Mathathon: A cooperative virtual mathathon

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If you are interested in math, at the level of advanced High School up to publishable research, please join us for an experiment in cooperative mathematics: a non-competitive math "hackathon" to solve a set of specific "open-to-us" problems. This is a fully virtual event, running from Friday evening to Sunday at noon. This may be the first event of its kind. Our goal is to cooperate, perhaps by forming teams on the spot, to solve a set of specific geometry problems. The problems all involve chains of simplices---that is, triangles in 2D or tetrahedra in 3D. Some of the problems are probably easy, some of are probably hard. The spirit of this "mathathon" is cooperation.

At this time, no cash awards are planned, but we will judge submissions and announce a large number of awards. Every submission will be made through "git", a distributed online versioning system. Submissions must be licensed under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) (in other words, all submissions are "free software", or, in this case, "free math".)

Because this may be a new and confusing kind of event, we are planning to have facillitators present at all times (except for a break at night in the U.S.) available online via video chat and Slack for the purpose of answering questions. We encourage international participation, though the language of the mathathon is English.

As a changing work-in-progress, we have published the current list of problems and the current rules of the mathathon:

We encourage team participation, and the facillitators will attempt to help you form teams if desired.

We've written an interactive web page that let's you graphically play with solutions to the easier problems defined by the mathathon:


How can I contact the organizer with any questions?

Contact Robert L. Read, PhD, via email at:

What is the technology that will be used?

Will we be using a Zoom room which allows up to 100 participants: for video chat and a Slack Team for text communications.

How do I start on Friday night?

Come to the kick-off in the Zoom room Friday night, a video and audio chat, and join the Slack Team. The kickoff will include instructions and may have a brief keynote by some famous math educators. All questions will be answered by our moderators at that time.

Is there an age restriction?

No, but unless you are the equivalent of a very motivated high school student none of the problems will likely be addressable for you.

How hard are these problems?

We have attempted to create a broad spectrum. The easiest are probably solvable in a weekend by any motivated college statement. The hardest problems are almost certainly publishable if solved.

How much have you researched these problems? Are they really "open problems"?

Public Invention has published an academic article in the Journal of Mechanisms and Robotics: Transforming Optimal Tetrahelices Between the Boerdijk–Coxeter Helix and a Planar-Faced Tetrahelix, so we have good reason to believe that some of the harder problems have never been studied before. However, these are not "recognized open problems" that will make you famous if you solve them. The are, we hope, interesting and publishable problems in some cases. In the case of the easier problems, we have not researched them so much; the answers to these questions may already be published or well-known.

If you have published a paper on this, isn't this whole thing for your benefit?

Not really. This is a free invent and Public Invention makes no income from it. To publish anything that comes out of the hackathon without properly attributing it would be both plagiarism and illegal. We do benefit from having more research in an area we are interested in, but only very abstracly.

Then why are you doing this?

I've been to a lot of hackathons, and I don't like the competitive nature of them. As the founder of Public Invention, I am dedicated to inventing things in the public good, and that includes mathematics. This is an experiment. Can we create a new culture of non-competitive hackathons around something deep: solving unsolved problems in mathematics?

What do we do if we get confused or stuck?

We have lined up volunteer moderators to be present via Slack and/or Zoom room all the time (except late at night.) They may be able to help. They will not be experts in the mathematics involved.

I am completely alone, but would like to participate. Can you help me join a team for the duration?

We intend to try. We will be using video chat to try to find out what people are interested and what their skills might be.

How will the submissions be made?

To be eligible to for our purely symbolic awards, you have to submit your work via "git". We will explain how to do this, or do this for you if we don't have too many people. The format can be anything, although we would prefer PDFs in combination with the source documents that generated them. By making a submission, you agree that your work is relased under the Creative Commons by Attribution 4.0.

What if I don't come up with anything, or if I am not sure it is correct?

We won't be sure if it is correct either! We think it will be more fun for everybody to submit everything, and to check in work before Sunday even it if is unfinished, so that others can build on your work.

What is the point of publishing stuff that is incomplete or wrong?

Junk and detritus are the raw materials of beauty. We don't believe in the myth of the genius mathematician. Math is hammered out with a million key strokes or pen strokes, and the more you make the more you are likely to produce something that has lasting value.

Do you have an anit-harrasment policy?

Yes. Although this a completely virtual conference, The Public Invention Math-a-thon is dedicated to a harassment-free virtual-conference experience for everyone. Our anti-harassment policy can be found at:

I think this a really good idea. How can I help?

Register so we know you are coming and get your math on! But if you would like to help moderate or organize or support the math-a-than by offering a cash award, contact .

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