This study explored the transformative potential of artificial intelligence (AI) in addressing the challenges posed by terahertz ultra-massive multiple-input multiple-output (UM-MIMO) systems. It begins by outlining the characteristics of terahertz UM-MIMO systems and identifies three primary challenges for transceiver design: computational complexity, modeling difficulty, and measurement limitations. The study posits that AI provides a promising solution to these challenges. Three systematic research roadmaps are proposed for developing AI algorithms tailored to terahertz UM-MIMO systems. The first roadmap, model-driven deep learning (DL), emphasizes the importance of leveraging available domain knowledge and advocates the adoption of AI only to enhance bottleneck modules within an established signal processing or optimization framework. Four essential steps are discussed: algorithmic frameworks, basis algorithms, loss-function design, and neural architecture design. The second roadmap presents channel state information (CSI) foundation models, aimed at unifying the design of different transceiver modules by focusing on their shared foundation, that is, the wireless channel. The training of a single compact foundation model is proposed to estimate the score function of wireless channels, which serve as a versatile prior for designing a wide variety of transceiver modules. Four essential steps are outlined: general frameworks, conditioning, site-specific adaptation, joint design of CSI foundation models, and model-driven DL. The third roadmap aims to explore potential directions for applying pretrained large language models (LLMs) to terahertz UM-MIMO systems. Several application scenarios are envisioned, including LLM-based estimation, optimization, search, network management, and protocol understanding. Finally, the study highlights open problems and future research directions.