The Theory of Formal Discipline (TFD) suggests that studying mathematics improves general thinking skills. Empirical evidence for the TFD is sparse, yet it is cited in policy reports as a justification for the importance of mathematics in school curricula. The study reported in this article investigated the extent to which influential UK advocates for mathematics agree with the TFD and their views on the arguments and evidence that surround it. Quantitative and qualitative analysis of data from structured interviews revealed four themes: broad endorsement of the TFD; reference to supportive employment data; the possibilities that mathematics education might not always effectively develop reasoning and that study of other subjects might have similar effects; and concerns about causality and the extent of the evidence base. We conclude that advocates broadly support the TFD despite being aware of its limitations.