Why I Love Reading About Abstract Math Theory
By: Gabriella Gricius
Tags: Math, Theory, Mathematics, History, Reading

As someone who can’t do the slightest bit of math without double-checking via Google, you might not peg me as someone who loves to read about abstract math theory. And yet it’s one of my favorite subjects to read about. The answer as to why is a bit more complicated than can be so easily summarised in one sentence.

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There is something fascinating about math theory.

When all is said and done, math is a man-made concept. Derivatives and theorems are names and concepts that we created to make sense of the world. Numbers make the unknown comprehensible. Graphs put relationships and patterns into a different 2D or 3D framework so that we can understand them. There is nothing more satisfying than understanding that which is confusing to us at first. But reading about math theory, particularly that which is abstract and attempts to explain concepts like infinity, reminds us that for many questions, there aren’t any direct answers.

No. In fact, there are just more questions. Which is the second reason I love reading about mathematics.

It is because these concepts are confusing that they become all the more interesting. In the same way that books can become boring if the hero triumphs every time, so too can math and science if the answers are easy to find. Reading a book about how to determine the angle of a triangle would be boring because we already have the answer to that particular problem within the framework of Euclidean geometry. Take out that framework though, and it becomes infinitely more interesting.

Ask questions about how there are different levels of infinity, how there are versions of ‘infinity’ that smaller than others — and it opens up a completely different world of thought. When there are no complete answers, the world suddenly seems more open to adventure and investigation. There aren’t any limits when it comes to creating a theory or experimenting on numbers that have been so thoroughly experimented on that they become moot. Which leads into the third reason why I love reading about abstract math.

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Because it is challenging.

Without a math background, it’s difficult to read about the intricacies of logical theory and try to understand the P v. NP problem. It requires the reader to sit down and actually contemplate the page they have read. There is no speed reading in this field. There’s a reason that there aren’t so many mathematicians. It’s hard. So take then, if you will, a book built for people with MAs and PhDs and hand it to someone like me, who has neither.

It’s a different kind of reading experience, and it’s one that I treasure. When I’m reading about history or politics, the pages can fly by. The story of how people interact with one another, whether on paper or through the tips of their guns and swords is like any other fantasy story. Depending on who writes it, there are villains and heroes of every different stripe. With abstract math, however, there is no such option. Certainly there are stories behind the theorems, but on its face, the theories themselves require a certain form of dedication and focus of thought.

But behind every math theory is a story.

And this is perhaps one of the more convincing reason that I love to read about these theories. In popular fiction books, the narrative of the story is obvious. They explain the background and nature of the tale. In abstract math, that part is usually skipped over. There’s no debate of who created what theory or a chapter of background knowledge of how certain ideas came to be fact. But quite obviously, it exists.

That body of knowledge is part of what makes it so fascinating to me. Take something simple like Pythagorean theorem.

a² +b² = c²

On its face, we can all compute that if you square the legs of a 90 degree triangle, it will equal the hypotenuse squared of that triangle. But how did that train of thought come to be? What kind of experiments had to be done? Did Pythagoras sit around and measure random triangles until he got one to work and then test his hypothesis from there? Did he think the whole theory out and only then test it in real life? How did he even come up with that kind of thought experiment?

Like any other subject, math has a history. And because abstract math is so complex, so confusing — often times, these math writers spend more time writing about the history and nature of the problem than the actual mechanics of the math itself. That different approach to math means that to those of us without the math degree, the problems become thought experiments that drag over time, fluctuating from person to person and overlapping depending on the country and the time.

Perhaps you won’t go and pick up an abstract math theory book the next time you enter a bookshop, but maybe take a moment to at least read the back cover. Even to someone who practically failed every single math class since 4th grade until college, math can transform to something wonderfully exciting. Surprisingly, there’s more to math than our collective societal trauma from pre-calculus and algebra.