In the course of being a math person on Twitter, I have run across some math-related Twitter bots and feeds. It would just be mean to grade my human tweeps, but I have no qualms about rating the bots! Taking a page from the Aperiodical’s integer sequence reviews, I’m rating them on a scale of 1 to 5 on novelty, aesthetics, and explicability.

@_primes_ tweets one prime number per hour. I’ve never been especially interested in big numbers, numerology, or primes, so I’m surprised by how much I love this little bot. Seeing the primes one at a time instead of in some massive list gives me a chance to enjoy them aesthetically. When I’m in the right mood, I have a lot of fun tweeting about them and passing judgments on them or observing whether they would make good poker hands.

I highly recommend this feed to anyone who wants to feel a little more connected to the prime numbers.

Novelty: 3

Aesthetics: 5

Explicability: 5

Rating: 13

@p_lnp is the youngest bot on my list, and I’m proud to say I helped make it happen. @p_lnp piggybacks off of the @_primes_ bot and tweets the value of p/ln(p) for each prime that @_primes_ tweets. I suggested this on Twitter a few weeks ago as a way to watch the prime number theorem in action, and @michiexile made it happen last week. The prime number theorem, which I wrote about earlier this year, says that as n increases, the number of primes less than n approaches n/ln(n). In other words, we understand a lot about how primes are distributed as we skip away to infinity.

Each time @p_lnp tweets, you can look in the @_primes_ feed to see how many primes there have been up to that point and compare that number to p/ln(p).

For example,

71889 was the 7117th tweet by @_primes_, so using p/ln(p) as an estimate for the number of primes less than 71889 is off by about 700, less than 10% of the number of primes up to that point. Not too bad. As @_primes_ keeps tweeting, p/ln(p) will get proportionally closer and closer to the actual number of primes @_primes_ has tweeted.

Once again, I’m not a huge number theory person, but seeing it in little pieces makes the theorem more relatable to me. The numbers @p_lnp tweets are necessarily less interesting in and of themselves than the ones @_primes_ tweets. The prime number theorem says that in general, @p_lnp should be moving up by approximately one every time it tweets, and that’s what it does a lot of the time. Every once in a while it jumps up by two or three, but it doesn’t have the unpredictable, sporadic nature that @_primes_ seems to. But slow and steady is fine with me.

Novelty: 5

Aesthetics: 5

Explicability: 5

Bonus point because I’m super excited that @michiexile made this feed for me: 1

Rating: 16

@Hexagonbot is the wackiest math twitter bot I follow. Like many people, I found out about it when I tweeted something containing the world “hexagon” and immediately got a retweet from this bot. In it’s description, @Hexagonbot links to hexnet.org, the “global hexagonal awareness resource center.” Six is my favorite number, but I’m not nearly as committed to it as the good folks at hexnet are.

When you follow @Hexagonbot, you see a very interesting cross-section of Twitter. Some of the main topics you’ll encounter are the hexagon-shaped storm on one of Saturn’s poles, the Super Hexagon video game, crafts with hexagonal motifs, items for sale on Etsy and Amazon with hexagons in them, the hexagonal rocks at a waterfall in Iceland, and professional wrestling that takes place in a six-sided ring. You’ll encounter “love hexagon” (as opposed to "love triangle") jokes and jokes from students who say that the only thing they learned in organic chemistry was how to draw hexagons. And of course, there are a few spam accounts that just spew incoherent jumbles of words.

You'll also run across quite a few people who feel like I did when I first discovered @Hexagonbot.

Novelty: 4

Aesthetics: 2

Explicability: 6i

Rating: 6+6i

@FlipADay: tweets the result of a coin flip every day. I’ve been following for a few months now, and heads have been in the lead for a while. I like peeking in on the stats every once in a while. It’s a good reminder that randomness doesn’t look the way we think it should. If I were making up “random” coin flips, I’d never make write down 11 heads in a row, but there's one in @FlipADay's past. WolframAlpha tells me there’s about a 10% chance that there’s a run of 11 heads somewhere in a sequence of 452 flips.

Novelty: 3

Aesthetics: 3

Explicability: 5

Rating: 11

@RollADay tweets the result of a roll of two dice (or perhaps two rolls of one die) every day. Sorry, @RollADay, even though you’re in the same spirit as @FlipADay, I don’t like you as much. Even though your stats page has more information (number of doubles and dice sums), I’m just more beguiled by the simplicity of the binary.

Novelty: 2

Aesthetics: 2

Explicability: 5

Rating: 10

@InterestingNums is “on an endless search for the first uninteresting number.” There is a famous quasi-theorem in math that there is no uninteresting integer. If there were, there would be a smallest uninteresting number, and that would be interesting! For the past 163 days, @InterestingNums has been tweeting an interesting fact about a positive integer every day, demonstrating the quasi-theorem.

Novelty: 4

Aesthetics: 4

Explicability: 4

Rating: 12, the smallest abundant number.

@Pure_Numbers is the feed for the purenumbers tumblr. Every day, it tweets an equation using the numbers in the date. It might be fun to share with kids or students. You could even ask them to make their own number sentences about the day's date.

Novelty: 4

Aesthetics: 2

Explicability: 3

Rating: 9

@MathPaper tweets the titles of new papers uploaded to the mathematics section of the preprint server arxiv.org. Nothing fancy here, but it’s fun to scroll through every once in a while and just see what's out there. More than once, a title has jumped out at me, and I’ve clicked to find out that it’s by a friend of mine.

Novelty: 1

Aesthetics: 3

Explicability: 5

Rating: 9

@MathbloggingAll tweets the titles of new posts on the blogs that are listed on mathblogging.org. Once again, it’s nothing fancy, but it’s helped me find a few new blogs to follow. Unfortunately, there are some blogs that are only tangentially related to math and some pages that probably don’t qualify as blogs in the feed, so there are a few posts that kind of don’t make sense that get in the feed. But that's the nature of the beast. If @MathbloggingAll is too much like drinking from a fire hose, @MathbloggingEds is for the cream of the crop, with just a few posts a week.

Novelty: 1

Aesthetics: 3

Explicability: 4

Rating: 8

I also follow some math-related feeds that don’t really seem to qualify in a list of bots but are still worth mentioning.

@JohnDCook maintains 15 daily “tip” accounts! My favorites are @TopologyFact, @AnalysisFact, and @TeXtip.

@Thalesdisciple maintains the @GeometryFact feed, which shares interesting geometry blog posts and websites.

Have I overlooked your favorite math Twitter bot or feed? Let me know! If you’d like to find more mathematicians to follow on Twitter, I have two lists you can subscribe to: Mathletes and Mathy Ladies.