Mathematics: A Short Memoir

The first time I experienced The Cosmic Giggle was when my mom taught me arithmetic. I remember the intense euphoria that washed over me as I finally grokked how operations like addition, multiplication, and division each worked and fit neatly together.

Growing up, I did abnormally well on math tests. I received perfect scores on the standardized TAAS and TAKS tests, and when I later took the SAT, I scored a 1590 out of 1600. Unsurprisingly, the one question I missed was on the English portion of the exam.

Years later, I somehow convinced myself to transfer out of The University of Texas’ undergraduate math program into the McCombs School of Business, where I got a degree in the Management of Information Systems. I wish I hadn’t, now, but so it goes.

In The Real World™, I headed straight into tech. Before long, while working as a sysadmin at HostGator, I found Bitcoin. I promptly and dutifully tumbled down the beckoning rabbit hole. For the next few months, I found myself spending the bulk of my time researching, contemplating, and examining Bitcoin from every angle. This represented a reawakening for me, and I gradually fell back in love with learning, understanding, and the quest for truth. Books like Gödel, Escher, Bach and a long line of cryptocurrency whitepapers and technical deep-dives kept my mind engaged. I chased my dreams, I got a job at Factom, and I met the love of my life Cristina, who I am now happily married to.

 

Leaving Mount Stupid

One day, pretty much out of nowhere, I found myself pondering the question: “Are any powers of two divisible by three?”

Are any powers of two divisible by three?

Do you know the answer to this question? I certainly didn’t when I first asked it.

Let’s see… 2 is obviously not divisible by 3. 4 isn’t either. Nor is 8. Likewise, 16, 32, 64, 128, 256, 512, 1024 each proved not to divide evenly by 3. While my first batch of attempts didn’t produce any counterexamples, I didn’t see an obvious way to convince myself that this pattern would be upheld ad infinitum. After a few minutes, I decided to Google the subject, which led me to pages like this one, where there was talk of The Fundamental Theorem of Arithmetic.

Thus I came to learn one reason why prime numbers are, in fact, special and interesting and important. Of course no powers of two are divisible by three; deconstructed into their prime factors, these numbers are (by definition) collections of 2s. As soon as you introduce a 3 into the mix, it’s no longer a power of two! This is basic, elementary, one might even say fundamental number theory.

Mt. Stupid

From SMBC

Suddenly, my ignorance came into full, hideous view. For the first time I felt like I finally understood what Socrates meant by I know that I know nothing. Or as Isaac Newton so eloquently put it:

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

I set out to explore a little bit more of that great ocean. Books like A Transition to Advanced Mathematics, Spivak’s Calculus, Elementary Number Theory, and Introduction to Graph Theory nursed the flame of my mathematical soul to life in a new and wonderful way. I once again found myself overcome by The Cosmic Giggle, which swept back into my life like an old friend who knows they’re always welcome.

 

A Few Takeaways

The past few years have seen me start taking mathematical study more seriously. I have established the habit of learning and practicing what I call “real math” on a daily basis.

To distill down a few of my favorite revelations and insights gleaned during this period, I will say:

  • Math is the precise use of language and thought
  • Growth hurts
  • Not all math involves numbers
  • There are limits to math, and even truth
  • Understanding is beautiful for its own sake
  • History (not to mention the modern world!) is full of geniuses
  • Expecting to understand everything on the first read-through is setting yourself up for disappointment
  • The concept of infinity can bend the mind
  • Many things are related in the most interesting and unexpected of ways
  • Most people know incredibly little (including myself)
    • …and plenty of what we do “know” is wrong!
  • Prime numbers are neat
  • Often, it helps to re-frame the problem
  • It’s possible to understand almost anything with significant, concentrated effort

Today I find myself a humble mathematical neophyte who loves every precious step along the journey from almost-total-ignorance to ever-less-ignorant-than-before.

TL;DR: I love math.