Maturity and citizenship in a democracy require that laypersons are able to critically reflect on experts’ use of mathematics. Learning to critically reflect on the use of mathematics, including the learning of mathematics required to that end, have been repeatedly postulated as indispensable goals of compulsory education in mathematics. However, it remained unclear in how far control by reflection is possible, even for the well-educated layperson in mathematics. We use different discourses on the SARS-CoV-2 crisis in 2020 as examples of discourses with far-reaching individual and social consequences. The selected discourses build heavily on mathematical concepts such as mortality rates, casualty numbers, reproduction numbers and exponential growth. We identify the concepts and discuss how far they can be understood by laypersons. On the one hand, we found that some mathematical models are inappropriate, which can also be determined by laypersons. On the other hand, we found uses of mathematics where ideal concepts are intermingled with statistical concepts in the public discourse. While only the ideal concepts can be understood by laypersons, only the statistical concepts lead to actual data. The identification of both types of concepts leads to a situation where the use of mathematics evades social control and opens spaces for misconceptions and manipulation. We conclude that the control of experts’ use of mathematics by laypersons is not possible in all relevant cases, even if they had enjoyed critical mathematics education.