Exploring the Intersection of Mathematics, Philosophy, and Abstract Art

What do mathematics, philosophy, and abstract painting have in common? More than you might think. For Ritu Raj, the canvas is where logic meets feeling, and questions become form.

Circle Barbed Wire, 4ft x 4ft, Geometric Splendor, 2023

At first glance, mathematics, philosophy, and abstract painting may seem like separate domains — disciplines driven by different impulses and audiences. One is exacting, one contemplative, one expressive. But in my experience, they are deeply intertwined. Beneath their surface differences, all three are explorations of pattern, meaning, and the unknown.

My path has crossed all three. I began with mathematics — captivated by the elegance of equations and the strange beauty of abstract logic. I moved through the world of technology and systems thinking, where precision and innovation lived side by side. Along the way, I immersed myself in philosophy, fascinated by questions that have no final answers: What is being? What is truth? How do we know what we know? And now, in my life as an abstract artist, I find that these threads don’t just follow me — they shape the very way I make and understand art.

Mathematics trained me to see structure in chaos. It gave me a reverence for systems — not just systems of logic, but the invisible frameworks that hold form together. When I paint, I often begin not with an image, but with a rhythm, a tension between order and disruption. Geometric abstraction allows me to play with balance and symmetry, but I’m just as interested in the moment those structures begin to fall apart — when intuition interrupts precision.

Philosophy, on the other hand, taught me to sit with ambiguity. Where math seeks answers, philosophy values the question itself. I bring this same curiosity to the canvas. I’m not trying to “say” something in a fixed way. I’m trying to open something — a space of feeling or reflection that may be different for each viewer. This is why abstraction, for me, is not decorative. It is a form of inquiry.

In a single piece, I might weave together formal structure, emotional gesture, and conceptual tension. A line may echo a theorem; a brushstroke might carry the uncertainty of a philosophical paradox. The result is not a solution, but an invitation — to perceive differently, to feel something not easily explained, to confront what lies just beyond logic and language.

When people ask what my paintings “mean,” I often say: they don’t illustrate — they resonate. Like a well-formed equation or a philosophical koan, they invite contemplation, not conclusion. They aren’t meant to be solved; they are meant to be lived with.

In the end, mathematics, philosophy, and art all strive toward a deeper understanding of reality — each in their own way. They remind us that clarity can be found in complexity, that beauty and truth often reveal themselves through repetition, disruption, and form. For me, painting is where all these languages converge. It is where I stop seeking the perfect answer and start trusting the unfolding.

You can view the full Geometric Splendor Collection here.