FirstProof Challenge Benchmark

• FirstProof Challenge is a mathematics evaluation benchmark that rigorously tests AI systems on unsolved, research-level problems using a controlled, encrypted solution protocol.
• It spans ten diverse fields including stochastic analysis, differential geometry, and algebraic combinatorics, ensuring comprehensive assessment across pure and applied mathematics.
• The challenge employs innovative cryptographic measures to prevent data contamination and guarantees transparent, reproducible evaluation through scheduled public release of solutions.

The FirstProof Challenge is a mathematics evaluation benchmark designed to rigorously assess the autonomous research capabilities of contemporary AI systems on genuine, unsolved research-level mathematics problems. Each problem originates directly from active mathematical research and was selected to ensure no data contamination from prior public exposure, thereby providing an uncompromised test of mathematical reasoning and creativity. The challenge comprises ten problems spanning a broad spectrum of pure and applied mathematics subfields, with verified solutions encrypted and scheduled for timed public release. The protocol prioritizes transparency, diverse domain coverage, and methodological reproducibility (Abouzaid et al., 5 Feb 2026).

1. Objectives and Structure

FirstProof’s primary goal is to probe the genuine problem-solving ability of AI systems on research-level mathematics questions whose answers are known only to the authors and withheld from the public until after evaluation. Each problem in the set is deliberately chosen to arise “naturally in the research process of the authors,” to require at most approximately five pages of proof, and to ensure that the solution is not accessible through any means other than genuine mathematical insight or deduction.

The challenge covers ten fields:

• Stochastic analysis
• Automorphic representation theory
• Algebraic combinatorics and integrable probability
• Real-rooted polynomials and numerical analysis
• Equivariant homotopy theory
• Spectral graph theory
• Differential geometry of locally symmetric spaces
• Symplectic topology
• Multilinear algebra and tensor decompositions
• Numerical linear algebra and machine learning

Each question is precisely formulated in LaTeX, accompanied by background context, and labeled with its mathematical area. Solution keys are encrypted and hosted at https://1stproof.org, with decryption scheduled for February 13, 2026, to guarantee a time-locked evaluation window (Abouzaid et al., 5 Feb 2026).

2. Problem Summaries and Mathematical Fields

The ten challenge problems exemplify both diversity of domain and depth of proof requirements. A non-exhaustive summary follows, with precise LaTeX formulations as in the challenge documentation:

1. Stochastic Analysis ($\Phi^4_3$ Measure): Examines absolute continuity versus singularity of the non-Gaussian $\Phi^4_3$ measure under finite-rank translation, a question rooted in constructive quantum field theory and singular stochastic PDEs.
2. Automorphic Representation Theory (Rankin–Selberg Integrals): Probes the existence of test vectors for local Rankin–Selberg $L$-functions in the ramified, non-archimedean setting, with direct ties to the theory developed by Jacquet–Piatetski–Shapiro–Shalika.
3. Algebraic Combinatorics (Macdonald Processes): Asks whether there exists a nontrivial Markov chain on interlacing partitions, whose stationary distribution relates the ASEP and Macdonald interpolation polynomials, with constraints on the transition structure.
4. Real Algebraic Geometry (Finite Free Convolutions): Investigates a log-derivative Dirichlet energy inequality under Marcus–Spielman–Srivastava’s finite-free convolution, seeking new extremal relations for real-rooted monic polynomials.
5. Equivariant Homotopy Theory ($N_\infty$ Operads): Requests a characterization of slice connectivity for incomplete transfer systems within the $G$-equivariant stable homotopy category, in terms of vanishing homology of geometric fixed points.
6. Spectral Graph Theory (Light Subsets): Questions the existence of spectrally “light” vertex subsets of universal size lower bound, generalizing classical Cheeger-type sparsification problems.
7. Differential Geometry (Lattices in Lie Groups): Considers whether a uniform lattice in a semisimple group with 2-torsion can serve as the fundamental group of a closed manifold with acyclic universal cover, engaging with group cohomology and rigidity theory.
8. Symplectic Geometry (Lagrangian Smoothing): Explores existence of Lagrangian smoothings for specific polyhedral surfaces in $\mathbb{R}^4$, subject to four-valency at each vertex, with implications for Lagrangian skeleta and mirror symmetry.
9. Multilinear Algebra (Tensors and Minors): Asks for universal polynomial relations among determinant minors of collections of $3 \times 4$ matrices, seeking a scaling-invariant characterization in the flavor of the hyperdeterminant and principal-minor ideals.

10. Numerical Linear Algebra (Tensor Decomposition in RKHS):

Demands efficient algorithmic explanation of a matrix-free, block-preconditioned conjugate gradient solver for structured least-squares in infinite-dimensional tensor decompositions.

Each problem is accompanied by background literature, classical analogues, or partial cases where relevant (Abouzaid et al., 5 Feb 2026).

3. Protocol for Solutions, Encryption, and Evaluation

A key methodological innovation is the public commitment to encrypted solution release. All solutions have been precomputed and encrypted using a public key, then hosted at a publicly accessible location. The cryptographic protocol specifies that the private decryption key will be released on a fixed date. This guarantees the following:

• No participant or model has advance access to authenticated solutions.
• Benchmarking is immune to leakage or “contamination” from open web sources.
• Decryption is publicly verifiable and reproducible by any third party after the key’s release (Abouzaid et al., 5 Feb 2026).

In terms of evaluation, the FirstProof organizers recommend that all solution attempts be shared in transcript (prompt/response) form with the broader community, to facilitate both grading and future benchmark design.

4. Related Benchmarks, Partial Results, and Cross-References

FirstProof is positioned among several recent efforts to benchmark mathematical reasoning and proof synthesis at a high level:

• FrontierMath, IMProofBench, and RealMath are cited for providing public benchmarks, but unlike FirstProof, they make their questions and solutions simultaneously available (Abouzaid et al., 5 Feb 2026).
• The challenge references several significant mathematical frameworks and classical results, including:
  • The Cameron–Martin theorem for equivalence of Gaussian measures.
  • Jacquet–Piatetski–Shapiro–Shalika’s theory for local integrals and newvectors.
  • The interlacing families technique and the Kadison–Singer problem via finite-free convolution.
  • Hill, Hopkins, and Ravenel’s slice filtration in equivariant stable homotopy theory.
  • Kolda–Bader tensor methods in large-scale numerical linear algebra.
• Each problem is rooted in current research programs and can be cross-referenced by section and equation number according to the challenge paper’s organization.

No formal grading rubric is provided; verification is intended to rest upon consensus judgments by human experts once the encrypted proofs become available. The paper notes exploratory, one-shot evaluations of LLMs (e.g., GPT-5.2 Pro, Gemini 3.0 Deepthink), with initial results indicating that many problems resist solution from these models in a single-pass setting (Abouzaid et al., 5 Feb 2026).

5. Broader Significance and Contributions

FirstProof addresses previously unmet needs in the mathematical AI evaluation landscape:

• Data Contamination Control: By ensuring questions are new to the public domain, FirstProof enables a rigorous assessment of generative reasoning, not pattern-matching or retrieval.
• Field Diversity and Depth: The breadth of included mathematical areas (stochastic analysis, combinatorics, geometric topology, numerical linear algebra, etc.) mandates versatility and depth of understanding from solvers.
• Transparent and Reproducible Protocol: Public cryptographic precommitment and post-hoc community grading position the challenge as a reproducible experimental platform.
• Benchmarking for Future Systems: The release protocol and permanent transcript archives establish a high watermark for future proof-assistant and AI researcher benchmarks.

In summary, FirstProof sets a new standard for evaluating autonomous mathematical reasoning systems, through an uncompromising focus on novelty, rigor, transparency, and the breadth of mathematical content presented (Abouzaid et al., 5 Feb 2026).