What is science?
Are all masters curricula at universities scientific? Is something likely because it follows from solid reasoning based upon previous research or just because some authority says so? And what makes something or someone an authority? Is it solid research or many references in prestigious journals? Which boils down to authority again, as what makes these journals prestigious? Is it because the majority of the research that it publishes can be reproduced well and withstand many attempts to falsify them? But that is also true when both the particular journal and the community stay safely within the limits of the mainstream and never put the fundamentals of that mainstream to actual scrutiny. In that case, the community will not leave the mainstream as that means no or less prestigious publication, which means less income. In that case, the community is locked in. Which scientific communities are locked in? Why am I asking these question?
The above questions are important in a world where policy is affected enormously by just a few sciences. Especially when governments diminish spending in fundamental sciences that are then payed by commercial parties. It is impossible for laymen – most politicians – to distinguish between honest science and science that is tailored to produce results that especially favor the interests of the sponsor. Publication bias, retracted research whose results are "common knowledge" that has not been retracted. For example: Nobel laureate Friedrich von Hayek warned for the influence of economic science on society.1
Using math does not imply doing science
It is fundamental to understand that expressing a thought or model in mathematical form does not make it science. Mathematics is a great tool to explore, expand and derive theoretical models. However, it needs valid input. Input consists of assumptions (axioms) and other models. In most cases, input is accompanied by boundary conditions that define exactly when the mapping from the input to the mathematical model holds and thus when it breaks. The boundary conditions are important meta-data for the resulting model and must accompany al results from it. Applying the model without regard for the boundary conditions, results in faulty results. Building new models on top of it without propagating the boundary conditions, results in unreliable models.
Mathematics can produce perfectly consistent models but they reflect the quality of the input and are only valid within the boundary conditions. If the assumptions are bogus or unverified, the result will be consistent but describe a bogus world. If the boundary conditions are ignored, the outcomes are likely to be invalid and place new models based on it, at jeopardy. That is a large pitfall.
There are other pitfalls. There are many logical fallacies that can seep into reasoning and research. These can be hard to detect or contradict and this is why they are exploited in debating techniques. With a solid debating technique a discussion is easily won, even if the opponent has the better arguments.