D. P. Woodruff

Tony Feng, Junehyuk Jung, Sang-hyun Kim et al.

We report the performance of Aletheia (Feng et al., 2026b), a mathematics research agent powered by Gemini 3 Deep Think, on the inaugural FirstProof challenge. Within the allowed timeframe of the challenge, Aletheia autonomously solved 6 problems (2, 5, 7, 8, 9, 10) out of 10 according to majority expert assessments; we note that experts were not unanimous on Problem 8 (only). For full transparency, we explain our interpretation of FirstProof and disclose details about our experiments as well as our evaluation. Raw prompts and outputs are available at https://github.com/google-deepmind/superhuman/tree/main/aletheia.

David P. Woodruff, Vincent Cohen-Addad, Lalit Jain et al.

Recent advances in large language models (LLMs) have opened new avenues for accelerating scientific research. While models are increasingly capable of assisting with routine tasks, their ability to contribute to novel, expert-level mathematical discovery is less understood. We present a collection of case studies demonstrating how researchers have successfully collaborated with advanced AI models, specifically Google's Gemini-based models (in particular Gemini Deep Think and its advanced variants), to solve open problems, refute conjectures, and generate new proofs across diverse areas in theoretical computer science, as well as other areas such as economics, optimization, and physics. Based on these experiences, we extract common techniques for effective human-AI collaboration in theoretical research, such as iterative refinement, problem decomposition, and cross-disciplinary knowledge transfer. While the majority of our results stem from this interactive, conversational methodology, we also highlight specific instances that push beyond standard chat interfaces. These include deploying the model as a rigorous adversarial reviewer to detect subtle flaws in existing proofs, and embedding it within a "neuro-symbolic" loop that autonomously writes and executes code to verify complex derivations. Together, these examples highlight the potential of AI not just as a tool for automation, but as a versatile, genuine partner in the creative process of scientific discovery.

Bingyang Kelvin Liu, Ziyu Patrick Chen

While Joint-Embedding Predictive Architecture (JEPA) has emerged as a powerful architecture for learning rich latent representations, it fundamentally lacks generative abilities. Meanwhile, latent space reasoning attempts for Transformer models like COCONUT do improve performance, but they ultimately rely on token-by-token generation, which still accumulates compounding error and relies on context information to gain reasoning insights. To address these limitations, we propose JEPA-Reasoner, a novel JEPA model enhanced with generative ability that reasons in latent space. We augment it with a separate action-taker model, Talker, to produce human-readable sentences. Our approach demonstrates that decoupling latent space reasoning and token generation enables JEPA-Reasoner to produce mixed latent vectors that might lay the foundation for multi-threaded reasoning, while performing autoregressive generation with superior robustness to compounding error.