I regularly read blogs by three mathematicians, and occasionally run into others. Definitely they help me a lot studying mathematics.
But now I am more interested in the writers' perspective, and I wonder whether writing a math blog help study mathematics. What are the pros and cons for the writer himself, especially for a first-year graduate student?
A lot of users have tons of experience writing blogs. I really want to hear your opinion on this.
Thanks!
Maybe I just start writing some of my own thoughts: cons: 1. writing a blog consumes lots of time. pros: 1. writing a blog forces you to think deeply and clearly; 2. it helps you learn how to communicate mathematics; 3. it might help you connect to others who share your passion.
Best Answer
What do you want to do with your math blog? What can a math blog do for you? These are the questions you want to be asking before starting up a math blog.
Some people (such as myself) write a math blog much like people write other personal blogs. They may discuss their day-to-day lives (or the mathematically related pats of them) and the mathematics may be a recurring theme, but mathematical exposition might not always be the overall focus.
Others use math blogs to organize and disseminate mathematical exposition. One use is writing and posting notes on some mathematics you are doing at the moment. Terence Tao's blog is an example where you can catch glimpses of his research in some of his posts.
Some students use blogs to store notes on their studies, but I think this practice is meaningful if and only if you intend for others to view and benefit from or comment on the notes. Abstract Nonsense in one such blog. If you don't care for others reading and interacting with your notes, then it's probably best to keep them offline.
Some blogs are topic-oriented, like Sketches of Topology. They are useful for getting people interested in your research and finding people who share your interests to interact with.
Some blogs have an explicitly educational/organizational purpose. Secret Blogging Seminar is organized by a group of mathematicians who discuss topics that they or the community think are important. There is a blog at http://392c.wordpress.com/ that is devoted to a specific course.
Finally, many blogs are there because mathematicians want to reach out to the broader mathematical and scientific community, for reasons varying from research collaboration, idea-bouncing, community feedback, commenting on current events in the field, and so on. Terence Tao and Tim Gowers and others have blogs that exemplify this sort of use, as well as combining all of the above.
What you should do is see for yourself what needs you want to fill via a math blog. Many blogs are an eclectic mix of all the purposes I have described above, and some do other things as well, like Polymath. Always keep in mind, though: much like mathematics is no spectator sport, mathematical blogging is really a team sport. To get the most out of a mathematics blog, I think you should try to reach out to the community and make new friends and connections.