I think this is misunderstanding the role of math in science. Math is not used to "prove" scientific results, per se. Math is used to construct models, and prove that certain results would be expected from a given model. That doesn't mean the models work in the real world; all sciences use experiments to test models to see if they describe actual observations.
In this sense, you always need to be careful about replication, regardless of field. If you can't show replication, then there is no guarantee that the model will always match observations, no matter how much math went into the construction of that model.
In Physics the main problem is isolating variables, and setting up appropriate conditions. The good thing about Physics is that once the environment is set up and the experiment is well designed, it is easy to re-run the experiment for more trials. With chemistry and biology, this is usually the case as long as you have clean reagents in a clean lab, but you are introducing more factors of what you have to control as the complexity of your system scales up.
It is hardest to replicate results involving humans, because with humans you have a lot of complexity, so you know you can never control all influencing factors. Usually in the social sciences, it is easier to hope these factors cancel out with a large, non-homogenous sample size. The problem as these experiments like SPE demonstrate is that it is hard to build an ideal sample and, if the ethics or practicality of your methods are questioned, rerun the experiment to replicate results.
In this sense, you always need to be careful about replication, regardless of field. If you can't show replication, then there is no guarantee that the model will always match observations, no matter how much math went into the construction of that model.
In Physics the main problem is isolating variables, and setting up appropriate conditions. The good thing about Physics is that once the environment is set up and the experiment is well designed, it is easy to re-run the experiment for more trials. With chemistry and biology, this is usually the case as long as you have clean reagents in a clean lab, but you are introducing more factors of what you have to control as the complexity of your system scales up.
It is hardest to replicate results involving humans, because with humans you have a lot of complexity, so you know you can never control all influencing factors. Usually in the social sciences, it is easier to hope these factors cancel out with a large, non-homogenous sample size. The problem as these experiments like SPE demonstrate is that it is hard to build an ideal sample and, if the ethics or practicality of your methods are questioned, rerun the experiment to replicate results.