Update to the goals of this blog.

My journey into mathematics so far has been shaped by a single idea: structure emerges by ruling things out. Groups, rings, and fields stopped feeling like static definitions once I began seeing them as statements about which operations are reversible, when cancellation is allowed, and what kinds of collapse are prevented.

This theme has run through the recent posts on this blog. In algebra, it shows up as the distinction between groups, rings, fields, and modules. In number theory, as cancellation and non-collapse. 

To push this way of thinking further, I’ve started working through Frederic Schuller’s Lectures on the Geometric Anatomy of Theoretical Physics. Schuller begins with logic, then builds sets, topology, and geometry from first principles. It feels like a direct stress test of this constraint-based view, scaling it from discrete arithmetic to the continuous structures underlying physics. I fully expect to fail as this leap is immense. However, I've decided to give it a whirl with the same questions in mind: what rules are fixed at the start, what operations preserve information, and which definitions prevent collapse rather than describe outcomes?

Going forward, I’ll also be writing about developmental biology, especially developmental neuroscience, through the same lens. I’m interested in development not as instructions being executed, but as possibilities being progressively removed. Gradients, transcription factors, and boundaries act as constraints that preserve distinction and make reliable structure inevitable.

This is not a departure from mathematics, but an extension of the same way of thinking into biology. Across all of these domains, definitions and structures are safety guarantees. The goal here is not coverage, but clarity, where I document the moment when a system stops feeling clever and starts feeling inevitable.