Some people think philosophy and mathematics don’t mix. Those people are wrong.
By the time I began my final year of high school, I was thoroughly sick of maths—I never wanted to see another calculus problem in my life. I was going to study music at university and knew I didn’t need derivatives to do that! I was going to drop maths in year 12 but my mum convinced me to “keep the easy maths, just in case!” I slept through class for most of the year… In the end, I didn’t study music at university. Worse, I studied philosophy.
As an undergraduate philosophy major, I studied work by Pythagoras, Descartes, Leibniz—
“but, wait!” I hear you cry, “Weren’t they mathematicians?”
Yes, they were. My most favourite philosopher, Hypatia of Alexandria, was also a renowned mathematician. The divide between philosophy and mathematics is a recent phenomenon, and not a positive one. At its core, philosophy is about questions. Sometimes those questions seem nonsensical, but philosophers still try to answer them. And mathematics? Mathematics is also about questions. Sometimes they seem nonsensical, but mathematicians still try to solve them.
After my philosophy degree, I spent some time working as a digital copywriter. The internet is driven by numbers, and IP addresses are only the beginning. User metrics, audience demographics, and return on investment are all numbers and I – a copywriter – was swimming in them. I wasn’t just writing words, I was collecting statistics, analysing algorithms, and optimising publishing schedules. I thought breaking down statistics was fascinating; maximising search engine rankings was interesting; and coordinating the logistics of digital content production was fun. I was doing maths! And I liked it!
I wanted to know more about the maths behind the work I was doing so, naturally, I enrolled in a mathematics degree.
“That’s all well and good,” you say, “but what does that have to do with philosophy?”
Here’s the thing: as a philosophy student, I studied conditional tables, symbolic proofs and Gentzen sequent calculus. I asked questions about the nature of existence, the construction of time, and what it means to think imaginary thoughts. As a mathematics student, I study tables and proofs and calculus, and I’m asking those same questions. If a thing is proven mathematically, does that mean it is real? Is time a continuous or discrete measure? Why do complex numbers work?
It turns out when I was studying mathematics at school, I was also studying philosophy. And I never stopped studying mathematics, I just went about it a different way.
The philosopher asks: how do we conceptualise the absence of something?
The mathematician asks: how do we evaluate division by zero?
And I ask: why aren’t we considering these questions together?