Research on reasoning assistants tends to focus on interactive theorem provers that can mechanically verify fully formalized, rigorous proofs. In practice, however, little mathematics is formalized to such a degree. Instead, proof is treated as a social process, meant to convince and communicate an argument or insight to other human mathematicians. This extended abstract surveys work on weak reasoning assistants, i.e., tools that assist mathematicians in that social task without requiring a fully mechanized proof.