Changes in the meaning of mathematical correctness during the enculturation of graduate students in physics: conflicts and tensions

The starting point of our research is the detection of a small but relevant and alarming frequency of reviewed works published in high-standard journals of physics that present “evident” (basic) and invalidating mathematical mistakes. Such mistakes go unnoticed by referees and even worse; these works are subsequently quoted as correct results by other practitioners. We interpret this as an indication that problems arise along the enculturation of science students and in the way some subcommunities of physicists uses mathematics. By “evident” we mean that science students are instructed in the use of simple metacognitive tests to detect such basic errors. For example: “A general method of calculation, when applied to particular cases that are accessible by other direct method(s), must yield a result coincident with that of the direct approach(es).” Some errors we detected in high-standard journals are below the “pass” level of the first elementary course in Analysis. In particular, we find cases where a “general expression” when applied uncritically to the specific case in study (without noticing that it lies outside the validity range of the