words might seem as if they would never fit together. However, as I said before, mathematics is not composed of a finite set of rules. Math is all about finding patterns and playing with these patterns. Many accomplished mathematicians have alluded to the importance of patterns in math, including G. H. Hardy, Ronald Graham, and Steven Strogatz.

Some say that the beauty of math lies in the power and simplicity of it. Junaid Mubeen gives an example of this with Euclid’s Proof of the Infinitude of Primes in an article, Mathematics is Art:

“Suppose there are only finitely many primes, let’s say nn of them. We denote them by p1,p2,...,pnp_1 , p_2 ,..., p_n. Now construct a new number

p=p1×p2×p3×⋯×pn+1p = p_1 \times p_2 \times p_3 \times \cdots \times p_n + 1

Clearly, pp is larger than any of the primes, so it doesn’t equal one of them. Since p1,p2,...,pnp_1 , p_2 , ..., p_n constitute all primes pp can’t be prime. Thus it must be divisible by at least one of our finitely many primes, say pmp_m (with 1≤m≤n1 ≤ m ≤ n ). But when we divide pp by pmp_m we get a remainder 1. That’s a contradiction, so our original assumption that there are finitely many primes must be false. Thus there are infinitely many primes.”

And how does this all relate to math education? Many seem to forget that formulas and theorems were first created by a human mind by looking at the patterns and symmetries of numbers. So, why don’t we let children play around and discover their own theories in the classroom? We analyze texts in English—why not theorems in Math? Junaid Mubeen writes later, “Curriculum and assessment must evolve to take account of the holistic nature of mathematics.”

If we can incorporate this other, wonderful side of mathematics in our schools’ math curriculum, it would almost certainly be guaranteed that more students would enjoy math. It is not just the formulas in math that are important; it is also the thoughtfulness and the history of mathematics.

After all, what’s the fun behind learning a new rule in math without understanding the actual math behind it?

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