This is life: In a world where truth seems to be at a premium and the future unsure, it’s comforting to know precisely when the sun is going to come up and that when it does, it will do so… Read More ›
Math
When will I ever use this in real life? (No one ever “solves for x”! (Or do they?))
As I wrote eight years ago, it seems that I discuss this topic every couple of years. But there’s always a new reason to do so. Here is the 2020 reason, expressed in this cartoon: What we have here is a… Read More ›
Surreal numbers
Surrealism. That’s Dali and Magritte, right? Well, yes… but surrealism is not just in art. It also pops up in mathematics — mathematics of all things, much to the surprise of those who are not in the world of Donald… Read More ›
Can turtle graphics really help you solve cubic equations? Sounds unlikely…
Wow! In less than half an hour, you’ll learn lots of exciting new math from Burkard the Mathologer! So watch his Turtle Math, in which you’ll learn how to use turtle graphics to solve cubic equations. Along the way you’ll… Read More ›
I know it’s hard to believe, but you too can use a simple formula to generate all the prime numbers!
You probably thought that there is no such formula — one that will generate all and only the prime numbers (formula, not sieve). Right? Well, it turns out that there is! (More or less.) Keep reading… Just start with the… Read More ›
A number of galactic proportions
Take, say, 73 little cubes (blocks or ordinary D6 dice). Could you arrange them into three perfect cubes? I’ll wait while you try to solve this problem… OK, you probably started by taking 64 of them to make a 4×4×4… Read More ›
Sorry, but we’re just not going to be able to get rid of the Electoral College.
Finally the American people have woken up and understand the Electoral College (EC), or at least its importance. Well, at least somewhat. My Quantitative Reasoning (QR) students at the Crimson Summer Academy (CSA) certainly understand it: how many electors each… Read More ›
Grey elections
Who cares about the mathematics of elections? We all should, of course — especially now. An informative, even entertaining way to learn about this topic is to watch the videos of CGP Grey. For a scary example, take a look… Read More ›
How have I forgotten this number system?
That’s easy. I couldn’t have forgotten it, as I had never known about it in the first place! We’re talking about the Cistercian number system. Sounds monkish, doesn’t it? Yes, that’s what it is; it was developed by Cistercian monks… Read More ›
Really? You’re saying Ranked Choice Voting is too hard for adults in Massachusetts?
My former Quantitative Reasoning (QR) students know that Ranked Choice Voting (RCV) is superior to First Past the Post (FPTP), the system we use in Massachusetts for most elections. So why did Massachusetts adults vote it down by a convincing… Read More ›
Hexagonal squares???
Taking a much-needed break from watching the nail-biting election returns, we will consider hexagonal squares. “No such thing,” you say, since you are a knowledgeable geometer. I first saw the phrase “hexagonal squares” when I was 13 or 14, reading… Read More ›
What’s so special about the Mandelbrot Set?
Nobody tires of Mandelbrot Set images, especially the zoomed-in ones. But there aren’t very many non-mathematicians who can explain them — though I hope my former Precalculus students can do so. For everyone else, you really need to watch a… Read More ›
Is this really what (male) math professors are like?
The philosophers in the program were kind and excellent teachers, but the math professors I met in those days were somewhat less skilled at teaching or relating to people. One told us that we should think of him as a… Read More ›
How do I know that they know?
What do we lose by teaching remotely? Here is another follow-up inspired by Patrick Honner in this age of COVID. Honner makes the following important observation: When I taught the IVT last week, I couldn’t walk around class and look… Read More ›
National Museum of Math: new comments
What’s wrong with the National Museum of Math??? A lot, apparently, including race and class discrimination as well as horrible management policies. I wrote a mixed review of this museum last year. I had observed that a lot of the… Read More ›
Popularizers V: Raymond Smullyan
A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet two inhabitants: Zoey and Mel. Zoey tells you that Mel is a knave. Mel says, “Neither Zoey nor I… Read More ›
Popularizers IV: Douglas Hofstadter
Gödel, Escher, Bach — what more do I need to say? Quite a bit more, you reply, especially since only 8% of you have actually read this amazing book. (Statistics gladly invented on the spot, of course.) If you’ve heard of… Read More ›
A math problem for the season
From this week’s issue of The New Yorker:
Popularizers III: George Gamow
What? Why was I reading without my eyeglasses? That’s easy. This photo, my semi-official portrait at age 11, was taken just before I got glasses. And that was all because of a substitute teacher! My regular teacher always had always… Read More ›
Facts, truth, math, and Donald Trump
Given Donald Trump’s uneasy relationship with facts (and a few other flaws), we all wonder how he has managed to maintain rock-steady approval from about 40% of Americans for the past four years. I was unwillingly forced to think about… Read More ›
Learning Strategies 