*This article is published in the February/March 2012 issue of *MAA FOCUS.

A blog can become one of your mathematical homes.

Use it for expository writing, for commentary on research, application, or math in the media. Make it a vehicle for personal anecdotes or teaching tips or advice to student mathematicians. Open an online window on mathematical thinking through math-inspired artwork and other inventive displays.

As specialties deepen and research results become less broadly accessible, such informal mathematical writing is becoming an increasingly valuable tool for bringing math to the general public, schoolteachers, and those in academe.

Even professional mathematicians may further their career goals by reading, commenting on, or writing posts. Indeed, with their built-in commenting capabilities, blogs can foster collaborative research. Blogger Tim Gowers goes so far as to suggest that print journals may eventually be supplanted by an arXiv-like preprint site where academics can review or rate their peers’ work in real time.

Here are a few reasons to turn your attention blogward.

### Generating and Recording Ideas

A good idea rarely emerges without being preceded by a hundred poor ones. Blogs can serve as an online logbook or sounding board, whether for mathematical research or teaching. (The word “blog” comes from a conflation of “Web” and “log.”)

Granted, publicly posting raw thoughts can expose writers to embarrassment. But we should take inspiration from biologist Martin Schwartz’s 2008 essay “The Importance of Stupidity in Scientific Research.” His sentiments were echoed last year on the physics blog BackReAction (see “It’s the Stupidity, Stupid”).

For those looking for research questions to ponder, blog posts can serve as a starting point. For instance, Jesse Johnson discusses the reducible automorphism conjecture in a post on the group blog Low Dimensional Topology. On the more recreational front, the blog Uncover a Few presents interesting questions to ponder, such as “How many regions can be enclosed by two *n*-gons in the plane?”

### Showcasing Exposition

Tim Gowers points out on his blog (Gowers’s Weblog) that “a piece of unoriginal mathematical writing can be useful if it explains a known piece of mathematics in a new way . . . or if it explains something that ‘all the experts know’ but nobody has bothered to write down.” This is a founding principle of the blog Second-Rate Minds, whose title is an ironic reference to G. H. Hardy’s *A Mathematician’s Apology*.

Also referencing Hardy is The Unapologetic Mathematician, where a former academic enjoys discussing differential geometry topics at a level accessible to many math students.

### Fostering Collaboration

The format of a blog, in which comments can be commented on and events are recorded chronologically, can lead to mathematical collaborations. This might be less appealing to those who are concerned about having too many coauthors. Indeed, the polymath project that recently led to a paper about the “density Hales-Jewett” theorem (arxiv.org/abs/0910.3926) was written via The Polymath Blog in just over a month with contributions from more than 20 people.

Some might worry that too much online collaboration will lead to many mediocre papers being published. But a quick look at a blog like The *n*-Category Café, which has promoted discussion among physicists, mathematicians, and philosophers, leads me to feel that such interdisciplinary endeavors are more likely to enrich results than dilute their quality.

### Studying from Afar

For all those students who yearn for that rarely offered special topics course, blogs may provide the informal presentation students crave as well as a chance for interaction with a top-notch mathematician in that area. For example, Danny Calegari’s blog Geometry and the Imagination is home to several sets of notes, including some on hyperbolic geometry and geometric group theory. Undergraduates might like to see what they would learn from Fields Medalist Terence Tao in his real analysis course. His notes are available on his blog, What’s New?

In addition, many mathematicians write about how they came to think about a certain topic. For instance, Conan Wu wrote in his blog Area 777 about how attending a talk on the simple geodesics on a 2-sphere led to his asking a new question, talking to postdocs, formulating conjectures, looking into the literature, and learning about the most recent progress on the topic. Reading this sort of research diary can inspire students and junior mathematicians.

### Getting Advice

Trying to publish your first paper? Applying to grad school? Taking your first college math class? Want advice on using a certain teaching technique? Many mathematicians include at least a few advice-related posts on their blogs. For instance, one recent post on the Secret Blogging Seminar discusses whether participation as a student on MathOverflow, a question-and-answer forum, will make an applicant more attractive to a school.

The AMS-sponsored blogs PhD + Epsilon (by Adriana Salerno, a member of the *MAA FOCUS* editorial board) and the AMS Graduate Student Blog often offer tidbits of advice. Pearls of wisdom can also be had in the form of philosophical discussions, such as the one on Math for Love that draws parallels between playing Go and doing mathematics.

### Cultural Enrichment

Reading a quick blog entry about a new result, award, or piece of mathematical folklore might help us and the general public widen horizons. Certainly, it will make conversation among colleagues a little more fun.

For instance, Ian Stewart discusses the idea that given enough time monkeys can type Shakespeare in his *Psychology Today* blog Math’s Eye** View**. Or in Vi Hart’s blog, we can find many creative videos, including one demonstrating the universe as experienced by an anthropomorphized triangle living on a Möbius strip. Not to mention, by reading the *New York Times *blog Numberplay, we might see how the general public relates to mathematics as readers tackle various kinds of mathematical puzzles.

To search the mathematical blogosphere, check out the new website Mathblogging.org, which aims to categorize all math blogs and give the hosts’ weekly picks. Also, check out and add your blog to the roster on the nLab wiki page. To start your own list of top picks, subscribe to your favorite blogs via RSS feed. In lieu of hosting a blog, simply subscribing to or commenting on posts will be a point of entry that may help you find a geodesic on the blogosphere. It is these lines of communication between blogs that create a sense of community and connectedness.

*Brie Finegold is a postdoctoral teaching fellow at the University of Arizona. *

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