Let me start out by apologizing for two things, first the horrible pun in the title, and second my absence from the blog for the summer. Between moving twice (once cross-country), graduating, getting set up at a new job, buying furniture, trying to finish some papers, and being academic coordinator at Mathcamp I was pretty swamped. As a result I missed out on some developments in the math blogging.
Frequent commenter Danny Calegari started a blog in May. It pays to occasionally click on the links in comments here as sometimes you’ll find brand new blogs. My mathcamp friend, Matt Kahle, who is a postdoc at Stanford also started a blog. It has a fun mix of some elementary stuff (like the Rubik’s cube) and some of his research (which as an interesting mix of topology, combinatorics, and statistical mechanics, it definitely involves a lot of sending n to infinity in ways that would make my advisor happy). I’ve been meaning to link to both of those since sometime in June but just haven’t gotten around to it (though I did manage to add them both to the blogroll). It’s been that sort of summer, just ask me about my passport. Also, low dimensional topology has become a group blog. I find group blogging a great model both as a reader and blogger because it promotes conversations and allows one to maintain a reasonably updated blog even when someone disappears a whole summer.
Finally, over the summer there was a great conversation about what mathematicians need to know about blogging. Here’s my two cents. One thing incredibly valuable thing about blogging is the opportunity to have discussions and get advice about how to be a mathematician. It’s often hard in real life to have a discussion involving people at many different places in their careers about professional questions. In that spirit, here’s a question I’ve been wrestling with lately. How do you balance your research time between the following three activities: working on problems you basically know how to solve, working on problems you don’t know how to solve but are important problems, and learning new tools. When I was in graduate school I felt like it was pretty easy to balance things because any time I had any idea that was at all worthwhile I just worked on it and when I didn’t, I learned new things. I had few enough research-worthy ideas that it was feasible to think about all of them. Now that I know more I can’t keep doing that because I simply don’t have time to work on all the easy problems that I could solve. So the need comes to prioritize. I was wondering how other people strike this balance.