Read “hard” books

How do you know a “hard” book when you see one? 

For most of us, it’s a personal thing and based on what’s already in your brain. What’s “hard” for me could be “easy” for you, so make sure you’re choosing based on personal preference.

So why “hard” books, what’s wrong with “easy” books? Nothing! 🙂 – I’m a fan of all books and would never have anyone shy away from reading. Let me explain… 

Over the past year, I’ve begun to mix in more books that I would consider “hard” and it’s been an amazing experience. I’ll be honest, when reading a “hard” book, depending on the content I might walk away only understanding 30% of it… But that’s the thing! This 30% is a massive leap in my understanding of the world around us. 

Another benefit of reading “hard” books is that they get easier and guess what that means?! That means you’re building your mental muscle for reading “hard” books. 

Here are some examples of “hard” books I’ve taken on recently:

I know this is computer science and machine learning heavy, so I plan on branching out into different worlds soon. 

This brings me to a “hard” book I’ve just finished – Love and Math: The Heart of Hidden Reality + a helpful lecture series (parts 1, 2, 3, & 4)

Now this book might be labeled as friendly for the general public, but there are some chapters that completely put me on my ass. To the point where I just began to replace every symbol or word I didn’t know with “blaa blaa blaa”, but this technique is surprisingly useful when you’re just aiming for what’s intuitively being said. Ha! 

Even though I “blaad” over certain parts of this book there are some amazing insights here I’d like to share with you… 

Secret Math

If math were a planet that we’re exploring most of us have only discovered 10% of that world, with the assumption that we’ve found everything there is to find. I know… I’m as surprised as you. 

When you think of math I’m assuming something like basic arithmetic (e.g. plus, minus, multiply, etc.), algebra, geometry, and maybe calculus come to mind. But my friend, the school system is only showing you the tip of the iceberg… It goes much much deeper. 

Math can be broken into two major sections – Pure math and Applied math. Here’s a beautiful video animation explaining this better than I ever could. 

Pure math can seem extremely abstract and useless in our everyday lives, leading some of us to question why we waste time in this field at all. But without Pure math, we would struggle to understand most of the world around us. Plus the amazing technology we rely on every day directly draws from Pure math whenever we’re trying to advance anything. 

An example given in this book is the discovery of “quarks”. The average person walking on the street might think atoms are the most fundamental thing to our universe, maybe they even know atoms are made of neutrons, protons, and electrons… But there’s something even smaller, which makes up those things and that’s “quarks”. You can think of “quarks” as the most fundamental building blocks of our universe. Everything there ever was, is, and will be is made from quarks, but quarks are so tiny that we would never be able to actually see them… This is where Pure math comes into play. 

Before we knew quarks existed we assumed atoms were as small as things can get, but a guy named Murray (pretty important dude) hypothesized that there was something smaller. He didn’t do this through massive computers, microscopes, or any of that… He was limited to two things – Imagination and Math. By just using these two powerful tools Murray theoretically discovered quarks, which were then observed many years later in the Large Hadron Collider in Switzerland

Amazing, right?! By just using math and creativity we’re able to discover something so fundamental to our existence. 

Connecting puzzle pieces

Puzzles are hard, but imagine how hard it would be to put together a 4,000-piece puzzle without the box cover for reference. Well, this is kind of like Math… In the world of math, there are thousands of really smart people working on their own section of the puzzle hoping to connect more pieces. These mathematicians are building out their section of the math puzzle, with very little understanding of what the other mathematicians are doing, even though their all working on the same puzzle. Solving this separation can be seen as one of the ultimate problems of math. 

I mentioned earlier that math has two major sections, within each of these there are many different branches of math. I want you to think of these branches as different islands with their own languages, inhabited by natives. Something like Game Of Thrones, but for math.

Examples of the natives and their islands could be – Algebraists on Algebra Island, Number Theorists in Numbertopia, and Geometers in Geoland. Each island has its own way of thinking and speaking, which slows down progress. 

In this book, the author speaks about an idea called the “Langlands Program” (most math concepts are named after people, making everything much more confusing). This idea is an attempt to bridge all these math islands together. Kind of like the Theory of Everything for math. 

It’s hard to stress the importance and impact a theory like this could have on all of science, not just math. Let’s jump back to our island analogy. 

Imagine the Algebraists working on a problem for years on Algebra Island, but they realize that the problem is unsolvable. But along comes an adventurous Number Theorist deciding to explore Algebra Island uncovering this problem as well. After finding the problem this Number Theorist takes the problem back to their island, attempting to solve it in their language. And boom! The problem was solved in a single try… 

The “Langlands Program” attempts to translate problems from one math language to another making unsolvable problems solvable. Pretty cool, right?!

Created vs. Discovered

There are many hot debates happening in the world of math, but one of the longest-running debates is if math is created or discovered. This goes all the way back to Plato.

The basic argument is that one group thinks that math is created by humans, so we’re able to understand the world better… On the other hand, there’s a group arguing that math actually sits in a realm of its own slowly being uncovered by humans. The group arguing for discovery looks to be winning at the moment. 

There’s an example about aliens that helped me understand this a bit better… In the future when (not if) we encounter aliens there’s a high chance that they will have similar mathematical concepts to us. That’s because math is actually baked into the universe and humans are just putting names to things so we’re able to study these math concepts. 

If you’re interested in going a bit deeper down the philosophical rabbit hole check out the videos here, here, and here.

Never-ending pursuit to understand

Here’s a beautiful quote from the book… 

That’s how it is in mathematics: each new result pushes back the veil covering the unknown, but what then becomes known doesn’t simply encompass answers – it includes questions we didn’t know to ask, directions we didn’t know we could explore. And so each discovery inspires us to make new strides and never leaves us satisfied in our pursuit of knowledge.”

After finishing this book I’ve realized the world of math can teach us a lot about how to live life.

In our personal lives, we’re aiming to uncover questions we didn’t know to ask and paths we didn’t know to explore. This evolving journey (e.g. life) has no final answer, instead, we slowly peel back the layers uncovering different interests, exciting problems, and pain we’re willing to endure or even enjoy.  

Here’s a final thought I want to leave you with… 

Once you realize life isn’t a finite game of winners or losers, but an infinite game to explore our personal unanswered questions and paths, then life gets way more enjoyable. 

Until next time my fellow Wanderers!