Things add up.
I have been hoping to keep a record of my daily thoughts for quite some time. However, as a mathematics student in my junior year I have to struggle with floods of assignment everyday and I am not that kind of quick-smart guy. Moreover, I was persuaded to take some graduate-level courses and they are really difficult. So, maybe it is not the best time to start a blog.
However, I have been so lucky to go through some great blogs recently, especially What’s new by the star mathematician Terence Tao, which gives me true inspiration.
What I find so special about mathematical blogs, comparing to the textbooks, is that they record the trajectory of the development, rather than just give some well-established theorems. Some textbooks are just so into this kind of results that I sometimes can hardly believe they are works by human-beings. This is somehow extremely discouraging for some ordinary people like me. With no offense, Rudin‘s Complex and Real Analysis is on this list in my opinion.
Of course good mathematics should be clear and pure like crystal but this does not mean it has to be crystal-like cold and hard. Mathematicians, as far as I know, also have their passion. However, few clues to these can be found in that kind of textbooks and well, for many years it has to be so because it took so long for mathematicians to establish something and I guess that they just like to write it in the most economical way.
But mathematical blogs changed everything, they show the recent development as well as thoughts of mathematicians, so you can see mathematics is not just a collection of facts and theorems but a developing sport, and you don’t have to be a genius to do it. Although some giants greatly changed mathematics with almost their works alone, yet they come along so rarely that shed no light on the paths walked by us. Moreover, putting to much emphasize on talent just do us no good.
One more thing those great blogs teach me is that even humble idea may have further implications and hence deserves to be recorded.
Anyway, mathematics is a σ-finite process. Each step may be small but things add up.
SO, I am here, writing my blog, keeping a record of my Undergraduate level thoughts.