Solving, modelling, and designing with large language models: situations and forms of engagement in mathematical work. This article examines the transformations of mathematical work induced by large language models within the tension between discursive plausibility and logical necessity. Drawing on situations of problem-solving, modelling, and design, it highlights the differentiated effects of generative and symbolic AI on reasoning, validation, and the structuring of knowledge. Building on the Theory of Mathematical Working Spaces, it introduces the notion of technological counterpoint to characterize human-AI interactions as a tension between heterogeneous regimes of production. The analysis shows that desirable forms of delegation do not concern the epistemic control of mathematical work, which remains a human responsibility and a condition for the idoneity of the process. Artificial intelligence thus appears less as a cooperative partner than as a critical instrument for the reconfiguration of mathematical work