To fully analyze, mine, and utilize the information and knowledge implied in problem resolving use cases, this paper proposed the autonomous learning method based on machine inducting, hypothesis formulating, and result verifying, which was similar to the biological process of cows ruminating, called rumination computing. Firstly, after inducting and summarizing over 1080 mathematic application problem, the system architecture and general algorithm for humanoid automatic resolving mathematic application problems were represented, which typically included functional modules such as commonsense knowledge base, domain knowledge base, and local knowledge base, preprocessing, word segmentation and part of speech tagging, semantic framework matching, global semantic analyzing, thinking mechanism implementing, etc. Secondly, after the use case solutions were approved, three typical rumination computing modes, including vocabulary sequence, semantic relationship, and computing action, were introduced based on the correct results, resolving steps, and basic rumination actions. The rumination computing step plan was formulated, new knowledge was obtained from the commonsense and results verification, so the continuous autonomous learning loop for machine thinking was formed. Detailed explanations were provided for the three core algorithms implemented (rumination framework algorithm, rumination semantic algorithm, rumination action algorithm). Then, by specific mathematic application problem humanoid resolving user cases, the above three types of rumination computing modes were illumined.