Pigeonhole Principle


Math… equations, formulas, integrals, trigonometry. You’re not alone if some of those words give you cognitive dissonance. Unfortunately, math feels like the study of boredom rather than the study of patterns. That is not what math is. Math has had the terrible rap of being all about computation and memorization of complex formulas for solving problems. But why? I think that a lot of it has to do with the fact that it’s harder to teach somebody an idea than it is to teach somebody a formula to remember. But that’s not math. Anyone can remember a formula, but how many can derive it, or make it more general/better.


What is math? Unfortunately, math is tough to decipher. The reason I like it is not the reason other like it, which is not the reason society likes it. Often times it takes so much math for one to see its benefit that it’s not worth going that far into it past basic arithmetic, and maybe trigonometry. I want to build a different perception. I’m gonna talk about a part of math I really enjoy and tell you how it relates to everyday life, I hope it doesn’t get too boring, but it’s math so no promises!


There are two people, (non-bald)in New York with the same number of hairs on their head.

How would one even go about proving such a thing, would I need to look at every person in New York and count each of the hairs on their head? How much time would that take? What if I miscount? What if midway through counting somebody grew hair/got a haircut? Who would actually let some random guy count the hairs on their head? Why does anybody care? All jokes aside, that last question is both the most and least important question on this list, most important for obvious reasons, but least important because it impedes our ability to solve this thought experiment, surprisingly, a majority of math is thought experiments which prepare you for real questions that people care about. Without too much commentary, onto the proof!

It is known(weirdly, that the maximum number of hairs on one’s head is roughly 500,000.) There are currently 8.5 million people in New York. So if everybody had a different number of hairs on their head, there would have to be somebody with 8.5 million hairs on their head, impossible!

Although the answer was simple and the question useless, it is the process and way of thinking outside the box which drew me to math, so despite its simplicity, the process is actually quite deep.

One Comment

  1. Austin,

    I enjoyed reading your first post to your passion blog! I think that you presented your topic in a fun, simple, and entertaining way. As an actuarial science student and math nerd, I agree that math is one of the most important subjects of school for its applicability to many other topics. Nevertheless, certain topics in math are sometimes hard to describe in a single sentence! I’m glad to see that another classmates likes math as much as I do. Are there any topics in particular that you’re going to dive into during the semester? Maybe you could discuss some of the most famous mathematical theorems and proofs in fun, interesting ways for all readers. Great job!

    Billy Young

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