This paper's first aim is to prove a modernized Occam's razor beyond a reasonable doubt. To summarize the main argument in one sentence: If we consider all possible, intelligible, scientific models of ever-higher complexity, democratically, the predictions most favored by these complex models will agree with the predictions of the simplest models. This fact can be proven mathematically, thereby validating Occam's razor. Major parts of this line of reasoning have long preexisted within the depths of the algorithmic information theory literature, but they have always left room for doubts of various kinds. Therefore, we increase the generality, completeness, clarity, accessibility, and credibility of these arguments by countering over a dozen objections. We build our mathematical proof of Occam's razor on the shoulders of the exact 'chain rule' for Kolmogorov complexity. Concerning physics, we then go on to diagnose the primary amendable root cause of the present stagnation of the research field of fundamental theoretical physics. We show that the effective antidote would consist in a practically feasible upgrade to the theoretical physicists' research methodology: When proposing new theoretical models, physicists should simply calculate and report the total amount of information that their models consist of. We explain why this methodology would be highly effective as well as how these calculations could be performed efficiently.