A Feral Mathematician is a public notebook for mathematics pursued with one foot inside the academy and one foot outside the walls.

This site is a place for diagrams, algebra, geometry, representation theory, mathematical physics, astronomy, and stray ideas that refuse to stay politely inside a single subject. I am especially interested in the old and still unfinished conversation between mathematics and physics. Before the modern division of departments, journals, and professional territories, these were not separate kingdoms so much as different dialects of the same language.

My own pull is toward the modern frontier of that conversation: quantum field theory, topological quantum field theory, string theory, and the long-running search for unification. I am especially interested in the categorical and diagrammatic machinery being developed to make parts of those theories precise. In the longer term, I am drawn to Hilbert's sixth problem and to the question of what it would mean to axiomatize physics.

The word feral is meant partly in jest, but only partly. It names a way of doing mathematics that is serious without being domesticated. Rigorous, but playful. Historically aware, but not antiquarian. Willing to wander through category theory, knot diagrams, Lie algebras, Temperley-Lieb algebras, analysis, and mathematical physics without asking too anxiously whether the border crossing has been approved.

It also names something more personal.

I was diagnosed fairly young with multiple sclerosis, young enough that it was considered juvenile-onset MS. The symptom that led to my diagnosis was sudden blindness in my left eye. I woke up one morning and my universe was different. I never regained vision in that eye. Since then, MS has sometimes announced itself by making me wake up with some new difficulty: a body that no longer quite obeys, a hand that has forgotten some part of its old confidence, a frightening proximity to paralysis, or a new compromise in how I see the world.

My right eye has also been affected more mildly. Its pupil no longer responds well to changes in light, and color itself is sometimes less certain than it ought to be.

That experience shapes how I think. It has made me attentive to fragility, adaptation, and the strange persistence of form under deformation. A life with MS is, in part, a life of repeated relearning. It means finding new paths when old ones fail, and learning again how to move, read, play, think, and make.

I am, or perhaps was, a guitarist, though I am reluctant to put that entirely in the past tense. I have played classical, blues, and jazz guitar, and the classical position and fingerstyle technique have become more than musical habits. They are also ways of preserving dexterity, working around numbness, and keeping contact with a body that sometimes feels like it is negotiating against me.

Since early childhood, I have also been fascinated with the night sky: naked-eye observing, binocular astronomy, telescopes, astrophotography, and someday perhaps radio astronomy. The night sky has always appeared to me as this grand arena where mathematics, physics, patience, and wonder fight for my amusement. It is humbling, as it should be: nature is stark and terrifying and at the same time elegant and soothing. It reminds me that abstraction is not an escape from reality, but one of the ways reality becomes visible, visceral, tangible.

This blog is not meant to be a polished encyclopedia. It is closer to a scriptorium, a lab notebook, or a field journal: fragments, explanations, computations, diagrams, questions, false starts, and occasional attempts at synthesis. Some posts will be expository. Some will be technical. Some will be speculative. Some will simply record what I am trying to understand.

The guiding conviction is simple: mathematics and physics belong together, and mathematics itself should remain large enough to include rigor, beauty, play, illness, adaptation, and mischief. Serious work need not be joyless.