Hexagon
There was no personal problem, no world problem, whose eloquent solution did not exist— somewhere in some hexagon.
—Jorge Luis Borges, “The Library of Babel” [1]
New repository
I am writing to announce Hexagon,
a new repository for research works in the mathematical sciences and theoretical computer science.
This has been a joint effort of many people over the last couple of months, starting in early
August 2026. We felt that the proliferation of results proved with LLM assistance required a
new model for collecting the associated papers. Besides wanting these
works to be citable and reliably stored for long periods of time, we wanted to allow lower
barriers for authorship and for community interest than the arXiv. We also wanted for
these works to have a home besides random GitHub repositories or X/Bluesky/Mathstodon/LinkedIn posts.
In order to support the development of this project, we founded the Hexagon Mathematics Foundation in the state of Delaware and we intend to apply for recognition of tax-exempt status under section 501(c)(3). The Board of Directors consists of Mohammed Abouzaid, François Charles, Bryna Kra, David Savitt, and Lauren Williams. I serve as the first Executive Director. And, we have a wonderful Advisory Board, where Kevin Buzzard, Akhil Mathew, Johannes Schmitt, Steinn Sigurðsson, Nikhil Srivastava, Ravi Vakil, and Rachel Ward serve. For more details, see our who we are page.
My personal interest
When working with a group of people brought together by an FRG grant, we clicked a button and
discovered a new result, namely derived invariance of Hodge numbers of fourfolds in characteristic
zero. In the past, this would be a result I would have submitted to an excellent, but not
top, journal. In this case, there is no way I would put my name to the result. Instead, I blogged
about it here. This is a brittle way
to aggregate mathematics. Now, it is on Hexagon as hexagon:2609.00104.
The creation of new results happens naturally in working with LLMs. They bubble up, even as side results. My personal hope is that it becomes the community standard to identify these and submit them to Hexagon.
The Lifecycle of Hexagon Objects1
My ambition is that Hexagon is where mathematical ideas emerge from the water for the first time as they evolve toward community acceptance and understanding. Later, they should be written up in forms suitable for arXiv submission, publication, and canonicalization (Tao [3]).
Hexagon specifically allows submissions entirely generated by LLMs and even where the submitters claim no human understanding. These results should be available to the general community.
Submissions by the big labs
Hexagon welcomes submissions by large labs working on language models. These results should be available to the mathematics and TCS communities by default on a platform that the community maintains. We also welcome submissions by large collaborations or other organizations.
FAQ
How was Hexagon created? At some point, a group of people convened in early August, brought together by our social networks with the common theme of interest around creating a home for mathematical results which were rapidly being produced with the assistance of LLM tools. This group included most of the current members of the Board and Advisory Board of the Hexagon Mathematics Foundation, as well as several other academic mathematicians who did significant work but preferred not to be named. In August we discussed ideas on a private Zulip channel (thanks ICARM!) as we started building the site itself.
We talked to a lot of people at that time, including arXiv leadership, and we also examined
closely-related AI-era repositories. From the arXiv we learned that they were not going to
provide the home for these results we were looking for; instead they are focused on maintaining
their project as it is today, and I am happy for that. None of the other repositories had gained
sufficient traction or had all of the policies we were hoping for.
The foundation was incorporated as a nonprofit in Delaware and we intend to apply for recognition of tax-exempt status under section 501(c)(3).
The entire system was created with the help of OpenAI’s Codex and is hosted on widely available commercial cloud servers. This is rather easy nowadays. What takes time is deciding exactly what features you want and carefully writing the text on the website.
How is Hexagon funded? So far, it is entirely funded by the people involved, although we are exploring other funding routes and paths to sustainability. Today, except as customers of cloud infrastructure companies, we have no relationship with any for-profit company or other organization.
Why Hexagon? At some point, the group started talking about names involving Babel, which refers to Borges’s story The Library of Babel [1]. But, because it has other connotations as well, we did not go that route. Instead, someone suggested Hexagon in reference to the shape of the halls in Borges’s library.
Does Hexagon accept micro-results? Hexagon welcomes small, incremental improvements as long as they are of interest to the mathematics and TCS communities.
Is formalization required for a Hexagon submission?
No, Hexagon is not primarily a formalization project, but it links to formalization projects, like mathlib, Palomar, prove2.me, and TauCeti.
What is the difference between a contributor and a submitter? On Hexagon, Contributors are humans or organizations responsible for the creation of submissions. Submitters are humans with ORCID-validated accounts on Hexagon. In some instances, Hexagon will provide individual account holders the capability to submit on behalf of other humans or organizations.
Are there rate limits?
Yes, Hexagon limits the rate at which one can submit. It starts at 1/day, and grows at Hexagon’s
discretion. This growth is based on previous submissions passing through moderation. (The arXiv recently announced
its own repository-wide submission limits [4].)
Is there API access?
Yes, Hexagon provides both read-access via API (in the style of the arXiv) and submit-access via API tokens
available from users’ account pages.
Why is Hexagon marked as being in beta? We are still adding features and testing scalability. We welcome any recommendations for how the site can be made more usable.
References
[1] Jorge Luis Borges, “The Library of Babel,” translated by Andrew Hurley, in Collected Fictions, Penguin Books, 1999, publisher page.
[2] Ted Chiang, “The Lifecycle of Software Objects,” in Exhalation, Vintage, 2019, publisher page.
[3] Terence Tao, Mathematics in the age of AI, 2026, arXiv:2608.16753.
[4] Kat Boboris, Fair Moderation, Equitable Access, and AI: arXiv’s Updated Rate Limit Policy, arXiv Blog, 1 October 2026, article.