I’m writing this because I must. What I’ve noticed is a dissociation of sorts between how I do programming vs math. For one the expectations are in line with reality, they have to have become so given how much time I’ve spent on it but for the other I feel like I’m always rushing, not giving it the respect, time and effort it deserves.
Let me elaborate. For doing say a leetcode hard problem, the expectation is that it’ll take a few attempts, atleast half and hour if I’m lucky, much more if I had to think through or am not able to see a direction. That a pen and paper reasoning is essential, that I HAVE to do all those bits to even have a shot at getting to a solution.
But take a more complicated mathematics problem, what I’ve noticed is that I’m always trying to run towards some solution, that there is this incorrect belief that all it takes is just a couple lines of writing, a fear of rigour I would say and I must call it out for otherwise I’ll always find myself running away from it. The idea of spending an hour or several pages, carefully deriving each part, re-using the results, each one building on top of the previous to finally be able to get to a solution is entirely foreign to me. There’s no denying that that is how it’s supposed to be, even I agree, but unless I write it down, like in this note, there would always be that subconscious bias to cut corners and escape the rigor or time or pages that a problem demands. Such a pursuit is not just futile, it consumes time and leave me with nothing, I’ll only be deceiving myself.
That is all that I wanted to say here. Mathematics, for me atleast and I believe in general for others too, is a harder discipline than silly leetcode problems, any single equation that has survived so far, would be the effort of many geniuses of their times; and yet I treat it as somehow “secondary” in my goals and endeavors. Such foolishness, I pray my future self would be better.