Math Part 1: We have to talk about your Math Problems

Recently, I’ve read the book Mathematica: a secret world of intuition and curiosity, and it blew my mind.

This blog series is an attempt to help distribute its content! So let’s dive in!

Intro

Do you hate mathematics? Perhaps it shattered your self-esteem once. Math is for smart people with glasses, who play D&D and boardgames, who lack social sensitivity and physical fitness. So, you decided to walk away from numbers altogether.

Or, you were never really good at math and nowadays it’s merely a distant forever-more-closed high-school chapter?

Or, you’re pragmatic, and math was just a necessity to pass a degree. Other than that, it never really meant much to you. You’re more of a warm touchy-feely person than a cold numbers person anyway…

Maybe, just maybe, you are one of those that have seen the other side of mathematics. The sunny side. The side where things intuitively make sense. The side that knows the pure joy of discovering math’s secrets. The rush of dopamine caused by a sudden understanding so profoundly, almost as if things are being unfolding magically right in front of your eyes. As if you can just suddenly see it in front of your eyes and changing your perspective forever in such a way you can never undo.

First, let me explain my relationship with Mathematics. Maybe you can relate to it too.

Math and Me

Woah, I got completely carried away writing this section. I am not that interesting, so I put the full account here. Instead, here are the highlights (and lowlights) from my mathematical journey:

• Elementary School: I started strong, consistently ranking at the top of my class in arithmetic and basic math. This love of learning only deepened as I mastered even the smallest concepts.
• Social Pressure: By around 11-12-13 years old, social pressure began to take its toll. I found myself suppressing my enthusiasm for mathematics, fearing that it made me appear “nerdy” to others.
• High School: I largely focused on passing subjects rather than genuinely engaging with mathematical concepts. It was a far cry from the math whiz kid I once was.
• The Turning Point: My focus shifted when I arrived at the Technical University of Delft, where I began to explore more advanced mathematics as a tool for problem-solving.
• Limited Understanding: At this stage, I didn’t fully grasp the underlying principles or ’thinking’ behind these tools. My focus was solely on mastering their application.
• The Epiphany: It wasn’t until I stumbled upon the axioms, theorems, and proofs at the University of Maastricht that everything clicked into place. Suddenly, math became beautiful, elegant, and powerful.
• Newfound Appreciation: This newfound understanding has profoundly altered my perspective on the world. Math is no longer a dry subject; it’s a language that speaks to something deeper within me.

What I’m trying to say; like so many people, I’ve been on top, struggled with the social perception people have of mathematics, struggled with math and feeling not smart enough, struggled with understanding why I need to learn math and why this is useful to me, struggled to understand the tools and finally realized that mathematics has altered my thinking and my perception of the world in profound ways.

In the end, I was also just lucky. So many people give up early, and often it’s not really their fault. I also would not have been introduced to its secret world of intuition as described so well by David Bessis in his book. I am not saying that mathematics has no secrets. On the contrary, there is so much of it I don’t understand or have intuition for, it would take more than a lifetime to get there.

But that’s okay, it should not be a problem. Let’s talk about that.

This is not about me though; this is about you

We don’t feel stupid when we fail to understand history, or biology. Perhaps we find chemistry, physics or economics ocassionally intimidating. Ocasionally, because sometimes it is not intimidating. Mathematics however, has the power to lift us up and to bring us down.

Why?

Well, let’s reflect on that, bear with me a little bit here.

Easy, simple. Now let’s make things more complicated. When driving on the highway, you might also be fully aware that accelerating will increase your speed, which will increase the distance required to come to a full stop but also decrease the required time to get home. You know how to drive a car, so you know what happens when you press that gas pedal.

Easy math! But now try to visualize that acceleration. How does it look like?

If you’re like me, you’ll be probably find it difficult to visualize what acceleration means like this.

Truth be told; to me acceleration only makes sense when comparing two different speeds. On its own, I don’t understand it at all. For example, I know earth’s gravitational constant equals $g = 9.81 m/s^2$, but I can’t really picture in front of my me what that means without comparing two different images. I’m seeing an image of somebody falling slowly, and somebody falling more quickly. But I can’t really see the person falling more quickly. If you’ve had an education in physics, or if you have jumped out of an airplane, please share how you visualize this, because I am not quite getting there.

In fact, there are a lot of things I can’t really visualize. I just don’t know how people do it. Perhaps you do too. Yet, I’ve completed a thorough study of some fields within mathematics (excluding those alluding to applied physics though), and people around me generally expect me to be the numbers guy, the engineer or perhaps even the smart one. Sometimes I am. Sometimes I think I am. And sometimes I overestimate myself heavily or slightly. Also, sometimes I am just not, perhaps even not at all. But that’s okay! In fact, it’s normal! And it’s so important to be aware of this. There is no shame in not knowing or understanding, only in not having the courage to ask stupid questions. That’s what mathematics is all about.

Learning how to understand the world around us, and making it understandable to other people as well. Great mathematicians know this, and some have even wrote about it. Isn’t that just amazing?

What is even more amazing is that:

• Those mathematicians are mostly saying the same things!
• It resonates with so many people (including me)!
• You do not need a PhD in Mathematics to understand and learn this too!
• The underlying ideas apply to many abstract domains!

Curious to learn more? Go here!