It is hard for me to state how much I love math. If I had to define what exactly mathematics is, I would make the argument that it is the essence of form. Behind every "thing" in this world - all that exists - is a constellation of mathematical ideas and principles. Explorations of these ideas, principles, laws, axioms, et cetera are all exercises in describing form. Contemplating what things are, how they change, and the interwoven entanglements between these ideas is the heart of mathematics. I am deeply inspired by mathematical endeavor as it is our purest attempt at describing and understanding our universe. It is simply beautiful - and it's why we learn math.
Unfortunately, our education system does this pure introspection into the essence of form a disservice. It instead focuses on calculation, rote memorization, and the utility in getting from A to B. Many have lamented this issue so I won't belabor this point. Instead, I'd like to contribute my own thesis on how to inspire and engage all with maths. I'm fortunate in that I have a very visual brain - I can easily construct an image of what's happening mathematically in my mind's eye. As I have gotten older, I realize that many who hate, despise, or otherwise dismiss math have rarely been able to see the descriptive beauty of mathematics. It's like writing a paragraph describing the Grand Canyon when, what one really needs, is to see it for themselves. Only then does one understand the majestic and awe-inspiring beauty of this place.
As a kid, I always thought I was going to grow up to be a math professor. Albert Einstein, Isaac Newton, Leonardo Da Vinci, and many others were my heroes. I loved mathematical puzzles and riddles. When I learned multiplication, I learned how to calculate sales tax on my own before we learned about it in school. And the more I learned, the more I was fascinated by how simple rules could explain so many things in the world.
As I entered my teenage years, I learned more about physics and computer science. This expanded my sense of wonder at the vastness of the universe and inspired me with humankind's ingenuity at applying math to our everyday life. Google's use of linear algebra and eigenvectors to create the most useful tool for intellectual exploration - the search engine - continues to inspire. Who would have thought that mathematics could be used to search for relevant websites and articles to an intellectual query? We take this for granted now, but at the time I was awestruck that some person had created this deeply useful tool. And I wanted to be where those people were - Stanford University.
As such, when college application season came around I applied early and gratefully was accepted. And for the next decade I dove headfirst into a slight detour - software engineering and creating startups. Saving that story for another day, let's suffice it to say that COVID-19 created a crossroads in my life wherein I had the space to transition to something new. I had spent the previous decade focused on solving business problems and making money without cultivating or following any deep passion, principle, or value. And I wanted that to change.
It was at this time that I returned to my childhood wonder in math. I decided to dive headfirst back into re-learning math as a hobby. At first I realized my skills were rusty - very rusty. I had to restart at pre algebra and work my way up through algebra 1, algebra 2, geometry, trigonometry, and calculus. I then continued into linear algebra, proofs, geometric algebra, discrete differential geometry, knot theory, and other intellectual excursions. It was a ton of fun and I enjoyed the satisfaction of solving a problem correctly. But there was one problem.
It was hard - and not for the reason that it's math. It was hard because many of the resources I used - books - were limited in their ability to explain and explore concepts. Sometimes an analogy would stick, but many times I'd be staring at a page and wonder how they got from step A to B. This was especially true with the higher maths - sometimes I'd simply have to skip a section until at a later point the dots were connected. And with my background building software applications that were dynamic and interactive, I realized how deeply I wished there were tools for exploration that took advantage of what computers are great at. Despite watching Youtube videos and the occasional blog post exploring a concept, there was no organized structure in which to play with these ideas. And this is where my hobby turns into an exercise in sharing my passion with others like you.
It is my wish to share this intrinsic beauty of math on this website. I believe the best way to do this is by creating visually interactive and dynamic tools that help one explore and understand the rich world of mathematical ideas. Instead of getting lost in the notation of math - how its written and what these symbols mean - I want to instead create a world of playing with notation so that the ideas, concepts, and relationships come alive and make it easy to see in action.
With all that said, the structure of this exploration is going to be pretty straightforward. I intend to retrace my own steps starting with pre-algebra through concept-oriented articles both explaining and exploring what each idea is and how it relates to other ideas. Every article will have visual, dynamic, and interactive aspects to it. Think of it as a reimagination of the textbook from first principles using a computer instead of a collection of paper.
After finishing with pre algebra, I'll move along into algebra 1 & 2, geometry, trigonometry, and pre calculus. Depending on how all that goes, I might make an excursion into linear algebra, statistics, lambda calculus, geometric algebra, proofs, or other college-level mathematical concepts. If you're interested in tagging along, please sign up for my newsletter. I'll only send it once a week and it'll provide updates on what's changed and relevant links to explore if interested. Now onto the maths!
This introduction to pre algebra will focus on the basics of mathematics. For most students, this is what is commonly expected to have been learned by the end of 8th grade. We'll first start with the what's - whole numbers, integers, fractions, decimals, percents. Then we'll dive into the basics of how they are manipulated and changed - addition, subtraction, multiplication, and division. Finally, we'll dive into the structure and deeper manipulation of these concepts - notation, equivalence, order of operations, simplification, and finally solving linear equations. At the end of this, we'll have built a basic foundation from which to branch in many directions. Links will be added and updated as they're written.