A little bit of math can go a long way. The design of a system can be hampered not only by having too little mathematical analysis go into it, but also too *much*. One familiar example of this is with password requirements in cybersecurity. Mathematically, the more complex that a password is required to be - for instance, by mandating minimum length, special characters, or no reused passwords - the more secure the password becomes. However, make the requirements too complex, and users and service providers will then seek workarounds to the complex requirements, such as easy ways to reset or recover the password, or storage of such passwords in insecure systems - that in fact can serve to *decrease* the security of the overall system, rather than *increase* it. Overoptimizing on just a single metric - the security strength of the direct user/password login system - can serve to compromise the broader objective - a textbook example of "Goodhart's law" in effect https://en.wikipedia.org/wiki/Goodhart%27s_law . Roughly speaking, the security of this direct entry method should be strengthened to be comparable to the security of alternate entry methods, but beyond that any further strengthening tends to be counterproductive. There is little point putting in more locks on the front door of a building beyond the first one, if the windows are unsecured, and in fact doing so may even lead to a dangerous false sense of security. On the other hand, if the windows are harder to access than the front door, then putting at least one lock on the front door makes excellent sense. (1/3)