RefacteMathematical writing by Henry Shin
Changing what becomes elementary.
Find the representation that exposes the decisive constraints.
Essays, worked mathematical arguments, and research on what a useful description makes possible.
Featured essay · Research direction
The old refuge in abstraction is over. I argue for discovering better diagnostic and repair rules where spectral graph algorithms, matrix analysis, and numerical analysis meet, and explain how a specialist must earn an advantage beyond strong AI.
Read the essayExplore the mathematics
Each article develops its own argument. Start from your background; there is no required sequence.
Separate a recurrence, count spanning trees, and prove a matrix identity.
Explore 6 articlesTurn words and edge labels into calculations with paths and loops.
Explore 4 articlesMake first-order change exact, then test what happens at the next order.
Explore 4 articlesThese exact constructions show how to choose a representation and prove what it preserves. The featured essay asks what further guarantees are needed when approximation, accuracy, and computational cost enter.
Also browse notes and problems in algebra, arithmetic, and analysis.
A research case
A finite incidence description exposes incompatible coverage and girth requirements, closing the specified triple-girth Taiko assembly route across all support sizes in the theorem.
The paper is an exact example of strengthening an insufficient description—the practice that the essay takes into sparse numerical computation.
Related essays
Choose a weighted difference and remove the remaining interaction.
A working example
Start with sn+1 = sn + sn−1. Try un = sn − c sn−1.
At c = 1, the extra input remains. The ordinary difference has not separated the recurrence.
Derive the weight, step by stepCompare the identity with the shear J(x, y) = (x + y, y). Both have eigenvalues 1, 1. Iterating the shear gives Jⁿ(0, 1) = (n, 1), whereas the identity leaves (0, 1) fixed.
The eigenvalue list cannot calculate this difference. Retaining the off-diagonal action can.
Read the comparison, or construct a basis of operator chains.
A short biography and notes on current work.
Patterns on large twisty cubes and notes on playing Brood War and Overwatch.
Complete earlier studies, their reading versions, and fixed dated editions.