The Deranged Mathematician: Heuristics and Numerics

What place, if any, does the scientific method have in mathematics? It's often claimed that mathematics doesn't use it---hell, I have said that in the past. But that is not true. The scientific method isn't really the final arbiter of truth in mathematics, yes. However, we still rely on it quite heavily when we build examples, heuristics, and numerics. Moreover, it is a significantly more nuanced problem than simply "collect data, see what is true." As an example, I ask the reader to ponder the following question: if I identify all twin primes less than 101000 and show that they divide 101000!, is that evidence for or against the conjecture that all twin primes divide 101000!? I claim that it rather depends on how those twin primes are distributed. All of this is crucially important when we are trying to build proofs---we need to understand this to be able to build good examples as part of our proof strategies. Read the full post (for free) on Substack: Heuristics and Numerics