While staying home on paternity leave, I had more time to ponder the meaning of life, away from hectic programming day job. This is coupled by my grandma’s accidental fall in the bathroom, and the less than optimistic prognosis that her rib bones were fractured and heart and lung got infected as a result. I think even God appeared to me one night to give consolation, since this is a justifiably depressing time, despite the smoothness of the newborn. In any case, reflecting on my first 9 months at my current job, one trap I repeatedly fell in was that deep down, I wanted to innovate and make big news so bad, that I lost sight of the lifelong pursuit of learning. As a programmer, there are many ways to absorb old and new technology. The whole industry evolves around making learning more accessible to both the insiders and outsiders. Maybe the abundance of resource pushed me into the other extreme, by completing shutting my brain off from learning and focusing on continuous philosophizing and hypothesis testing. This break allowed me to realize this as a critical vice that would hinder my long term productivity.
So having regained some intellectual energy, I revisited a branch of mathematics that I detested as a graduate student, namely analytic number theory, as partially motivated by Terence Tao’s most recent blog post on the Bombieri heuristic. Yesterday I managed to get a systematic education on the Mobius function. Today I started reading his earlier post on Goldston-Pintz-Yildirim, Motohashi-Pintz, and YT Zhang’s result. I got tripped by a seemingly innocent estimate, that the Hardy-Littlewood constant relevant for the prime constellation conjecture is bounded away from 0. It turned out to be an elementary consequence of the Prime Number Theorem, which I have always held in awe and dared not to apply it to real questions of interest. It sounded like going through the whole post would be both rewarding and challenging, but I have set my mind to do so, and hopefully come up with some followup learning items. After all, number theory is an exact science and a mediocre mind like mine should still be able to penetrate it, given enough volition. Hopefully I will then find some common ground with past grad school friends and borrow analytic ideas to solve my own problems in Lie theory and probability. Thank you God for the latest revelation.