Like many mathematicians, I have some of the tools to understand finance and economics, but I’m naive about both subjects. After reading some of Bernanke’s blog, I wanted to look at some math blogs that focus on finance. I’ve had the Mathematical Investor in my feed for a while. It’s written by David H. Bailey, Jonathan M. Borwein, Marcos Lopez de Prado, and Qiji Jim Zhu and is a result of their “growing concern with the usage of less-than-fully rigorous mathematical and statistical methodologies in the financial/investment world.”

Recent posts have been about the 2010 “flash crash,” conflicted financial advice, and an assessment of 2014 market predictions. The authors are especially concerned about “backtest overfitting,” which is basically the error of making investment decisions that are based too heavily on historical data; one of their posts announces an online tool that demonstrates the problem.

Cathy O’Neil is my other main source of blog posts about finance, and I’m eagerly awaiting Weapons of Math Destruction, her forthcoming book about big data and the dangers it poses to democracy.

I poked around for some other financial math blogs and stumbled on Fermat’s Last Spreadsheet, a blog that hasn’t been updated in a while but has posts on coding, normal subgroups, and poker in addition to the main focus on fixed-income trading. Fermat’s Last Spreadsheet also introduced me to Magic, Maths and Money by Timothy Johnson of Heriot-Watt University. He concentrates on moral/ethical aspects of finance and the recent financial crisis.

Do you have any recommendations for financial math blogs?

]]>Well, it’s official, I’m an unrelenting fangirl for Dustin Cable’s Racial Dot Map and everything it stands for. If you’re not yet familiar, it’s one of the coolest data visualization projects to come out of the census data. The map does the following simple thing: every person in the country is represented by a dot on the map, and every dot has a color based on the person’s race. Black, white, asian, hispanic, and other.

The map, a non-trivial feat in data handling, paints a beautiful picture of the racial breakdown of the USA with little commentary beyond what you see in front of you. But it is a rich source for discussion, especially if you are someone who likes to analyze statistical trends, and let’s be real, who doesn’t love a good regression line?

Most recently, Nate Silver on the data science blog FiveThirtyEight, coined the index of dissimilarity, a measure of diversity vs. segregation of American cities with the racial dot map as inspiration. The basic idea is that a city can be simultaneous diverse and segregated. How does this happen? On a city-wide level there can be many people of all different races living in the city, but on a neighborhood level they night be totally distinct.

The beauty of this measure is that it is totally quantifiable, by counting people in cities/neighborhoods and then counting the percentage of their neighbors that are of a different race. If that number is high on both the city and neighborhood level, that means city is both diverse and non-segregated. I always find it satisfying when you can really apply a metric to these types of questions. You can check out the search function in post to see how your city stacks up. Pittsburgh — the Paris of Appalachia that I call home — has a citywide diversity of 50%, which basically means that half of the people in the city are different from you. But the neighborhood diversity is only 35.5%, which means that on the more local scale, things look pretty segregated.

It’s fun to see how different cities and regions of the country look under this metric. As always, a good handling of data and statistics is a great way to start a conversation about the deeper implications that this has for out communities and lives.

]]>I’ve spent a good amount of time thinking about that question recently, and I figured I’d inflict it on you as well. It’s not my fault, though. Sam Shah, a high school math teacher, wrote about the question on his blog, Continuous everywhere but differentiable nowhere, after Matt Enlow shared it. I’ve been reading Shah’s blog since 2012, when he posted a really interesting calculus class project investigating the Gini index, a measure of wealth inequality.

The stuffing sacks problem appears in the good math problems tag on his blog, which certainly lives up to its name. Plenty of nerdsniping there. Some of the problems are fun brain teasers like stuffing sacks, but some of them are more geared towards making sure his math class is about thinking instead of formulas. For example, what’s the derivative of log(log(sin(x)))? It’s easy to use the chain rule to come up with an answer without stopping to consider the small detail that log(log(sin(x))) doesn’t make sense for any real numbers. Oops.

In addition to puzzles that will help you pass the time waiting for the bus, Shah often writes about how he cultivates deep understanding in the classroom. He recently wrote about the way he has students make conjectures at the beginning of the semester and then the eventual payoff when they finally have the tools to prove the conjectures. Outside of the classroom, he helped launch a student math and science journal at his school. Even if you don’t teach high school, a trip to his blog will probably give you some ideas for your classroom or just for talking about math with people.

So how many ways are there to stuff sacks? It’s not hard to figure out the values for the first few numbers *n*. But holy overcounting, Batman, things get complicated as *n* increases! There’s an OEIS sequence that will get you the answer, but that would take all the fun away.

As academic mathematicians, we spend a great deal of our days performing deeds of service to the mathematical community. Editing papers, organizing workshops, contributing to open-source software initiatives. One could even argue that it is out of sheer benevolence to the mathematical community that we even write papers at all. In a blog I just discovered by mathematician and Clay Prize winner, Michael Harris, the dynamics of this community get a very thorough and thoughtful analysis.

Mathematics without Apologies is, in the words of Michael Harris, “an unapologetic guided tour of the mathematical life.” Harris takes us on a tour of some of the very compelling — and highly fraught — issues that arise when you start to think about the mathematical profession, and its community, from a sociological point of view. Michael Harris is a professor of mathematics at Université Paris-Diderot and Columbia University.

In a multi-part post, Harris explains the much debated Elsevier boycott initiated by fellow mathematician and blogger, Tim Gowers. The boycott was proposed in 2012 in opposition to the extremely high price tag the Elsevier puts on its research papers that are essentially donated to them. Harris addresses some of the alternative publishing models that people have proposed. One idea is that the math community should be doing our own reviewing and publishing through Yelp-style real time user reviews. Harris is not so keen on this idea.

I don’t like the fact that unpaid Customer Reviews have undermined professions (as Tom Waits pointed out). I’m wary of replacing a practice that has evolved over several centuries to serve the needs of the profession by a model of sociability that in less than a decade has led to the creation of massive fortunes and an enormous shift of power with practically no democratic oversight.

What I really appreciate about Harris’ blog is that it is very mindful of the community aspect of the mathematical profession. In one post he writes about Mathematics as a gift community, where we are defined by the gifts that we bring to it. He reflects on the amount of time and effort that it takes to be a good community member, and that it should be in all of our best interest to improve our community through deeds of service. I suppose this is true across all disciplines in academia, but it’s nice to think of things that way. It makes me happy to mow my mathematical lawn and take out the trash to help my whole mathematical neighborhood look a bit more sparkly and clean.

]]>Christine Rueter, who writes the astropoetry blog Tychogirl (featured here last November), is celebrating National Poetry Month by writing a poem a day. I’m partial to “The LM (after Blake)” and “color leaked in,” which was based on the first color images of Pluto and Ceres from the New Horizons spacecraft.

I’ve written previously about JoAnne Growney’s blog, Intersections–Poetry with Mathematics, but it is still my favorite math poetry source and a great place to visit this April. If you live in the DC area, you can even see Growney at a poetry reading tonight (if it’s still April 20 when you read this)!

Earlier this month, Growney shared a link to an interview with Enriqueta Carrington at the Art Works blog. Carrington is a mathematician at Rutgers and a poet in both Spanish and English. She currently has an NEA translation fellowship to support her work translating the work of Sor Juana Inés de la Cruz, a 17th-century poet from New Spain (now Mexico). In the interview, Carrington talks about how mathematics and poetry are linked for her and about the challenges of translation.

The other math poetry blog I have in my feed, appropriately named Mathematical Poetry, is by Kaz Maslanka. He primarily creates and shares visual poetry that uses mathematical symbols to express relationships between ideas. Two common types of these poems are orthogonal space poems and congruent triangle or proportional poems, where a fairly simple equation expressing proportion can be interpreted in several subtly different ways. (There is a whole blog devoted to proportional poetry here.) I also recommend his post about various types of mathematical poetry. In addition to his own poetry, he shares works by other visual mathematical poets. While I am more comfortable with verbal poetry, it’s interesting to see the way words, pictures, and mathematical symbols flow together in these works. Maslanka’s most recent posts share the sad news of the passing of Bob Grumman, another visual mathematical poet who wrote a series called M@h*(pOet)?ica for Scientific American a few years ago.

Do you have a favorite poem or poet inspired by math?

]]>To begin, the metaphoric Phillips head screwdriver in my online toolbox is a highly specified and but oft-used resource: the number field database. This database was compiled and maintained by John Jones and David Roberts, and a few other contributors — both human and software. It is basically a tool that takes in a list of field parameters and spits out a list of number fields satisfying every item on the list. Let’s say, for example, that I’m trying to get my hands on every imaginary degree 2 number field with discriminant bounded by 100, and just for fun, let’s say it can only ramify at 3 and 5. You plug those parameters into the database, *et voilà*, it returns the number field with minimal polynomial *x ^{2}-x+4*.

And as if the database on its own wasn’t cool enough, you can actually load it into Sage and do number field computations to your heart’s content. Speaking of Sage, if the number field database is the Phillips head in my toolbox, the Sagecloud is the hammer.

Even the most amateur toolbox isn’t complete without a reasonable selection of flat-head screwdrivers, and the L-functions and Modular Forms Database (LMFDB) is exactly that. The LMFDB can do a lot of things. In particular it hosts the number field database mentioned above, and then some. It is an ever growing library of tables, formulas, links, and references for L-functions, modular forms, and related objects. Generally, L-functions are just the analytic continuation of a Dirichlet series which have an associated Euler product. Examples of L-fucntions come out of modular forms, Diriclet characters and elliptic curves, but perhaps the most famous example is the Riemann zeta function.

The LMFDB has a similar setup to the number field database, in that you can ask for an object with the prescribed characteristics and you get back a full list of candidates. But now the search has broadened. Say, for example, I want to see every possible elliptic curve over the rationals with conductor 389. The LMFDB returns a list complete with each curve’s rank, Weierstrass coefficients, j-invariant, and index in the Cremona elliptic curve database.

Finally, every toolbox has that one item (for me it’s my level) that I’ve never actually used, but it’s still fun to take out and play with from time to time. And that, for me, is the Online Encyclopedia of Integer Sequences. This is not to say that it’s not a useful tool, I know plenty of people who use it in their research, but I’ve never had occasion to use it beyond blissfully throwing in random strings of numbers and learning about new sequences. Math writer Alex Bellos wrote a very nice piece about the OEIS for The Guardian in honor of its 50th birthday.

These are just a few tools for the number theoretic among us, and surely there are many more. Let us know if there are other online tools and databases that help you in your research. And if you know how people did research before the internet, tweet it at me @extremefriday.

]]>A few weeks ago, my social media world got pretty excited that Ravens offensive lineman John Urschel and his collaborators recently published a paper in the *Journal of Computational Mathematics: *“A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians.” (That link is to the arxiv version.) I’m pretty sure this is the most the world has ever cared about the eigenvector corresponding to the second smallest eigenvalue of a matrix. There were quite a few articles and blog posts about his paper, although not always from the usual math suspects.

Deadspin reported Ravens lineman John Urschel loves math more than you love anything. Rolling Stone published an interview with this lover of graph Laplacians. Bloomberg informed us that one of the Baltimore Ravens just published an insanely complex study in a math journal, and I’m going to pick on them a little bit. How silly! “Oh no, I can’t immediately understand a technical paper in a field I’m not an expert in. It must be insanely complex!” It’s not that the paper isn’t impressive. The Journal of Computational Mathematics is a fine, upstanding journal, and it’s a legitimate result. But calling it “insanely complex” just makes me roll my eyes. And this isn’t just a case of a hyperbolic headline. The article, instead of presenting a gentle explanation of linear algebra or graph theory, shows us an equation-filled page to prove to us how “insanely complex” this paper is.

Luckily, Urschel himself wrote an explanatory post about his paper on Forbes. It’s clear, easy to read, and even has a few football analogies for good measure. He defines all the terms in the title and gives us the idea of what the main idea of the paper is: use simpler graphs to approximate a problem on a more complicated graph. I couldn’t use it to compute the Fiedler vector of a graph Laplacian, but I have an idea of why someone might want to.

I was unaware that the Ravens had a mathematician on the team until I heard about this paper, so I went poking around his online presence. Urschel has a bachelor’s degree in math and a master’s in math education from Penn State, and he’s taught a few classes there. He seems like a really fun guy, at least as measured in topology jokes on Twitter, and I’d like to meet him. (Sadly, my request to be his bestie has so far gone unanswered.)

Urschel also writes the Advanced Stats column for the Players’ Tribune, a relatively new website that features articles by pro athletes. There, he’s written about the transitive property as it relates to head-to-head matchups and the distribution of college majors among football players. I really admire his public math outreach, especially his constantly positive, upbeat attitude, and his defiance of the stereotype that jocks aren’t good students. (Of course, there are many college and professional athletes who show us that, but another one doesn’t hurt.) I hope that when his NFL days are over, he’ll be able to share math with students who will see him as a role model for both sports and academics.

]]>Did you know that a group of six women programmed the first ever electronic computer? Just one of the interesting facts I’ve learned this March, and in honor of Women’s History Month I wanted to give a well-deserved tip of the hat to math blogs about, by, and for women.

Several years ago on this very blog, we posted about Grandma got STEM, a blog maintained by Rachel Levy of Harvey Mudd College. After more than two years, I am happy to report that the blog is still actively receiving submissions about our badass foremothers in STEM, many of whom are mathematicians. Recently there have been profiles of Else Hoyrup, a Danish topologist turned women’s science historian, and Fannie M. Gordon, the woman behind Lanczos’ algorithm.

Obviously, a major part of what makes profiles of women in math so compelling is that they seem to be relatively rare. And while women have certainly gained a larger footprint in the field — according to the most recent AMS annual survey nearly 30% of 2014-2015 math PhD recipients were female — there are still serious hurdles to clear.

Some of these obstacles are discussed in great detail in award-winning mathematician Izabella Laba’s blog, The Accidental Mathematician. Laba writes thought provoking pieces about gender policitics in the mathematical sciences. In her most recent post Laba discusses how matters of gender discrimination shape the world of math conferences, a topic also covered very eloquently by blogging physicist Athene Donald (not a mathematician, per se, but one of our sisters in STEM nonetheless).

On calling attention to the problems at hand, Laba says, “We sure talk about gender. In terms of pure volume, we may be close to the saturation point already. It is not clear that this is helping.” Rather, her post is a call to action for the men and women of mathematics to treat fairly the “women and minorities who are absent, hypothetical, or nonexistent,” as well as those women who are already there, by considering our implicit biases.

And sometimes, as male mathematician and veteran blogger Jordan Ellenberg expresses so poignantly, seeing the gender imbalance swing in the opposite direction allows us to see the subtle biases that we — otherwise good people — allow to inform our actions.

To all of the pioneering women in math who have done so much to advance the field and our collective standing it it, we are proud to walk in your well-heeled footsteps. Hear more about the ladies of ENIAC on Science Friday, keep up with the latest gossip on twitter with #womeninSTEM, and if you see a mathematician hard at work today, be sure to tell her you admire her work.

]]>Like many mathematicians, I’m pretty lukewarm about Pi Day. I’m generally a scrooge about most holidays, but I do appreciate the fact that Pi Day has given me a chance to write about some cool math topics I probably wouldn’t have otherwise. Last year I wrote about π(x), the prime counting function, and this year, I wrote about continued fractions, which get cooler every time I learn more about them. (I can’t help but brag about the fact that Mike Lawler did some continued fractions with his kids after reading my post. I love seeing my work in action!)

Of course, there were quite a lot of nice Pi Day posts around the math blogsphere this year. Pat Ballew wrote about pi and the Kruskal count, a fun mathemagic trick. JoAnne Growney posted at at her math poetry blog about Pilish, the “language” whose word lengths follow the digits of pi. Alex Bellos wrote a short post in Pilish for the Aperiodical. Dick Lipton and Ken Regan took the opportunity to discuss another pi: products. Specifically, how much does integer multiplication cost? Rafael Irizarry wrote about empirical evidence that pi is a normal number for Simply Statistics

The Aperiodical pulled out all the stops for Pi Day. If I counted correctly, they posted 15 articles about pi this past week. I especially enjoyed their first one, a video of mathematicians using various methods, from measuring the period of a pendulum to filling water balloons, to estimate pi. I also appreciated Katie Steckles’ rumination on the appropriate time to celebrate pi in several different timekeeping systems. Aperiodical contributor Christian Perfect bought the domain three.onefouronefivenine.com, where you can scroll down and see lots and lots of digits of pi.

Education-focused blogs Math Munch, Let’s Play Math, and Moebius Noodles used the occasion to publish fun, accessible posts about pi. Stuart Price, inspired by Joshua Bowman, wrote about π-th roots of unity, which relate quite nicely to continued fractions. Mike Lawler also used that activity with his kids.

I understand why math bloggers write about Pi for Pi Day, and they write a lot of neat stuff. General interest news media, however, can get weird about it. On the one hand, it is nice for math to get a little bit more focus than it usually does. On the other hand, the stories often divide the world into “us” and “them”: regular folks and freaks who like reciting numbers. Is there really no such thing as bad publicity? As Dan Meyer said on Twitter,

@lodish Publicity that promotes an image of math as obsessed with cryptic numerology and obscure rituals is bad publicity. My opinion.

— Dan Meyer (@ddmeyer) March 13, 2015

Some big media outlets did pretty well on Pi Day. Phil Plait wrote a fun piece for Slate, Alex Bellos wrote a few nice posts for the Guardian, including one about the first person to use the letter π for circles, and Manil Suri wrote an op-ed in the New York Times. Gary Antonick wrote a very nice post for the New York Times Wordplay blog. He focused on Euler’s identity and included an excellent new-to-me video explaining how exponentiation works when you start messing around with complex exponents.

Daniel Ullman wrote a good article for the Conversation that includes the fantastic tongue-in-cheek suggestion to celebrate Earth Day by eating foods that start with the letter ‘e’. Or, of course, we could do that to celebrate *e* Day on February 7th (2/7 for the US and Belize), July 2nd (2/7 for most of the world), or September 28 (the 271st day of the year in non-leap years, 272nd in leap years—either would be appropriate as *e* starts 2.718). Steven Strogatz wrote a lovely article about the Pi Day dilemma for the New Yorker. Pi is an important number, and it really is stunning that is appears in so many places. It’s frustrating when our attempts to talk about it are reduced to lists of digits.

Some big news outlets…didn’t do so well. *Time* gave us Pi Day Deals, Freebies, and Events for Math Lovers and Haters Alike. Select quote: “There are plenty of deals meant to appeal to C students who hated math too.” Thanks for making sure we “normal people” know that it’s still OK to openly despise math! (Can you imagine St. Patricks Day deals explicitly marketed to people who hate the Irish? It’s not a good analogy because the Irish are people and math is an idea, but it’s pretty odd to focus holiday coverage on people who hate the idea behind the holiday.) *USA Today* asked us to watch these stunning videos of kids reciting 3.14. The headline is bizarre, but the kids are lovely, and if they enjoy memorizing the digits of pi, good for them. I just wish the coverage had less gawking at non-mathematical activities in it.

Next Pi Day, 3/14/16, is a better approximation of pi than 3/14/15. I guess we’ll be meeting back in a year for another “Pi Day of the century”!

]]>When I was in graduate school I mostly worked really hard all the time. Like we all do, right? But occasionally, my officemates and I would get a bit punchy, and the need to blow off steam would momentarily supersede our desire to compute Dirichlet characters. At these moments, one of our favorite diversions was mathematical pictionary. Basically like regular pictionary, this game had us drawing the names of a famous theorems, concepts, or mathematicians. It provided hours of fun, and a gallery of *incredibly* bad math pictures. See example above. Happily, I was reminded of this recently when I was hanging out at one of my favorite blogs, Math with Bad Drawings.

The blog is written by Ben Orlin, a math teacher in Birmingham, England (so I suppose he’s actually a maths teacher). Orlin wields a dry-erase marker like a young Picasso, writes incredibly thoughtful posts about his observations in life as a teacher and learner of mathematics, and the product is something that is part narrative and part long-form comic. He says, “you could call this a “math blog,” or a “teaching blog,” but I would call it a blog about owning up to weakness and drawing strength from successes, however transient or trivial they may seem.”

In one recent post Orlin gives a thoughtful answer to the controversial question: Why do we pay pure mathematicians? Aside from the fact that pure mathematicians are really good at equations — even the really long ones — Orlin draws out some important ideas, namely, how essential the study of pure math is to the world we live in. Had those 19th century mathematicians not become obsessed with provability, we wouldn’t have iPhones today. Beyond the massive life-changing breakthroughts he points out that it’s also just really nice to look at, “come for the pretty patterns, stay for the cosmic insights.”

In an older, but equally thoughtful post, Orlin explains what it feels like to be bad at math. No surprise, it feels bad. But Orlin explores where the badness comes from and what people can do to cope with those hurt feelings.

Some posts are just a series of clever jokes (yes, math jokes exist) that seem to hit really close to home, like “Math Experts Split the Check,” or “A Math Professor Consults On A Hollywood Movie,” and my favorite, “The Student Every Teacher Dreams About.”

You can check out the archives on Math With Bad Drawings, and follow Orlin on Twitter @benorlin. And while you’re over on Twitter, let me know if you figured out the pictionary puzzles @extremefriday.

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