Journal

Why this site exists, and where the first three months went

I studied for three months before building any of this. The notes lived in a spreadsheet. I made the site because I couldn't find the thing I was looking for — a place where Ricci flow is gathered in one spot for people arriving from outside.

This is the first entry, but it isn't the first day.

I started in June. For three months — all of Stage 1, Spivak and Axler, calculus and linear algebra — the notes lived in a spreadsheet on my laptop. One row per session: date, what I read, what I understood, what I didn't. It worked, in the way spreadsheets work. It was also completely private, unsearchable after about week four, and it had a column called "??" that grew faster than any of the others.

I'm not going to reconstruct those three months here. The entries would be written from memory and they'd be tidier than the truth. Stage 1 is marked finished on the path, and that's the honest summary: I can write an ε–δ proof now, I understand the derivative as a linear approximation rather than a slope, and the spectral theorem was the first moment the destination felt connected to the work — symmetric operators have orthonormal eigenbases, the Ricci tensor is symmetric, and suddenly "positive Ricci curvature" reads as a sentence about stretching rather than an incantation.

Why build a site at all

Because I couldn't find one.

When you decide to learn this subject from outside a university, the problem isn't a shortage of material — it's that the material is scattered and none of it is arranged for you. Papers are on arXiv, in a firehose sorted by date, where a newcomer can't tell a landmark from a footnote. Lecture notes sit on the personal pages of a dozen mathematicians, in whatever layout they used in 2006. Conferences are announced on institute calendars you only find if you already know the institute's name. Everything assumes you're already inside.

And there's no room for the rest of it. No obvious place to ask a naive question, no way to see what other people teaching themselves this are reading, no sense that anyone else is out here doing the same thing on their evenings. Mathematics has famously good communities — MathOverflow, arXiv itself — but they're built for people already fluent, and rightly so. Ricci flow in particular is a small enough field that there's no popular on-ramp at all.

So this is the thing I wanted to find:

  • Papers — everything new on Ricci flow and the Poincaré conjecture, pulled from arXiv automatically each weekday, tagged by topic so you can follow one thread. I can't read most of them. I collect them anyway.
  • Events — the conferences and talks, including online ones, which I'd never have known existed.
  • The Path — the reading order I'm following, with the books I'm actually using, written for someone who doesn't know where to start.
  • Concepts — the ideas waiting further down, so the destination stays visible.
  • People — who works on what, and how to write to a mathematician without wasting their time.
Note · The bargain

I keep the journal for myself. The rest of the site is for the person who, eighteen months from now, types "how do I learn Ricci flow" into a search box and finds nothing useful. That was me in June.

Stage 2 starts now: Tao's Analysis I, back to what a number even is. The spreadsheet is retired. If you're somewhere on this road too — ahead of me, behind me, or just curious what a neckpinch is — say hello. I'd like this to be less lonely than a spreadsheet.