Autonomous Scientific Discovery

Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this observation. Our system, conceived with research in mind, poses its own conjectures and then attempts to prove them, making decisions informed by this feedback and an evolving data distribution. Inspired by the history of Euler's conjecture for polyhedra and an open challenge in the literature, we benchmark with the task of autonomously recovering the concept of homology from polyhedral data and knowledge of linear algebra. Our system completes this learning problem. Most importantly, the experiments are ablations, statistically testing the value of the complete dynamic and controlling for experimental setup. They support our main claim: that the optimisation of the right combination of local processes can lead to surprisingly well-aligned notions of mathematical interestingness.

The rapid accumulation of Earth science data has created a significant scalability challenge; while repositories like PANGAEA host vast collections of datasets, citation metrics indicate that a substantial portion remains underutilized, limiting data reusability. Here we present PANGAEA-GPT, a hierarchical multi-agent framework designed for autonomous data discovery and analysis. Unlike standard Large Language Model (LLM) wrappers, our architecture implements a centralized Supervisor-Worker topology with strict data-type-aware routing, sandboxed deterministic code execution, and self-correction via execution feedback, enabling agents to diagnose and resolve runtime errors. Through use-case scenarios spanning physical oceanography and ecology, we demonstrate the system's capacity to execute complex, multi-step workflows with minimal human intervention. This framework provides a methodology for querying and analyzing heterogeneous repository data through coordinated agent workflows.

Across the natural and life sciences, images have become a primary measurement modality, yet the dominant analytic paradigm remains semantics-first. Structure is recovered by predicting or enforcing domain-specific labels. This paradigm fails systematically under the conditions that make image-based science most valuable, including open-ended scientific discovery, cross-sensor and cross-site comparability, and long-term monitoring in which domain ontologies and associated label sets drift culturally, institutionally, and ecologically. A deductive inversion is proposed in the form of criteria-first and semantics-later. A unified framework for criteria-first structure discovery is introduced. It separates criterion-defined, semantics-free structure extraction from downstream semantic mapping into domain ontologies or vocabularies and provides a domain-general scaffold for reproducible analysis across image-based sciences. Reproducible science requires that the first analytic layer perform criterion-driven, semantics-free structure discovery, yielding stable partitions, structural fields, or hierarchies defined by explicit optimality criteria rather than local domain ontologies. Semantics is not discarded; it is relocated downstream as an explicit mapping from the discovered structural product to a domain ontology or vocabulary, enabling plural interpretations and explicit crosswalks without rewriting upstream extraction. Grounded in cybernetics, observation-as-distinction, and information theory's separation of information from meaning, the argument is supported by cross-domain evidence showing that criteria-first components recur whenever labels do not scale. Finally, consequences are outlined for validation beyond class accuracy and for treating structural products as FAIR, AI-ready digital objects for long-term monitoring and digital twins.

Large language models (LLMs) are beginning to reshape how organic-synthesis workflows are represented, queried, planned, and connected to experimental automation. Assessing their contribution is not straightforward because reaction-specific transformers, chemistry-adapted LLMs, tool-using agents, optimizers, and autonomous laboratories are often discussed under the same broad terminology despite operating at different levels of the synthesis workflow. This Review traces the progression from reaction prediction and retrosynthetic planning to reaction development, literature-to-protocol translation, and robotic execution, with representative numerical claims verified against primary sources available through 4 September 2026. We examine where language models provide genuine added value, where established specialist methods remain the principal source of performance, and how retrieval, uncertainty-aware optimization, deterministic chemistry tools, robotics, sensing, and human oversight alter system behavior. The evidence shows a clear transition from isolated language-model demonstrations toward modular scientific systems that combine broad language priors with specialized computation and experimentally grounded feedback. Emerging work on multimodal reaction understanding, standardized tool interoperability, provenance-aware execution, and programmable laboratory infrastructure extends this transition further. Despite this progress, reliable deployment continues to depend on generalization beyond historical reaction corpora, calibrated uncertainty, transparent component attribution, safety controls, reproducible system state, and prospective experimental validation.

Equation discovery is a fundamental learning task for uncovering the underlying dynamics of complex systems, with wide-ranging applications in areas such as brain connectivity analysis, climate modeling, gene regulation, and physical simulation. However, many existing approaches rely on accurate derivative estimation and are limited to first-order dynamical systems, restricting their applicability in real-world scenarios. In this work, we propose Sparse Equation Matching (SEM), a unified framework that encompasses several existing equation discovery methods under a common formulation. SEM introduces an integral-based sparse regression approach using Green's functions, enabling derivative-free estimation of differential operators and their associated driving functions in general-order dynamical systems. The effectiveness of SEM is demonstrated through extensive simulations, benchmarking its performance against derivative-based approaches. We then apply SEM to electroencephalographic (EEG) data recorded during multiple oculomotor tasks, collected from 52 participants in a brain-computer interface experiment. Our method identifies active brain regions across participants and reveals task-specific connectivity patterns. These findings offer valuable insights into brain connectivity and the underlying neural mechanisms.

Despite long-standing efforts in accelerating scientific discovery with AI, building AI co-scientists remains challenging due to limited high-quality data for training and evaluation. To tackle this data scarcity issue, we present AutoSDT, an automatic pipeline that collects high-quality coding tasks in real-world data-driven discovery workflows. AutoSDT leverages the coding capabilities and parametric knowledge of LLMs to search for diverse sources, select ecologically valid tasks, and synthesize accurate task instructions and code solutions. Using our pipeline, we construct AutoSDT-5K, a dataset of 5,404 coding tasks for data-driven discovery that covers four scientific disciplines and 756 unique Python packages. To the best of our knowledge, AutoSDT-5K is the only automatically collected and the largest open dataset for data-driven scientific discovery. Expert feedback on a subset of 256 tasks shows the effectiveness of AutoSDT: 93% of the collected tasks are ecologically valid, and 92.2% of the synthesized programs are functionally correct. Trained on AutoSDT-5K, the Qwen2.5-Coder-Instruct LLM series, dubbed AutoSDT-Coder, show substantial improvement on two challenging data-driven discovery benchmarks, ScienceAgentBench and DiscoveryBench. Most notably, AutoSDT-Coder-32B reaches the same level of performance as GPT-4o on ScienceAgentBench with a success rate of 7.8%, doubling the performance of its base model. On DiscoveryBench, it lifts the hypothesis matching score to 8.1, bringing a 17.4% relative improvement and closing the gap between open-weight models and GPT-4o.

Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum. We introduce a framework that automatically discovers a low-dimensional and operable representation of system dynamics, including a set of compact state variables that preserve the smoothness of the system dynamics and a differentiable vector field, directly from video without requiring prior domain-specific knowledge. The prominence and effectiveness of the proposed approach are demonstrated through both quantitative and qualitative analyses of a range of dynamical systems, including the identification of stable equilibria, the prediction of natural frequencies, and the detection of chaotic and limit cycle behaviors. The results highlight the potential of our data-driven approach to advance automated scientific discovery.

Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the equation to be known and focus on the estimation of specific parameters, these algorithms aim to learn the structure and the parameters simultaneously. While the uniqueness and, therefore, the identifiability of parameters of governing equations are a well-addressed problem in the field of parameter estimation, it has not been investigated for symbolic recovery. However, this problem should be even more present in this field since the algorithms aim to cover larger spaces of governing equations. In this paper, we investigate under which conditions a solution of a differential equation does not uniquely determine the equation itself. For various classes of differential equations, we provide both necessary and sufficient conditions for a function to uniquely determine the corresponding differential equation. We then use our results to devise numerical algorithms aiming to determine whether a function solves a differential equation uniquely. Finally, we provide extensive numerical experiments showing that our algorithms can indeed guarantee the uniqueness of the learned governing differential equation, without assuming any knowledge about the analytic form of function, thereby ensuring the reliability of the learned equation.