Generative artificial intelligence relies on generative models, which learn the underlying probability distributions of data and generate novel, natural samples through sampling. Developing an appropriate generative model for inorganic crystals could revolutionize materials discovery and design. However, crystals represent a unique data modality, inherently governed by symmetry principles that cannot be directly addressed using approaches developed for language or image generation. Nature favors symmetric structures, a preference rigorously defined by space group symmetry. In fact, nature provides two foundational tables—the periodic table of elements and the Wyckoff position table of space groups. To construct a crystal, one selects atoms from the periodic table and assigns them to Wyckoff positions. This process yields a structured, sequence-like representation of crystals—unexpected yet logically consistent. Recently, researchers from the Institute of Physics, Chinese Academy of Sciences (CAS)/Beijing National Laboratory for Condensed Matter Physics, in collaboration with Jilin University, developed CrystalFormer, a novel autoregressive crystal generation model explicitly designed around space group symmetry. The core idea of CrystalFormer is to learn from crystal databases, internalize solid-state chemical principles, and generate crystal structures in a sequence-based manner by predicting Wyckoff site occupancies and lattice parameters. CrystalFormer encodes solid-state chemistry knowledge using neural network parameters, leverages network activations to capture material space associations, and employs likelihood functions in probabilistic models to embody chemical intuition. This enables the model to explore configurations that may exist in nature but have not yet been discovered. Unlike traditional machine learning force fields, CrystalFormer does not rely on energy landscape optimization. Instead, it directly generates plausible crystal structures under strict symmetry constraints, effectively "guessing" reasonable arrangements based on symmetry. In practical applications, CrystalFormer can explore the entire materials space without constraints or focus on generating crystals with specific structural features. Moreover, its modular integration with property prediction models allows for inverse materials design using Bayesian inference. By unifying mathematical symmetry and chemical intuition within a compact, general, and flexible framework, CrystalFormer offers a powerful and adaptable tool for future crystal material discovery and design. The research was published in Science Bulletin. The work was supported by the National Natural Science Foundation of China and the Strategic Priority Research Program of the Chinese Academy of Sciences. A JAX-based open-source implementation of the model, along with application examples, is available for public use.