It isn’t every day—or every week, month, and year for that matter—you see a student clutching a math textbook while eating. For most students, mathematics is a routine: an often frustrating process of navigating formulas, equations, and tests. But for Sixth Former Joseph Kahana, math has become much more—a creative sandbox, a path to humility, and even a connection with the divine.
“When I was young, I did quite a lot of math. I just thought it was pretty cool,” Kahana said. “It was also due to how I was raised—I didn’t have video games or anything. My mom also somewhat pushed me forward.”
However, by sixth grade, that enthusiasm had faded. And by eighth grade, he wasn’t remotely interested in math.
“I turned to computer programming instead because I thought that was the next big thing. A lot of the successful people I saw did that, so I figured I’d just copy what they did,” Kahana said.
Then came a crucial turning point.
“Towards the end of my freshman year, I was trying to design my own programming language. I stumbled across the principle of recursive definition, which introduced me to set notation. After a series of internet searches, I found a book on set theory,” Kahana said. “It was sort of this completely new thing. It had no numbers. It was theory and logic. How we understand the world. It was super cool to me because it felt more real than anything I had previously done.”
This small book reignited his passion for math, and soon he started diving into other fields of math.
“After learning about set theory, I went through my mother’s math books. It was like discovering a new world, where you can move everything around and understand everything,” Kahana said. “It gave me this sense of control where I can be the player, rather than just a character or NPC with a given script.”
This curiosity grew as he went deeper into his studies.
“The thing is that the more you learn, the more questions that arise. Each new fact brings a dozen questions. It’s like a whirlpool of theories and definitions in which you can’t stop because you know you’ll be leaving your knowledge incomplete,” Kahana said.
Those questions became consuming for Kahana, reshaping his priorities and time commitments.
“They were really important to me, because they felt too fundamental to abandon. I realized these other things I thought I cared about, like money and power, meant less to me,” Kahana said.
Math has also brought him great humility.
“When you’re solving a difficult math problem or proof, you’ll hit the boundaries of your intelligence,” Kahana said. “There’s this special feeling, telling your brain to think about it, and it just can’t—it’s being pushed to its utmost extent. I’m yelling at my brain to work, and it’s just not working.”
This limitation, however frustrating, has brought Kahana spiritual insight.
“It showed me that I’m not gonna be able to make sense of everything. And it made this idea of there being someone who can understand everything, [which is] God, makes religion even more compelling to me,” Kahana said. “Another thing is that in math, you can’t prove infinity in math, and you can’t describe it fully—you can only describe its properties. Lots of math is trying to develop a relationship with infinity, which is important to almost every other aspect of math. So, I find that in some ways, I can connect with God by connecting with infinity.”
Most importantly, math is beautiful to Kahana.
“When you go deep enough in this world, it starts to make things. It feels real, just in a different sense than what’s classically ‘real.’ Math’s beauty sometimes makes me cry,” Kahana said.
While Kahana acknowledges that not everyone will find math as beautiful as he does, he believes many more students would discover an appreciation for it if given the chance to engage with its abstract beauty that is not taught in school.
“I think school math stifles people’s curiosity in math and in general. I think a lot of seven-year-olds would find the concept of pi cool, or functions and geometrical shapes. When math becomes—compute this equation under a certain time, or you’ll get a bad grade, and your parents will get mad—people lose interest. That approach, in tandem with Haverford’s switch to CPM, which is unnecessarily difficult and condescending, is quite horrible,” Kahana said. “Math shouldn’t make people feel stupid. It should make people feel greater.”
Kahana hopes Haverford can help students explore “true” mathematics by borrowing from its philosophy to humanities classes.
“If we could expand from timed tests to include more presentations, readings, and papers as we do in other classes, students would be able to explore concepts like number theory in school. I think more people would then be drawn to math,” Kahana said. “Actually understanding ideas at a deep level isn’t doable by a calculator, unlike the long, complex equations that we currently do in class.”