Ramanujan Challenge

To help evaluate the mathematical skills of current AI systems, we present a set of formulas for fundamental mathematical constants. These problems are attractive for AI evaluation because they are concrete and can be checked numerically to arbitrary precision, yet proving them may require non-obvious mathematics. Mathematical constants such as $\pi$, $e$, Catalan’s constant, and special values of the Riemann zeta function have fascinated mathematicians for centuries. The search for formulas evaluating mathematical constants has produced some of the most beautiful mathematics in the field, especially in cases that yield irrationality proofs or fast convergence rates. Ramanujan’s legacy is emblematic of this tradition. The list we provide contains two types of problems: formulas whose proofs are known to the authors but will remain encrypted for a short initial period; and formulas that are not yet proven. We are curious to see the achievements of AI in both cases.

The full challenge paper

Update [01/08/26]: The Ramanujan Challenge is now officially closed. Thank you for participating! In the coming weeks we will be analysing all submitted solutions – stay tuned.

See this manuscript for the solutions. See this repository for the supplementary code.

Submission Guidelines

The Ramanujan Challenge will be released on July 1, 2026. Submissions will be accepted until August 1, 2026, 23:59 UTC. After the submission deadline, the authors will evaluate the submitted solutions and report the outcome for each problem.

The challenge has two goals. The first is to test whether current AI systems can solve research-level problems involving explicit formulas for mathematical constants. The second is to do this in a way that avoids an unstructured and overwhelming verification process. We therefore encourage submissions that include reproducible CAS-based or formally verified code.

What counts as a solution
For the purposes of this challenge, we will accept the following types of submissions, in descending order of priority:

• Formal proof. A proof written in an interactive theorem prover such as Lean, Rocq, Isabelle, or another comparable system. For a formal proof, the code must be accompanied with comments for each major proof block. All definitions, abbreviations and lemma statements must have an explanation and/or intuition.
• CAS-based derivation. A reproducible derivation using established computer algebra systems or symbolic libraries. Examples include, but are not limited to, Mathematica, Maple, SageMath, Magma, PARI/GP, SymPy, RISC packages, and ramanujantools. The code must explicitly expose the symbolic steps used in the derivation.
• A human-readable proof. Since such submissions may require substantially more human evaluation, they will be evaluated when possible.

If a submission relies on code for a nontrivial mathematical step, that code must be included, readable, documented, and justified as part of the proof. Submitted code must contain the source files needed to reproduce the results, with proper inline documentation. Each submitted solution is required to have a solution.tex or solution.pdf file containing a human-readable derivation.

Any established symbolic system or library may be used, provided that it was publicly available before July 1, 2026. This rule is intended to avoid turning the challenge into an evaluation of newly generated mathematical software.

New code written during the challenge is allowed when it serves as a solution script or implementation of the submitted derivation. However, newly written code, including AI-generated code, will not be treated as a trusted external oracle. Submissions may not rely on hidden remote services, private APIs, or unverifiable computations. Any code needed to verify the solution must be available to the organizers.

For transparency, we encourage all participants to submit through this page, which will record and present the names and timestamps of all submissions. We encourage parallel submissions via email to ramanujan.machine@gmail.com.

Public discussion and confidentiality
Participants are encouraged to discuss the challenge publicly. However, to preserve the integrity of the evaluation, we ask participants not to post complete solutions publicly before August 1, 2026.

Errata and clarifications
If ambiguities or typographical errors are found in the problem statements, the organizers may issue clarifications or corrections on the challenge website. Submissions will be evaluated against the corrected official statement.

Reporting results
After the evaluation period, the organizers will report, for each problem, which submissions were accepted, which were partial, and which tools or AI systems were used. For open conjectures, any accepted proof will be treated as a new mathematical contribution with authors being given due credit via a post explaining their solution according to order of submission.

For any questions please contact us at ramanujan.machine@gmail.com.