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I’m looking for open source math research projects as I know computer science students can easily have access to material they can contribute to but this is not the case with math as far as I’m aware. But I am looking for a possible answer with open source or crowd sourced math research projects that someone in their last year of getting a bachelors or during a Masters could contribute to. Given they have the ability that is.

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I'm surprised nobody's yet mentioned the various (interrelated) projects for formalising mathematical proofs on a computer, in the Lean theorem-proving software:

Those are all open-source projects hosted on GitHub.

I'd personally claim that these projects constitute "research", although maybe not all mathematicians would agree with that; and they certainly offer lots of opportunities to contribute for anyone with maths training up to bachelor's degree level (while also offering the opportunity to engage with much more advanced material if you want to).

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  • $\begingroup$ Also the consistency of NF (github.com/leanprover-community/con-nf), which as I understand it is essentially a student summer project (with lots of input by Randall Holmes) of exactly the type the OP is asking about. $\endgroup$
    – Patrick Stevens
    Commented Sep 18, 2022 at 19:03
  • $\begingroup$ The Natural Number Game is also worth a mention for anyone who hasn't used a proof assistant before -- it guides you through proving the properties of Peano arithmetic using Lean. I used to think proof assistants were just for specialists in that subject but this changed my mind and it's pretty fun too. $\endgroup$
    – Daniel Shapero
    Commented Sep 18, 2022 at 20:13
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Polymath is one example of crowd-sourcing mathematics. It may or may not be suitable, depending on your energy, talent, and expertise. https://asone.ai/polymath/index.php?title=Main_Page

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    $\begingroup$ Thanks! This is very close if not exactly what I was looking for. Do you think working on this would improve my resume for grad school? $\endgroup$
    – Jayden Maryott
    Commented Sep 17, 2022 at 23:05
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    $\begingroup$ Are you capable and committed enough to make a contribution to these projects is probably the more relevant question. $\endgroup$
    – kodlu
    Commented Sep 18, 2022 at 7:00
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There are two examples (that I know of) of open source mathematics projects. The first is the polymath project. Sadly progress seems to have dissipated recently, but perhaps with a few more people joining it can start up again.

The second open source project is currently going at full steam, with many new people coming in and plenty of places to contribute. The Busy Beaver Challenge, attempting to find the value of BB(5). There are many ways to help, from programming deciders to finding new behaviors to proofs of validity. It is a perfect place for a Bachelors or Masters student to contribute.

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  • $\begingroup$ @bubba's earlier answer also mentions the Polymath project. $\endgroup$
    – LSpice
    Commented Sep 18, 2022 at 1:24
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    $\begingroup$ I didn't see that one until I posted my answer $\endgroup$
    – Thomas
    Commented Sep 18, 2022 at 1:30
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    $\begingroup$ Thanks! The Busy Beaver Challenge sounds and looks super interesting! $\endgroup$
    – Jayden Maryott
    Commented Sep 18, 2022 at 2:10
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There's PrimeGrid:

"PrimeGrid's primary goal is to advance mathematics by enabling everyday computer users to contribute their system's processing power towards prime finding. By simply downloading and installing BOINC and attaching to the PrimeGrid project, participants can choose from a variety of prime forms to search. With a little patience, you may find a large or even record breaking prime and enter into Chris Caldwell's The Largest Known Primes Database with a multi-million digit prime!"

And there's ZetaGrid:

"ZetaGrid is a platform independent grid system that uses idle CPU cycles from participating computers. Grid computing can be used for any CPU intensive application which can be split into many separate steps and which would require very long computation times on a single computer. ZetaGrid can be run as a low-priority background process on various platforms like Windows, Linux, AIX, Solaris, HP-UX, and Mac OSX. On Windows systems it may also be run in screen saver mode."

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    $\begingroup$ Does contributing to these projects actually involve participants doing any interesting mathematical thinking? It sounds like these projects are crowdsourcing spare CPU cycles, not spare human brainpower. $\endgroup$
    – David Loeffler
    Commented Sep 18, 2022 at 8:05
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    $\begingroup$ @David, you may be right. But I think any interested participant could look into the mathematics of what their spare cycles are doing, and learn some interesting math that way. $\endgroup$
    – Gerry Myerson
    Commented Sep 18, 2022 at 12:39
  • $\begingroup$ I tried to undo accidental downvote- not sure if I succeeded. $\endgroup$
    – Geoff Robinson
    Commented Sep 18, 2022 at 14:15

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