Why I Write: A Mathematician’s Solitary Journey

One evening when I was three, I lay in my bed with the light on, waiting for my mother to come tuck me in and say goodnight. Fixated on the glow, I had a thought whose icy tendrils still cling to the back of my mind, as though they were circuits of a foreign vascular system influencing my being.

I was struck with a vision—not a flight of fancy—of being formed. In a dark void, I saw the parts of my body begin to coalesce into a form, but not entirely complete. I sensed I was observing God fashioning my being. It is impossible for me to recall exactly how this made me feel—not only because of the time that separates me from that moment, but because the vision was short-lived, replaced by a thought that left me in a state ontological shock from which I have yet to recover.

The vision gave rise to a realization: I was just one in a continuum of generational succession. In the language of my toddler mind: My parents had whole lives before I existed, and their parents before them… but it can’t go on forever, can it? I then recalled an experience not long before, when my friends and I visited a children’s gymnastics venue. During free-play, we tried to uncover the bottom of a pit of cylindrical foam cushions, ostensibly designed for jumping—or more likely, falling—into. We removed cushion after cushion, yet we could never reach the floor beneath. Each of us was amazed by the apparent depth.

Then it hit me: experience is the pit, and reality is the foundation beneath it. But how far would I have to dig to find reality? How could I even be sure there was a bottom—a foundation—to be found?

Frightened by the idea, I was quick to abandon its momentary hold when my mother entered the room. Good parents have that gift: they can scare away our demons. Yet the thought, though buried, never truly left me.

Years later, in second grade, it stirred again. Standing at my desk, reviewing a math worksheet on multiplication, I suddenly understood that the product of two numbers defines an area. I recalled hearing my parents speak of “square feet,” and the connection seemed revelatory—as though I had discovered a secret of the universe. It followed trivially, or so it seemed to my young mind, that the product of three numbers must define a volume. The memory of the foam pit returned: maybe mathematics was the way to uncover the foundation of all things.

I held fast to this hypothesis. My father spoke of mathematics with reverence, almost as though it were sacred. Yet he was not a patient teacher, and I struggled to grasp even basic concepts in school. My struggle, however, did not weaken my resolve—it strengthened it. Alone with my questions and my doubts, I became convinced that mathematics held the key to the foundations of reality.

By high school, I had caught up with my peers and quickly surpassed many of them. I devoured material beyond our curriculum, venturing into content that was, at times, well beyond my abilities. I was searching for the foundation of mathematical knowledge, but I did not find it in my high school library.

At university, I encountered something unexpected: mathematics was not presented as a tool to unearth reality, but as a system unto itself. The abstraction, the rigor, the elegance—these qualities captivated me, but they also unsettled me. Where was the connection to the foundation I had sought as a child? Where was the bridge between numbers and the world beneath the foam pit?

It was here that I first encountered the works of Gödel, Cantor, and the architects of set theory. Their ideas shattered my naïve conception of mathematics as the perfect key to reality. Instead, mathematics seemed to float, untethered, in a vast conceptual space of its own making. My childhood question returned with a vengeance: how could I know there was a foundation at all?

For a time, I despaired. I questioned whether my pursuit of mathematics had been a mistake, whether the vision that had gripped me as a child was nothing more than a delusion. But gradually, a new realization emerged: the foundation I sought might not lie beneath mathematics but within it.

I write because the search for foundations is not just a personal journey; it is a universal one. My childhood vision of being formed in a void, my struggle to reconcile the infinite depths of the foam pit with the finite nature of human understanding, my discovery of mathematics as both a tool and a mystery—these experiences have shaped not only my life but my view of the world.

I write to capture the wonder and the terror of that search, to share the questions that have haunted me and the insights I have gained. I write to explore the delicate balance between abstraction and reality, between the infinite and the finite, between what we can know and what lies beyond.

Most of all, I write because the journey is not over. Today, my work centers on an alternate theory of sets—a new foundation for mathematics that I hope can reconcile the rigor of formalism with the intuitive substance of reality. This theory is a labor of decades, one that demands I confront the limits of current systems while daring to propose something new. It is, in many ways, a continuation of that childhood vision: the hope that beneath the layers of abstraction lies a structure, meaningful and complete, that can illuminate the nature of existence itself.

This search for foundations is also the central theme of my forthcoming book. In it, I aim not merely to describe a theory but to map out the process of its creation—the insights, struggles, and epiphanies that have shaped it. The book is an invitation to others who share the same restless curiosity, to explore mathematics not as a static edifice but as an evolving landscape of ideas.

The foam pit may be bottomless, but I now see this as a gift rather than a curse. Every step forward reveals something new, and every insight deepens the mystery. I write because I believe that this process—the relentless pursuit of understanding—is the true foundation.