We are now about a week into 2017 and as usual, I'm my usual self. Resolutions? Didn't write any but I figured I should do less of the social media (not making FB active in the background while I'm working). The social media has changed so much from simply keeping in touch and sharing information with friends to plenty of propaganda, ego boosting posts and business advertisements and become extremely distracting. I guess this can't be helped; people eventually would take advantage of the social media according to their wimps.
My own use? I like to share information which I thought would be useful to my students, colleagues and even staff. If I am on leave, I would post saying as such, so that staff and students would know I'm not around. If there is a conference relevant to my group's interest, I would share them. If not related, I pick and choose what I would like to share. I also like to share my ideas and witty remarks that make people think. For instance, on January 1st, I posted on FB that "2017 is a prime number". I did consciously try to find something different to post and then I thought to myself that 2017 does look like a prime number (wasn't running any algorithm in my head). I checked with Mathematica, PrimeQ and it returned True. Hence posted it and seemed to get some attention. Any other reason? None really, particularly I'm not suggesting any form of numerology (lest I be accused as a university lecturer teaching others to be stupid - with reference to a recent tabloid article).
However 2017 being prime is interesting with respect to number theory. Only much later, that I looked up what is known about it. It is the 306th prime number. The next prime number for the forthcoming years is 2027 (another ten years). Apparently the prime number before it, was 2011, six years before. This pairing of six-year primes seem to have a name: sexy primes! I have no idea what's sexy about it but according to its Wikipedia article, the name stems from the Latin word for six, sex (no that does not make me an expert in linguistics, but I can still talk about it, right? - with reference to a recent tabloid article). What else is known about 2017? It is a zero of Mertens function. At present, I do not know what is its significance, but it is interesting to observe that there is a connection to hyperbolic geometry.
My interest in number theory is really cursory; my bigger (mathematical) love is geometry and topology. It was during the research of quantum mechanical wavefunctions on hyperbolic surfaces that makes me cross path with number theory. Still, I do not fully grasp the deep significance but I have formed deep interest in the interplay of discrete structures with continuous ones for several years now. Collected stacks of papers within this topic and still hoping to read their details. Presently I'm reading back the popular book "Fearless Symmetry" by Avner Ash and Robert Gross, all prompted by my 2017 FB post. Hidden underneath all this is my dream of venturing into new research areas. Earlier in my conversation with my postdoc more than a month ago, we have contemplated on learning noncommutative arithmetic geometry as the middle road of marrying his interest on noncommutative quantum mechanics and geometry with what we have done on energy eigenfunctions on hyperbolic geometry. This would be nice and it has applications in things that I have mentioned in this popular article (topological materials). However we got sidetracked for now by a competing interest in phase space quantum mechanics and symplectic topology, But even in here, number theory crops up in topics like discrete phase spaces using finite fields whose order is powers of primes.
So much for 2017! Hope no one gets stupid reading this.