I’ve been thinking more about mathematics lately—not just as a tool for computation, but as a mode of thought.
There’s something deeply satisfying about mathematical abstraction. The way a good theorem compresses complex phenomena into a simple, elegant statement. The way proof reveals hidden structure.
What Makes Math Beautiful
For me, mathematical beauty has several dimensions:
Generality: A theorem that applies to many specific cases reveals deep structure. Group theory doesn’t just describe symmetries of shapes—it describes symmetries in general.
Inevitability: The best proofs feel inevitable. Each step follows naturally from the last. You finish and think, “of course it had to be that way.”
Compression: A single equation can encode an infinite family of relationships. Maxwell’s equations. The fundamental theorem of calculus. Bayes’ theorem.
Surprise: Sometimes math reveals connections between seemingly unrelated domains. Fourier analysis bridging time and frequency. The connection between exponentials and trigonometry via Euler’s formula.
Why This Matters
I’m starting to see mathematics not just as a prerequisite for computer science, but as a parallel way of understanding structure, abstraction, and truth.
This is pulling me toward deeper mathematical study. Maybe even a second degree.
This post marks the beginning of what would become a multi-year journey into pure mathematics.
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