031. The Zeroth Case

tldr: spread kindness

Dear Professor Sabuwala,

I have been planning to write this blog post for quite some time. I didn’t quite know how to start it, let alone when the best time to post it would be. But given that September has come and gone, I think it is finally time.

I started attending Fresno Math Circle at the beginning of my Junior year. I was really worried to apply, because in the past when I had attempted the application problems I could only solve 1 or 2. I only decided to turn them in when I figured out a third solution– and it was an extremely inelegant one at that. But it was more than just my lack of confidence in mathematical problem solving skills that kept me from applying.

Did you know that when I had applied I was transitioning? For (almost) the entirety of my sophomore year of high school I had identified as nonbinary. It wasn’t until spring of 2018 that I realized she/her pronouns fit better, and it was only two months earlier when I started going by Paige. So, when I had turned in my application I put my pronouns as she/her, but I filled in all the textboxes still using they/them. And one of the first emails I had ever received from you and Dr. Nogin was asking for clarification on which pronouns I used so that they could make my experience as comfortable and accommodating as possible. It felt like I had finally found somewhere I belonged in Fresno that wasn’t connected to my high school.

While I had been a member of the club for two whole years, I still remember the first weeks like it was just yesterday. We first studied the Pigeonhole Principle. It was insane to me that this was the first topic, because when I first met you my Freshman year this was one of the mathematical concepts you brought up in a math-magic trick. To those who don’t know what this concept is, it isn’t terribly difficult to wrap your brain around:

If you have 13 friends, you know at least two of them are going to share the same birthday month, given that there are only 12 months in the year.

Similarly, if you have 120 distinct integers, you know that there are at least two with a difference that ends in 00. This is because there are only 100 possible combinations of the last two digits of a number: 00-99. Therefore, at least 2 of the 120 distinct integers will have the same last two digits, and thus their difference will end in 00.

Here is a question for you to try:
Lets say, you lived in a town of 100 people, and you knew that no one in this town had more than 101 strands of hair on their head. Do you know with absolute certainty that there are two persons with the same number of hairs on their heads?

I’ll give you a moment to think about it.

Answer right below.

Think about it a second longer. Annnnnnnd okay:

If you said yes, you would be exactly in the same mindset as I was when I first did the problem too. However, the answer to this question is no, and it’s because of a very simple reason: The Zeroth Case. There are people with 0 hairs on their head. In fact, there are many people for which this is the case. Thus, it is possible that 100 of the inhabitants have different numbers of stands of hair on their heads, and the additional one to be bald– therefore, we don’t know that there exists two people with the same number of hairs.

Every time I have tried to write this blog post I keep coming back to this concept. The Zeroth Case. Going back to where you started to make sure there is no stone unturned. Maybe it’s because I am a sucker for stories of mathematics that can apply to a bigger concept.

I had a plan. I thought it was infallible. Apply to college. Sit in on your Number Theory class that spring. Tell you and Dr. Nogin that I had gotten accepted to MIT (or, any college really when I first imagined this plan). Tell you that it wouldn’t have been possible without your support. Have an amazing last year at Fresno Math Circle.

Turns out this plan wasn’t as fool proof as I had hoped.

Life is cruel and difficult, and it can feel like nothing we do matters. But whenever I start to feel this way, I go back to where I started. Fresno Math Circle. Dr. Sabuwala, you were by far one of the happiest people I have ever met. You had a thousand yard smile, and you strived to bring joy to those around you– especially the joy of mathematics. And I know that my actions matter. I can find joy in the little things, and I can be kind to those around me. My time on this planet may be finite, but the impact I make on those around me can be endless.

Thank you for all you have taught me. And if ever I forget, I will go back to where I started.

PS: I got into MIT. And it wouldn’t have been possible without your support.


Published by Paige Bright

Hi- my name is Paige Alexandria Bright. I am a rising junior at MIT interested in mathematics and philosophy. I have been writing this blog since the beginning of COVID. Lets see where this goes.

2 thoughts on “031. The Zeroth Case

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: