The Deranged Mathematician: When All Else Fails

In the Surviving Proofs series, we have been going through the fundamental techniques for constructing proofs; we close this off now with two approaches, which both amount to changing the problem, albeit in different ways. One thing you can do is to try to simplify the problem, with the hope that solving the easier version will give you the insight you need to solve the harder one. The other thing is to try to move laterally, finding an equivalent formulation that is nevertheless more manageable. Easy to say, but hard to put in practice! Nevertheless, as I hope the examples I furnish show (which include one of my favorite symmetry arguments), it is: a) surprisingly common, and b) incredibly powerful. Read the full post (for free) on Substack: When All Else Fails