To theorize is to put forward an explanation for something you cannot yet check — you have a fact or an event, you do not know its cause, and you build an account of it out of reasoning. It is stronger than 'guess', because a theory is supposed to hang together and fit the known facts, but weaker than 'prove'. The word almost always signals that the matter is still open, so it turns up constantly in reporting: 'Police theorize that the fire started in the kitchen' means exactly that they think so and cannot yet show it. Common patterns: theorize that + a whole clause ('scientists theorize that the moon was torn from the Earth'); theorize about + a topic ('he theorized about the causes for years'); or standing alone ('we can only theorize'). Watch the spelling: British writing prefers 'theorise', American 'theorize', and both are correct in their own place — Taiwan textbooks usually follow the American -ize. Note also that the verb can carry a faint criticism when someone theorizes instead of finding out: 'stop theorizing and go and look' is a real thing people say.