I had known about primes since my own schooling, but they didn’t fully intrigue me until I connected them with atoms. While doing a science lesson with my children, we read about how early philosophers believed atoms were the indivisible building blocks of reality, a theory that held until modern science finally split them apart. That image made primes suddenly feel alive to me: not just arithmetic curiosities, but numbers standing alone as the unbreakable foundation of mathematics.
My mind has never been quick with rote facts. Multiplication tables, for example, slipped past me when I was young, not because I wasn’t trying, but because I kept straining after the pattern beneath. Things take their time to settle, sometimes for years, but when they do, they do not sit shallowly. They sink deep, like water finding hidden roots. Primes only opened themselves to me in this way when I could see them not as columns on a chart, but as building blocks of reality, carrying weight far beyond the classroom.
From there, the connections spread. If atoms were once thought indivisible, and primes still are, what does that say about the deeper structure of reality? Thomas Aquinas’s cosmological argument from efficient cause has always drawn me: the idea that every effect needs a cause, leading ultimately to a first cause that itself has no cause. Primes feel like a numerical reflection of that same impulse, the need for bedrock. But here, too, the ground shifts. Just as atoms turned out not to be indivisible, quantum physics unsettles our classical notions of cause and effect. The vacuum itself is restless, particles appear and vanish, and even nothing exerts a measurable force.
The zeta function shows up here like a bridge. The series 1 + 2 + 3 + 4 + … diverges in the ordinary sense, yet through analytic continuation it takes the startling value –1/12, a result that predicts the Casimir effect, where two plates in a vacuum are pushed together by the weight of nothing at all. A mathematical impossibility becomes a physical truth.
Primes, atoms, first causes, quantum vacuums, they all circle back to the same mystery: what looks simple or random at first often conceals a deeper order, one that both reveals and unsettles. Even the strongest structures may fracture, but in the fracture something else is glimpsed, a reality stranger and more subtle than we imagined. Truth is like that: often hidden, often stranger than we expect, but never nothing. Just as primes quietly undergird every number, and just as the vacuum itself is never empty, truth endures even when it looks fractured.
