Time to make some goals for 2013! I’ve tried give more weight to goals that I would be less likely to aim for if I hadn’t made them (hence, less maths stuff this year). The points total around 100 (though I have 10 more points from “secret” goals not written here).
- Pick 12 questions or ideas, explore them, and write >=5 pages on each of them.  I want to shift my way of learning towards starting with a math question, and then looking for the resources to answer that question, rather than starting with a math subject.One big problem/month is a good amount. For instance, something like “number of representations as sum of squares” counts as one question. I know some of the ideas but I haven’t really “absorbed” a full solution. It relates to modular forms, algebraic number theory, and is quite open-ended (4 squares, for instance, is classic and already uncovers lots of nice ideas; 3 squares gives relations to modular forms of half-integral weight, class numbers, etc. if I’m not mistaken).Traditionally, I’ve learned by just taking courses, and reading textbooks or papers. Now that my undergrad years have given me a good toolbox, it’s time to get a broader view. Surf blogs, stackexchange, mathoverflow, etc. Ask questions there. Talk to math people more: post answers, comments, write my own entries (blog about each of the 12 topics). Go bother professors with questions. In grad school, make friends and form an informal problem/study group to exchange ideas.
Think about random problems and work on them with paper and pencil, without looking stuff up, and then look stuff up.
- Number theory text: find at least 2 collaborators and add ~300 pages of new content. (For the record, it’s now about 561 pages.) In a project like this I have to find collaborators. I’ve tried to do a lot of this by myself. Take a chapter, and write it as perfectly as I can, using what I’ve learned from Gliya and all my other teaching experiences. Especially focus on adding VSNC-style overviews, explorations, guiding text, connections between different subjects and viewpoints, and problems. Then contact people. Let them know what they can contribute, and give them a working model to convince them to come on board. 
- Work on a research project. Discover something new, or at least learn a new idea in depth. 
Writing and Reading 
In 2012, I articulated many of the elements that go into good writing. In 2013 I want to build certain skills such as worldbuilding and research (i.e., finding the people and resources that I need for a story) and devote a significantly larger time to writing, with the goal of creating finished products. I’ve grown more interested in fantasy and science fiction but feel that I lack the experience of crafting stories in these areas, so I want to immerse myself in a fantasy/sci-fi community. Finally, I want to make a few lasting writer friends to stay in contact with after college.
(Open-ended. Overlaps allowed.)
- Write a science fiction story. 
- Write a story that addresses some “larger” issue. (One thing I really want to address is education. See Mathew’s post.) 
- Finish at least 3 short stories. 
- Work on a story that requires significant research. Read history books, talk to people. 
- Work on in-depth worldbuilding for one world. 
- Finish my dreams novel. (This is probably the most ambitious goal here, and may or may not be feasible, but nevertheless I’ll keep it. At least try to have a sort-of skeleton for the whole novel in place.) 
- Get a piece of writing (any piece) published somewhere and make money out of it. 
- Read 40 books or 12,000 pages. For every book that I read, write at least a paragraph (for instance, about good ideas that I learned from the book, or what the book taught me about good writing). [4.0]
- Find one or a few friends who are writers, and correspond regularly. 
- Participate in a sci-fi/fantasy community. For instance, join a role-playing game club, participate in collaborative worldbuilding online, etc. Immerse myself in some other world. 
- Ask at least one interesting question every day, and write it down. Try to answer those questions. [3.65] Research is about asking questions. Writing is about asking questions. Especially sci-fi. “What if…?”
- Write a blog post, detailing what I learned from 4 years of college. Detail all the things that I wished I knew as a freshman, for the benefit of freshman, and anyone else, really. 
- Learn to converse with strangers. Break awkward silences. Sit at new tables. Say things I wouldn’t normally say. Make some friends through serendipity. Be able to answer the question in very specific terms by the end of the year, if someone asks, “Why would you want to talk to strangers? What can you learn from them?” 
- Do something new and interesting for UMA that brings the math community together. 
- Family bonding in ATS! 
- Every month look at this list again. Think about where I am, how I might change what I’m doing to reach my goals. Change my goals, if I change. [1.2]
- Travel in China. Take some fantastic pictures. 
- CETI: Teach in China. Meet new people. 
- Become more fluent in Chinese. Read a Chinese book, cover to cover. Keep a list of words I find myself reverting to English in, and look them up. 
- Learn to program a computer game (11.127). 
- Learn to make a robot (Maslab). 
- Keep in touch with family and friends more often. Let them know what I’m up to, and ask them what they’re up to. 
- Explore ways to put together math and fiction. Take a good long look at what’s out there. (Vi Hart, etc.) Then do something unique. 
- Do some crazy things that I haven’t anticipated in this list. 2 points for each crazy thing. No upper bound. Must be crazy enough to count. [2x]