RefacteAbout Henry Shin
Hello, I’m Henry.
I’m a mathematician working independently in San Diego. I studied mathematics at Harvard with Richard Taylor. My research has spanned group theory, algebra, additive combinatorics, and geometric analysis.
My research papers come with source editions, publication details, and corrections. The Taiko obstruction has a worked companion showing how a group-ring construction becomes a finite incidence problem. Research records and dated source packages are also preserved in the Tensorgami archive.
Current work
I’m interested in how a choice of variables or a different way of recording a problem can make its workings clearer. A weighted difference can separate a recurrence into independent updates; a labelled graph can turn a subgroup membership question into a path test.
I want to develop this practice further: carry difficult group-theoretic questions into finite incidence structures, graphs, or matrix problems; work with the resulting constraints; and prove what the answer means for the original question. Numerical optimization can help discover a witness when an exact certificate completes that bridge.
The expositions work through how these choices are found and checked. They range from short calculations to longer mechanism calculi, including Cayley–Hamilton by cycle exchange and an explicit basis of tensor chains. The notes on the approach explain what connects them.
My essay AI research and the remaining human advantage connects this practice to sparse numerical algorithms for finite weighted graphs and structured matrices. It argues that AI is rapidly eroding the advantage supplied by abstract proof construction, and proposes tests of where specialist knowledge can still improve the guarantees and cost of a dependable computational method.
Writing and intellectual life
My essays ask what a proof makes possible, how mathematical understanding develops, and how expertise is sustained. Understanding has value beyond competitive advantage; deciding where to build a distinctive research contribution is a different question. Mathematical Life in the Age of AI brings these questions together through learning, assistance, credit, and shared inquiry.
I also write about film. The Authority of a Vision considers knowledge, belief, and political allegiance in Villeneuve’s Dune.
Other pursuits
I make patterns on large twisty cubes, working out commutators that rearrange small groups of pieces. The pleasure is in composing the moves into a picture without undoing what is already in place.
I also play StarCraft: Brood War and Overwatch. I enjoy reading a changing game, coordinating with teammates, and finding where the next action matters. The Interests page has photographs, game recordings, and more about these pursuits.
Correspondence
If an argument here connects with your work, or you see a step that needs repair, I’d be glad to hear from you.