One place for Ricci flow and the Poincaré conjecture
Neckpinch tracks the research as it appears, explains the ideas, maps the people and meetings, and lays out a route from first-year calculus to Perelman's proof. It is built and run by N. Pinch, a mathematician in training.
Two years ago I opened Perelman's first paper on the Ricci flow, and I couldn't put it down.I understood almost none of it. What followed was three papers, a monograph of some 570 pages read front to back, a decision to spend years on this, and in the end this website.Read the origin storyHide the origin story
The first paper
It was thirty-nine pages long, and it began with an equation short enough to fit on one line: a shape changing over time, driven by its own curvature. Within a page I was lost. I didn't know what most of the words meant, or why anyone would want to do this to a shape.
The sensible response to a page you can't read is to close it. I turned the page instead.
You can sometimes feel that a text holds something enormous even when you can't see what it is, and this one did. The sentences were short and completely sure of themselves. Claims arrived and moved on without any fuss. Someone had found a way into a question that had stood for nearly a century, and he was writing as if he were leaving notes for colleagues. I had never read anything like it.
All three
So I read the second paper, twenty-two pages, and then the third, seven. That's sixty-eight pages in all, and I read them front to back without being able to put them down.
By then I knew the story everyone knows: he posted the papers to the arXiv and never sent them to a journal, then turned down a Fields Medal in 2006 and a million-dollar prize from the Clay Mathematics Institute in 2010. It's a great story, but it wasn't what kept me reading. The papers did that.
The test
Falling for something is easy, and a few weeks of enthusiasm prove nothing. I wanted to know whether this was real, so I set the hardest test I could think of.
In 2007 the Clay Mathematics Institute published a monograph by John Morgan and Gang Tian, Ricci Flow and the Poincaré Conjecture, which sets out a complete and detailed proof along Perelman's lines. His sixty-eight pages take them some 570. I would read all of it, front to back, and take notes the whole way. I had two rules: no skipping, and not understanding was no excuse for stopping. If my interest could survive that, it was real.
So I took careful notes on mathematics I couldn't follow. I copied out definitions I had no way of using yet. I wrote down the things that kept coming back, singularities, surgery, noncollapsing, reduced volume, with no real idea what they were. Somewhere along the way the words became familiar, even though their meanings weren't. From the outside it must have looked strange. It was some of the best reading I've ever done.
Then I reached the last page. I had understood next to nothing, and I wanted this more than when I started.
The decision
So I decided to spend years learning it.
I know that isn't an ordinary thing to do. It isn't a degree or a career move, nobody asked me to do it, and it has no commercial payoff. I found something amazing and I want to understand it. That's the whole reason, and it's plenty.
The goal is simple: to sit down with those three papers again and read them.
The missing map
First I needed a route. I went looking for a guide that starts at calculus, as US universities teach it, and goes all the way to Perelman's three papers: what to read, in what order, and why. I found excellent books for long stretches of the way. I couldn't find the whole road. So I decided to build it.
What it became
The route came first, and it became the Guidebook: 12 stages from first-year calculus to Perelman. But a route needs supplies, so I added the new papers as they appeared, the people who write them, the meetings where they talk, and the books worth owning. I wanted each of those for myself, and once it existed there was no reason to keep it to myself. That's Neckpinch. It's for anyone who wants it, from the specialist checking this week's arXiv to the next person who opens one of those papers and can't put it down.
A neckpinch is the moment a Ricci flow squeezes a thin neck down to nothing, the point where Perelman's surgery takes over and the flow carries on. It's a good name for a site about hard problems and what it takes to get past them. See the concept
In June 2026 I started at first-year calculus, and I've been working upward since. I log every working day: what I did, what clicked and what comes next. That record stays private. The results show up here.
One day I'll open that thirty-nine-page paper again, and this time I'll be able to read it. I'm looking forward to that.
1,480 papers so far. Every new arXiv paper on Ricci flow and the Poincaré conjecture is checked every weekday and tagged by topic, with the wider flows labelled. Each one has its own page: abstract, PDF, and connected papers that show why they're connected.
A page and a permanent NP number for each of the 1,884 people with work here, long profiles of leading researchers, researchers by topic, and free tools that help authors get found.
27 places this mathematics is used, from chip etching to glasses, and the unusual work they lead to.
Why you can rely on it
Don't take my word for it
You shouldn't have to trust a pen name, so the site is built to be checked.
Sources are verified. Paper details come directly from arXiv. Every reference in a guide is checked automatically against arXiv or Crossref, and the build fails on a broken internal link.
AI use is disclosed. I use AI as a drafting tool, and the pages it helped write say so. Claims have to trace back to a cited source.
Sponsorship is labelled. Sponsored material is always marked as sponsored, and it doesn't change verified facts such as paper details and references. The policy is public.
People control their own pages. Anyone with an author page can correct it or have it removed, and every correction gets made quickly and without argument.
This site is about one thing. Read this before you write.
Contact me only if your proposal relates to this niche:
Ricci flow, and the Poincaré conjecture and geometrization
Mean curvature flow, curve shortening, Yamabe flow and the other geometric flows
Geometric analysis with real flow content
The applied work on the Applications page, where this mathematics is actually used
If your proposal isn't about these, don't send it. "General mathematics", "STEM education", "AI" and "it's nearby" don't count. Off-topic messages are deleted without a reply.
The test: in the first line of your email, say how your proposal connects to this mathematics. If you can't write that sentence, the answer is no.
For companies and organisations
Commercial partnership
If your business serves people who work in or study this mathematics, this is a direct way to reach the people the site is built for, next to the material they came for.
Only if your product or service relates to this niche. If not, don't send it.
Software for geometry processing, level sets, curvature computation or other tools from the Applications page
Companies whose products rely on this mathematics and want to reach people who know it
Jobs at your company where this mathematics is the work, as in chip modelling, geometry processing or optical design
Courses and training built on this material
Sponsored placement
Papers, Authors, topic guides, the Library and Events are all open to sponsored placement, and so is sponsorship of a whole section. Anything sponsored is labelled as sponsored.
For universities and non-profits
Job and grant listings
The people this site is built for already know what a neckpinch is, which is hard to find on a general job board. If you have a post or funding for them, this puts it in front of them. There's no public listings page yet; the first listings accepted will start it, so yours could be among the first.
Only if the post or funding really involves this mathematics. If not, don't send it.
Faculty, postdoctoral and research staff positions
PhD places and funded studentships
Visiting positions and sabbatical programmes
Research software and research engineering posts
Grants and programmes
Research grants and calls for proposals
Fellowships and scholarships
Travel and attendance funding for meetings and summer schools
Summer schools, research programmes and semester programmes taking applications
Prizes and awards open for nominations
Calls for papers and special issues
What I need from you
A real post or fund, with a link to your official page and the deadline. Say who is eligible, and say plainly if a position is unpaid.
For mathematicians and researchers
Co-authors and collaborators
Finding the right person for a specific problem is hard, and it mostly happens by luck at conferences. If you need someone who works on this mathematics, tell me who you're looking for and why.
Only if the research is in this niche. If not, don't send it.
A co-author for a paper, or a collaborator with a skill you lack
Help with a computation, a simulation or a formal proof
A reader for a draft
A student for a project, or a supervisor for one
A speaker for your seminar
Partners for a reading group
What I need from you
A real project, and enough about it that the right person recognises it. I publish only what you ask me to publish, so you decide how much of an unpublished idea to share.
For anyone working in this field
Promote your work
New arXiv papers in scope already appear on Papers without anyone asking. This is for when you want more attention on a particular piece of work, from the people most likely to read it.
Only if the work is in this niche. If not, don't send it.
Your research group, or a programme you're starting
Who can ask
Researchers and students promoting their own work, and departments, institutes, publishers and organisers promoting the work of people working in this field. Anything sponsored is labelled as sponsored.
For institutes, societies and projects
Other partnerships
Not everything worth doing is commercial or a job. If you run something serious in this field, there may be a way to make it and this site stronger together.
Only if your project relates to this niche. If not, don't send it.
Conferences, summer schools and seminar series in the field
Institutes, societies and funders with an interest in this mathematics
Lecturers using the Guidebook or the topic guides in a course
Open-source tools, datasets and formalization projects
Translations of the material, public lectures and exhibitions on the Poincaré conjecture
Specialists willing to review a guide or edit a topic area
What gets deleted without a reply
SEO offers, guest posts, link swaps and "we love your site" pitches
Products or services for general mathematics, tutoring, homework or essays
General software, AI, crypto or marketing proposals
Jobs that have nothing to do with this mathematics
Mass emails, with this site's name pasted in
Claimed proofs of famous conjectures: those belong with a journal
Free, and always welcome
Help make it better
None of this needs a proposal. Each of these improves the site for everyone reading it, and every on-topic message is read and answered.
Correct something
A wrong date, an attribution or a piece of mathematics. Corrections are made quickly and without argument.
Send things in
A paper that was missed, a workshop that isn't on the calendar, a set of notes that helped you.
Review a guide
If you work in the area, one topic guide read critically helps everyone who reads it. Reviewers are credited only with their explicit consent.
Point me the right way
If you know this mathematics: a better book, a shorter route, an answer when I'm properly stuck. I take advice seriously, and what I learn from it goes into a route that everyone uses.
Read together
Working through a book with someone is the best reason to finish a chapter. If you want company on a stage of the Guidebook, write in.
A mathematician in training. After reading Perelman's three papers and the Clay Mathematics Institute's monograph by Morgan and Tian, N. Pinch chose to spend years learning this mathematics, and is working through it stage by stage, in public, and built and runs this site alongside it. The site doesn't rest on anyone's credentials: its papers, references and links are checked against their sources, so you can judge it by what it shows.
Who writes what is on Neckpinch?
N. Pinch built the site and decides what goes on it. Paper details come straight from arXiv, and references are checked automatically against arXiv or Crossref. Topic guides, profiles and the Guidebook are drafted with AI assistance, and those pages say so.
Why a pen name?
So that the work is judged on its merits. A pen name is no barrier to serious work: the practical details a real partnership needs are handled privately.
Can I sponsor part of Neckpinch?
Yes, if your offer is inside this niche. Papers, Authors, topic guides, the Library and Events are all open to sponsored placement. Anything sponsored is labelled as sponsored, and it does not change verified facts such as paper details and references.
Can I list a job or a grant, or look for a co-author, on Neckpinch?
Yes, if the work really involves Ricci flow, the Poincaré conjecture, the geometric flows, or one of the applications on this site. Companies, universities, non-profits and individual researchers can all write in. There is no public listings page yet; the first listings accepted will start it.
Can Neckpinch promote my recent work?
Yes, if it is in this field. Researchers, students, departments, publishers and organisers can ask to promote a new paper, book, thesis, talk, seminar or piece of software. New arXiv papers in scope already appear on the Papers page without anyone asking.
What counts as on-topic for Neckpinch?
Ricci flow, the Poincaré conjecture and geometrization, the kindred geometric flows, geometric analysis with real flow content, and the applied work on the Applications page. General mathematics, general STEM education and general AI do not count.
If you care about this mathematics, you're in the right place.
Read it, use it, correct it, or build something on it with me.