New Devlin's Angle posts can be found on the Mathematical Association of America's Math Values blog. This site will remain live as an archive for all previous posts ..read more

This month, it will be exactly 22 years since the MAA first went online. After its initial release in 1994, the web browser Netscape had, by 1996, started to acquire users rapidly, in the process turning the new World Wide Web from a scientists' communications platform into a citizens' global network. Like many organizations, the MAA was quick to establish a presence on the new communication medium. In December 1996, the Association launched MAA Online. It’s the platform on which you are reading these words, though the word “Online” was eventually dropped, when it no longer made sense to call ..read more

I sometimes use this column to float an idea I think deserves attention. Not on a whim, but after considerable thought and discussion with others expert in the relevant domain(s). This is one of those times. I already set the scene with last month’s post. Here is a nuanced, bullet-point summary of what I wrote then:  The heart of learning mathematics is mastering a particular way of thinking – what I (and some others) call “mathematical thinking,” sometimes also described as “thinking like a mathematician.” You can master mathematical thinking by focusing on any one branch of mathematics ..read more

“In math you have to remember, in other subjects you can think about it.” That statement by a female high-school student, was quoted by my Stanford colleague Prof Jo Boaler in her 2009 book What's Math Got To Do With It? I took it as the title of my June 2010 Devlin’s Angle post, which was in part a review of Boaler’s book. In a discussion peppered with quotations similar to that one, Boaler describes the conception of mathematics expressed by the students in the schools where she conducted her research. To those students, math was a seemingly endless succession of (mostly meaningless) rules t ..read more

The above tweet caught my eye recently. The author is a National Board Certified mathematics teacher in New York City who has an active social media presence. Is his claim correct? Not surprisingly, a number of other mathematics educators responded, and in the course of the exchange, the author modified his claim to include the word “just”, as in “It isn’t just about beauty …” In which case, I think he is absolutely correct. Like many mathematicians who engage in public outreach, I have frequently discussed the inherent elegance and beauty of mathematics, the wonder of its purity, and the p ..read more

By Keith Devlin You can follow me on Twitter @profkeithdevlin First, congratulations to Caucher Birkar, Alessio Figalli, Peter Scholze, and Akshay Venkatesh on being awarded the Fields Medal, an award that for regular “Devlin’s Angle” readers needs neither introduction nor description. (If it does, use Google.) With Fields Medals awarded only (at most) once every four years to mathematicians who produce truly exceptional mathematics before they turn forty, few of us who enter the field come close to getting one. (Indeed, in some ways they are more akin to Olympic Gold Medals than the Nobe ..read more

By Keith Devlin You can follow me on Twitter @profkeithdevlin 21st Century Math: The Movie All my Devlin’s Angle posts this year so far have studied the dramatic shift that took place over the past twenty-five years in the way professional mathematicians “do the math” in order to solve real-world problems. There have been parallel changes in the way pure mathematicians work as well, but those changes are somewhat less visible, and not as dramatic. In any case, I have been focusing on mathematics in the wild. Those changes in how math is done have put pressure on global education systems t ..read more

By Keith Devlin You can follow me on Twitter @profkeithdevlin Last month, my two greatest passions collided: mathematics and cycling. On my way back from a short biking trip to the Californian Central Coast (gorgeous in the late spring, when the grass is still green and the wildflowers are in full bloom), I stopped off in Morgan Hill (home of the American Institute of Mathematics) to watch part of Stage 4 of the seven stage, Amgen Tour of California. Wandering around the start area, where the teams warm up on stationary trainers and the big vendors show off their wares, I noticed a couple o ..read more

By Keith Devlin You can follow me on Twitter @profkeithdevlin Ever since mathematics got properly underway around 3,000 years ago, there was only one way to achieve access to the field. You had to spend many years developing a fairly extensive calculation skillset. In the first instance, to pass the graduation and entrance examinations to gain initial access to the field. Then, once accepted into the world of mathematics, calculation of one kind or another was what all mathematicians spent the bulk of their mathematical time doing. Arguably, for most of mathematics history, the subject ..read more

By Keith Devlin You can follow me on Twitter @profkeithdevlin NOTE: This article is the final installment of a four-episode mini-series posted here starting in mid-January. In writing it, I have assumed my readers have read those three earlier pieces. At the end of last month’s post, I left readers with a (seemingly) simple arithmetic problem. I prefaced the problem with the following two instructions: 1. Solve it as quickly as you can, in your head if possible. Let your mind jump to the answer. 2. Then, and only then, reflect on your answer, and how you got it. The goal here, I said, i ..read more