For all the talk of "best practices" and "training" the depressing truth is that guaranteeing correct software is incredibly difficult and expensive. Professional software engineering practices aren't nearly sufficient to guarantee correctness with heavy math. The closest thing we have is NASA where the entire development process is designed and constantly refined in response to individual issues to create the checks and balances with the lofty goal of approaching bug impossibility at an organizational level. Unfortunately this type of evolutionary process is only viable for multi-year projects with 9-figure budgets. It's not going to work for the vast majority of research scientists with limited organizational support.

On the positive side, such difficulty is also in the nature of science itself. Scientists already understand that rigorous peer review is the only way to come to reliable scientific conclusions over time. The only thing they need help with understanding is that the software used to come to these conclusions is as suspect as—if not more so than—the scientific data collection and reasoning itself, and therefore all software must be peer-reviewed as well. This needs to be ingrained culturally into the scientific establishment. In doing so, the scientists can begin to attack the problem from the correct perspective, rather than industry software experts coming in and feeding them a bunch of cargo cult "unit tests" and "best practices" that are no substitute for the deep reasoning in the specific domain in question.