Saw this quote by Littlewood from his famous Miscellancy, in Vicky Neale’s lecture from the very excellent Oxford Mathematics Public Lecture series.
Complete indecision netween yes and no in an exciting new problem is agonizing. When you all go out one way (either yes or no), the thought keeps nagging that it’s an even chance that it ought to be the other way. The difference when you do know (when, for example, we are looking for a new proof) is enormous.
I was reminded of my personal experience on the Skolem sequence. A colleague recounted how his son in primary school was given the problem, and it got a few of us piqued. I remembered putting in quite some effort including spending time coding in mathematica to get a feel of the initial cases. However, I gave up too easily and almost kicked myself when I read the solution about the non-existence proof for values of n. In my quest to improve the efficiency of my codes, I had used a different representation of the problem which was exactly that used in Skolem’s paper. Had a little birdie whispered in my ears that I was very close to the solution, I was sure I would have solved it.