My Life in a Nutshell
When I started school, I was 7. I was thrilled and excited. I learned to read, which I’ve used every day since 😊. I was a fast reader, and I took full advantage of that. But let’s stick to our topic: mathematics.
Our primary school teacher was an angry and grumpy man, though I liked him. Could it have been Stockholm syndrome? I don’t know, maybe.
Anyway, since I was afraid of him, I pushed myself to learn mathematics. But, as you can guess, I couldn’t manage to learn it properly. After those nightmarish years passed, I finally made it to high school.
High School Struggles
During high school, I was also bad at mathematics. If English allowed it, I would say I was WORST at it. I repeatedly got the lowest grades. However, one day, while attending a private mathematics lesson (yes, private lessons were essential for students like me), I was taught a proof in trigonometry.
The Proof That Shocked Me
It was the simplest proof one could imagine, involving a $30^\circ$–$60^\circ$–$90^\circ$ triangle. The teacher then derived all the properties of this special triangle. I was literally shocked I hadn’t known that mathematics could be proven like that. In fact, I didn’t even know what a “proof” was. Sue me 🔗.
At that moment, I told myself: “You should learn about mathematics.” I bought books on preliminary math. I remember one of them covered even the basics like addition, multiplication, and rational numbers. If I haven’t made it clear enough yet, let me clarify: I didn’t even know how to add two rational numbers. So, a nightmare for 16-year-old Arda might have been something like$\left(\dfrac{1}{5}+\dfrac{2}{11}\right) = ?$. Worse still, when I encountered an equation like $x + 2 = 7$, I couldn’t even bring myself to pick up my pencil.
So Far, So Good
But I was the persistent one, I set my mind on mathematics. I could give up on everything except mathematics. After a really short time (not sure but it could be two or three months) I was ready to learn derivatives and integrals.
I worked through topics like rational numbers, real numbers, set theory, and functions. Then I bought college-level books with the help of online forums likemathematics stack exchange. Back then, ChatGPT didn’t exist.
A Bit of Luck
I was lucky, too. My cousin, a brilliant mechatronics engineer whom I call the genius was the smartest person in our family. He was like one of those people you can’t help but admire. I remember thinking about his brilliance and his courage 🧠.
I can say that he was like a rock star, I could see him only on a monthly basis if I am lucky. But those moments were golden. He taught me not only mathematics, but also physics, chemistry, English, and biology. I even remember him proving the Riemann integral formula, which he recalled from his high school years. Thanks to his encouragement, I chose the right college major: mathematics.
College Was Different
When I first started college, I realized that there was a different kind of mathematics being taught. Still, I couldn’t have imagined just how huge the difference would be between high school and college-level math. I felt like a fish out of water.
Then I began taking courses like Analysis I, where I learned about functions, limits, continuity, and so on. Slowly, something began to change within me: a way of thinking. Mathematical thinking started to grow, almost unintentionally. After one or two semesters, I was thinking in a way I never had before.
I will try to share what I’ve learned and applied while studying mathematics at university.
For this and future sections (until I change the topic), I will use three books as references: How to Solve It by George Pólya, How to Think Like a Mathematician by Kevin Houston, and Matematiğin Temelleri by Prof. Dr. Halil İbrahim Karakaş.
At the end of each section, I will share a LaTeX-written PDF.