&gt;&gt;Being empirically observed phenomena rather than abstract mathematical facts, Benford’s law, Zipf’s law, and the Pareto distribution cannot be “proved” the same way a mathematical theorem can be proved. However, one can still support these laws mathematically in a number of ways, for instance showing how these laws are compatible with each other, and with other plausible hypotheses on the source of the data.<p>Interesting that some the most reliable and interconnected observed emergent behaviors in mathematics do not have an actual hard-and-fast proof, but merely a lot of &quot;evidence&quot;.<p>Is there such a proof? If so, would it be enormous like &quot;Classification Theorem of Finite Groups&quot; or &quot;Erdos discrepancy problem&quot;?<p>Or are such things purely outside the range of mathematical language, but can only be talked about in terms of observational data?