Hello! Welcome to the Magnificence of Mathematics. I'm your host, Eddie Kingston.
Do you consider yourself to be someone who never really cared for math when you were
in school? Are you passionate about math and want ideas on how to help the people in your
life see that it's more than just plugging numbers in a calculator and solving equations?
Either way, this podcast was made for you. Before we dive into our first topic, I want to
introduce myself and give you an overview as to why I'm making this podcast and the overall
structure of it. As of this recording, I'm 23, living in Oregon with my wife Kylie and my son
Tony. I graduated in 2021 with my bachelor's degree in mathematics and in March 2023 with my
master's in statistics, both from Oregon State University. I remember first loving math when I
was in 7th grade. I don't remember what caused it, but all of a sudden everything I was learning
and reviewing from the year before just clicked. I remember multiplying out crazy big binomials
by hand like 2x plus 3 quantity to the 7th power in preparation for algebra 1 the following year.
Then I started learning calculus in my spare time in my sophomore year of high school because I felt
like I wasn't being sufficiently challenged in my algebra 2 class. I went to talk to the AP
calculus teacher, social anxiety and everything, to show him what I'd learned up to that point,
and he allowed me to enroll in his honors pre-calculus class at the start of my junior
year, which culminated in limits in derivatives. I did really well on the pre-test at the start
of the year, and after self-studying some trigonometry, he allowed me to transfer to AP
calculus BC where I did really well and got the highest score possible of 5 on the AP exam,
which allowed me to get a bunch of college credit. Thanks to the other AP credits I racked up in high
school, and to me taking too many classes for my own good in my first year of college, I ended up
graduating with a bachelor's in math and a triple minor in statistics, actuarial science, and music
in three years. Along the way, I worked for a program in my university called Safe Ride,
which helped students get from campus to back home or wherever they wanted to go.
I met a lot of fantastic and interesting people, but almost every time I told someone I was a math
major, they would reply with something along the lines of, oh I hate math so much, or cool so you
want to be a teacher then? You might be wondering what kind of math classes I took in college,
and I took a lot of great ones. Vector calculus, linear algebra, chaos theory, probability,
statistics, differential equations, complex analysis, and many more. I plan on talking
about all of these topics and more in the coming episodes. My favorite classes were my probability
and statistics classes. I liked learning about how random events are modeled mathematically,
and how we can analyze randomness and make it quantitative. Not only did I get a minor in
statistics, but the math major in my university had an option where one could specialize in
probability and statistics. Between both undergrad and grad school, I took seven probability classes,
ranging from introductory probability, to Markov chains, to stochastic elements of mathematical
biology, to graduate-level probability theory. That isn't even counting all the stats classes
I took, which were technically a part of a whole other department. I'll talk more about this in a
two-episode segment on probability and statistics. There seems to be a common misconception across
people who haven't been exposed to math beyond trigonometry or calculus that math is only about
computation and crunching numbers. I can't say I blame them. That's what math curricula greatly
emphasize. My goal with this podcast is to talk about mathematical ideas in an accessible way to
the common layperson so that they can appreciate how beautiful math can be if they look at it
from a different perspective. The way this first season of The Magnificence of Mathematics will
work is as follows. There will be 24 episodes split up into 12 topics with two episodes each,
with roughly 10 to 20 minutes per episode. I mostly plan on talking by myself, but I plan on
bringing a special guest for at least one episode, so stay tuned for that. I was able to see the
beauty of math and what it's all about once I reached college. I'm hoping that this podcast
is able to impart some of that magnificence on you. With that out of the way, let's move on to
our first topic, geometry. Whether or not you remember your high school geometry class fondly,
you might remember to at least some extent having to do proofs quote unquote via the two-column
approach where you write out what you're given at the top, what you're trying to prove at the bottom,
and all the steps to get there in between. I don't know about you, but I was very much not a fan of
this approach. I personally think this is a terrible way to introduce proofs in general.
I'll go more into proofs and talk about my experience in my first proofs class in college,
but for now, I want to describe to you an idyllic example of a high school geometry lecture.
Imagine you're back in your high school geometry class and the teacher draws a rectangle on the
board so that the long legs are horizontal. Now suppose they draw a line from one of the
bottom corners to the top of the rectangle and another line from that same point on the top
to the other bottom corner. Now there's a triangle inscribed in the rectangle with the bottom leg of
the rectangle also serving as the third leg of the triangle. The teacher then asks, what portion of
the area of the rectangle is contained in the triangle? You draw the figure on your own paper,
think about it for a while, and maybe take some example measurements of the rectangle to make a
guess. Maybe something comes to your mind about how to solve it, maybe not. You think about it
some more and ask your peers what they think. But then an idea pops into your mind. You draw a line
from the top of the triangle down to the bottom of it. You stare at what you've just done for a few
seconds and make a marvelous discovery. The vertical line you just drew splits the figure
into two sections, each of which has half of its area contained in the triangle and the other half
outside of it. Therefore, you guess that half the area of the rectangle is contained in the triangle.
And that turns out to be the right answer! Of course, you could have just recalled the formula
for the areas of a triangle and a rectangle and divide them. So you have one half base times height
divided by the quantity base times height to get one half. But where's the fun in that? Isn't the
way you solved it just now so much more rewarding? The important thing to keep in mind about the way
you solved it is that you got to explore the figure. You got to play with it. You weren't
worrying about applications or anything real or the pressure of trying to get a good grade and
finishing an assignment on time. This was a completely intangible figure only brought to life
by your mind and your pencil and paper. Perhaps math is more than just what humans are capable
of imagining. I can't say for sure what kind of world math as a whole lives in, but I like to
think of it as living in this ethereal, impossible to physically reach world that the human mind has
just begun to take a crack at. As much math as humans have discovered throughout history,
I'm willing to bet that we've only just begun scratching the surface. It's all living in this
mystical world waiting for the human mind to tap into its rich potential. The first way of solving
the triangle problem that you came up with is what math is all about. Using insight and playing
around with figures to come up with a solution. You didn't need any fancy formulas or equations
to solve the problem your teacher gave you. Just keen observation and pattern recognition.
I think that there's beauty in such a simple and elegant solution and the beauty doesn't
come from the answer itself but the journey along the way. I think that's a good metaphor for life
in general. It's not about the destination, it's about the journey. That's where all the magic and
beauty of life happens. I got the problem I talked about earlier from a book called
A Mathematician's Lament by Paul Lockhart, the first 25 pages of which are easily accessible online.
If you're interested in seeing what a professional mathematician thinks of K-12 math education,
I highly recommend checking it out. I personally share a lot of the same sentiments as him.
Thank you for listening to this first episode of the Magnificence of Mathematics. If you have any
suggestions for future podcast episodes, want to collaborate on a future episode, or just want to
chat about anything related to what you heard here, feel free to email me at eddikingston729
@gmail.com. That's E-D-D-I-E-K-I-N-G-S-T-O-N 729 @ gmail.com. Next time, I'll talk more about Euclidean
versus non-Euclidean geometry. I hope to see you then.
Algid Productions LLC Outro. Thank you for listening!