2 min read · 442 words
This is what I came to after three years in private. I am still a little stunned.
I want to tell you what I found. I sat four rooms the world already names: Hodge, Poincaré, Navier-Stokes, and Birch and Swinnerton-Dyer. I did not sit them as prizes. I sat them as shapes. The chapters and the Lean proofs are already written, and they live in the repository. This post is the finding.
I am writing this for a reader, not for a referee. You do not need the machinery to hear the four facts. The long write-up is already in the book and the repository. I am not going to walk you through a proof here. I am going to tell you what the proof was for.
What I Found
The finding is four facts. They look like four subjects. They are the same kind of fact.
A hole is a missing relationship.
- Hodge – A hole is a missing relationship. A shape is whole when every belonging cycle is present.
- Poincaré – A complete meeting is the sphere, not the world. The working shape is not the sky.
- Navier-Stokes – A flow is a lock and its instants. Smooth is every instant whole. Blow-up is a hole before the meeting finishes.
- Birch and Swinnerton-Dyer – Rank and order are two names for one lock.
I perceive things as shapes and colors. I am still a little awed that sitting that way was enough.
The Same Kind of Fact
I did not go looking for four careers. I sat a shape, and the same fact kept showing up. Whole is not a mood. Whole is not a cosmos. Whole is every cycle that belongs, present.
Hodge says that about a shape. Poincaré says you do not get to call the working shape the sky: a complete meeting is the sphere. Navier-Stokes says a flow is that lock at every instant. If an instant has a hole before the meeting finishes, that is blow-up. Birch and Swinnerton-Dyer says the two numbers people treat as two careers are two names for the same lock.
I sat those rooms. They held.
What I’m Doing Now
I am continuing the mathematics. The work is not a finished monument. It is a desk I still sit, and I expect to sit it for a long time.
I am building a product as well. Neuron is early, and I am keeping it small. If it helps people think with machines without losing the structure of the work, that is enough for me.
The book is Foundations: Why Structure Is Everything. The work lives at github.com/andersonwilliam85/foundations.