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Hello! Welcome to the Magnificence of Mathematics. I'm your host, Eddie Kingston.

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Do you consider yourself to be someone who never really cared for math when you were

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in school? Are you passionate about math and want ideas on how to help the people in your

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life see that it's more than just plugging numbers in a calculator and solving equations?

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Either way, this podcast was made for you. Before we dive into our first topic, I want to

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introduce myself and give you an overview as to why I'm making this podcast and the overall

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structure of it. As of this recording, I'm 23, living in Oregon with my wife Kylie and my son

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Tony. I graduated in 2021 with my bachelor's degree in mathematics and in March 2023 with my

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master's in statistics, both from Oregon State University. I remember first loving math when I

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was in 7th grade. I don't remember what caused it, but all of a sudden everything I was learning

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and reviewing from the year before just clicked. I remember multiplying out crazy big binomials

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by hand like 2x plus 3 quantity to the 7th power in preparation for algebra 1 the following year.

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Then I started learning calculus in my spare time in my sophomore year of high school because I felt

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like I wasn't being sufficiently challenged in my algebra 2 class. I went to talk to the AP

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calculus teacher, social anxiety and everything, to show him what I'd learned up to that point,

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and he allowed me to enroll in his honors pre-calculus class at the start of my junior

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year, which culminated in limits in derivatives. I did really well on the pre-test at the start

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of the year, and after self-studying some trigonometry, he allowed me to transfer to AP

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calculus BC where I did really well and got the highest score possible of 5 on the AP exam,

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which allowed me to get a bunch of college credit. Thanks to the other AP credits I racked up in high

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school, and to me taking too many classes for my own good in my first year of college, I ended up

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graduating with a bachelor's in math and a triple minor in statistics, actuarial science, and music

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in three years. Along the way, I worked for a program in my university called Safe Ride,

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which helped students get from campus to back home or wherever they wanted to go.

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I met a lot of fantastic and interesting people, but almost every time I told someone I was a math

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major, they would reply with something along the lines of, oh I hate math so much, or cool so you

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want to be a teacher then? You might be wondering what kind of math classes I took in college,

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and I took a lot of great ones. Vector calculus, linear algebra, chaos theory, probability,

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statistics, differential equations, complex analysis, and many more. I plan on talking

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about all of these topics and more in the coming episodes. My favorite classes were my probability

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and statistics classes. I liked learning about how random events are modeled mathematically,

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and how we can analyze randomness and make it quantitative. Not only did I get a minor in

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statistics, but the math major in my university had an option where one could specialize in

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probability and statistics. Between both undergrad and grad school, I took seven probability classes,

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ranging from introductory probability, to Markov chains, to stochastic elements of mathematical

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biology, to graduate-level probability theory. That isn't even counting all the stats classes

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I took, which were technically a part of a whole other department. I'll talk more about this in a

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two-episode segment on probability and statistics. There seems to be a common misconception across

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people who haven't been exposed to math beyond trigonometry or calculus that math is only about

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computation and crunching numbers. I can't say I blame them. That's what math curricula greatly

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emphasize. My goal with this podcast is to talk about mathematical ideas in an accessible way to

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the common layperson so that they can appreciate how beautiful math can be if they look at it

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from a different perspective. The way this first season of The Magnificence of Mathematics will

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work is as follows. There will be 24 episodes split up into 12 topics with two episodes each,

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with roughly 10 to 20 minutes per episode. I mostly plan on talking by myself, but I plan on

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bringing a special guest for at least one episode, so stay tuned for that. I was able to see the

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beauty of math and what it's all about once I reached college. I'm hoping that this podcast

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is able to impart some of that magnificence on you. With that out of the way, let's move on to

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our first topic, geometry. Whether or not you remember your high school geometry class fondly,

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you might remember to at least some extent having to do proofs quote unquote via the two-column

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approach where you write out what you're given at the top, what you're trying to prove at the bottom,

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and all the steps to get there in between. I don't know about you, but I was very much not a fan of

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this approach. I personally think this is a terrible way to introduce proofs in general.

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I'll go more into proofs and talk about my experience in my first proofs class in college,

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but for now, I want to describe to you an idyllic example of a high school geometry lecture.

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Imagine you're back in your high school geometry class and the teacher draws a rectangle on the

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board so that the long legs are horizontal. Now suppose they draw a line from one of the

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bottom corners to the top of the rectangle and another line from that same point on the top

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to the other bottom corner. Now there's a triangle inscribed in the rectangle with the bottom leg of

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the rectangle also serving as the third leg of the triangle. The teacher then asks, what portion of

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the area of the rectangle is contained in the triangle? You draw the figure on your own paper,

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think about it for a while, and maybe take some example measurements of the rectangle to make a

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guess. Maybe something comes to your mind about how to solve it, maybe not. You think about it

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some more and ask your peers what they think. But then an idea pops into your mind. You draw a line

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from the top of the triangle down to the bottom of it. You stare at what you've just done for a few

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seconds and make a marvelous discovery. The vertical line you just drew splits the figure

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into two sections, each of which has half of its area contained in the triangle and the other half

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outside of it. Therefore, you guess that half the area of the rectangle is contained in the triangle.

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And that turns out to be the right answer! Of course, you could have just recalled the formula

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for the areas of a triangle and a rectangle and divide them. So you have one half base times height

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divided by the quantity base times height to get one half. But where's the fun in that? Isn't the

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way you solved it just now so much more rewarding? The important thing to keep in mind about the way

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you solved it is that you got to explore the figure. You got to play with it. You weren't

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worrying about applications or anything real or the pressure of trying to get a good grade and

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finishing an assignment on time. This was a completely intangible figure only brought to life

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by your mind and your pencil and paper. Perhaps math is more than just what humans are capable

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of imagining. I can't say for sure what kind of world math as a whole lives in, but I like to

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think of it as living in this ethereal, impossible to physically reach world that the human mind has

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just begun to take a crack at. As much math as humans have discovered throughout history,

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I'm willing to bet that we've only just begun scratching the surface. It's all living in this

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mystical world waiting for the human mind to tap into its rich potential. The first way of solving

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the triangle problem that you came up with is what math is all about. Using insight and playing

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around with figures to come up with a solution. You didn't need any fancy formulas or equations

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to solve the problem your teacher gave you. Just keen observation and pattern recognition.

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I think that there's beauty in such a simple and elegant solution and the beauty doesn't

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come from the answer itself but the journey along the way. I think that's a good metaphor for life

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in general. It's not about the destination, it's about the journey. That's where all the magic and

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beauty of life happens. I got the problem I talked about earlier from a book called

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A Mathematician's Lament by Paul Lockhart, the first 25 pages of which are easily accessible online.

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If you're interested in seeing what a professional mathematician thinks of K-12 math education,

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I highly recommend checking it out. I personally share a lot of the same sentiments as him.

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Thank you for listening to this first episode of the Magnificence of Mathematics. If you have any

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suggestions for future podcast episodes, want to collaborate on a future episode, or just want to

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chat about anything related to what you heard here, feel free to email me at eddikingston729

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@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

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versus non-Euclidean geometry. I hope to see you then.

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Algid Productions LLC Outro. Thank you for listening!