Mathematics will always be a key element of liberal education, since it promotes logical reasoning." You have likely heard this claim, or perhaps made it yourself. And we generally do a decent job of teaching our mathematics and statistics students how to avoid certain types of errors in their own deductive and inductive reasoning. But it is not so clear that we have done as good a job of preparing our students to examine critically the reasoning, mathematical and otherwise, of others who are trying to convince us to buy their product or adopt their position on an issue. In this presentation, the speaker will propose a three-category classification of types of fallacious mathematical arguments that have been used to try to convince the public of the wisdom of a policy decision or the safety of a new product, in the hope of starting a conversation about where and how in our mathematics curricula we could better prepare students to be suspicious when presented with arguments in each category, and help them think about the questions they should ask when their suspicions are aroused. Examples will be given, several with roots in applications of mathematics to climate science, one of the speaker’s interests.