Quick math-personality quiz: What is seven-and-one-fourth minus three-fourths, expressed as a mixed number (a whole number plus a proper fraction)? What matters isn’t what answer you get but how you arrive at it; your thought-process will reveal what kind of thinker you are. So please stop reading now and continue once you’ve found the answer. Got the answer? Here are two common ways of getting it: You could convert 7 1/4 into 29/4, subtract 3/4 from that to get 26/4, and reduce that fraction to get 13/2, or 6 1/2. Or, you could reason that, because increasing each of two numbers by 1/4 doesn ..read more

[This month’s post is a transcript of a talk I gave on March 13, 2024, as part of a UMass Lowell “Conversation Starter” event on the topic of scientific literacy and communication. I was addressing other members of the Kennedy College of Sciences, so I treated mathematics as a subfield of the sciences, though I feel that math is an art as well as a science.] Quick: What 19th century mathematician is this? If a journalist had buttonholed the nineteenth-century pure mathematician shown above and asked him what his revolutionary ideas about geometry were good for, and if the mathematician had ans ..read more

When people find out I’m a mathematician, they assume I’m into numbers. I find this assumption frustrating (and a little sad) since there’s so much more to math than numbers, but the truth is that I am into numbers — so into them that I’m writing a book about them. It’s also the case (though less than it used to be) that when people find out I’m a mathematician, they assume I’m into NUMB3RS. And I’m not. For those who don’t know, NUMB3RS is an award-winning crime show that premiered back in 2005 and ran for six seasons. The three main characters are Don Eppes (an FBI agent), Charlie Eppes (a ..read more

And how naive to have imagined that the series ended at this point, in only three dimensions!            − 2001, A Space Odyssey, by Arthur C. Clarke The German philosopher-scientist Gottfried Leibniz dreamed of a universal language and a method of calculation to go with it, so that, if disputes arose on any subject, a disputant could exclaim “Calculemus!” (“Let us calculate!”) and the method would yield the answer. It was an audacious dream and Leibniz knew it, but, hoping to bring one small corner of his dream-language to life, he attempted to invent a “geometry of situation” that ..read more

“To learn all that is learnable; to deliver all collected data to the Creator on the third planet. That is the programming.” (Vejur, née Voyager 6, in Star Trek: The Motion Picture) Imagine a vast growing sphere centered on the Earth with a radius of fifteen billion miles, the distance a beam of light travels in a day. This is the anthroposphere: the patch of the universe into which humanity and its artifacts have spread. At its periphery – indeed, defining its periphery – is a one-ton device hurtling away from us at forty-thousand miles per hour while sending radio signals toward E ..read more

No reckoning allowed save the marvelous arithmetics of distance (from Smelling the Wind by Audre Lorde) Suppose a child comes up to you and says “I know 1 is odd and 2 is even, but I think 4 is more even than 2, and 1/2 is more odd than 1.” You might be tempted to reply “There’s no such thing as ‘more’ or ‘less’ odd; a number either is odd or it isn’t. And fractions aren’t odd or even; they’re just fractions.” But if you did, you’d be missing an opportunity for some serious and far-reaching fun. Every adult who teaches kids about math should be aware that in advanced mathematics th ..read more

I didn’t have time to compose an essay this month1, so I can’t offer any of my own writing for you to read (unless this 500-word trifle counts). But I feel I should offer you something, so I decided I’d tell you what I’ve been reading lately in a pop-math vein. Or rather, what I’ve been listening to, since these days I mostly listen to audiobooks. If your tastes resemble mine, the enjoyment you’ll derive from the audiobooks I recommend will exceed the pleasure you would have taken from the essay that I didn’t write! My five recommendations are: Mathematics for Human Flourishing by Francis Su ..read more

To err is human; we all make mistakes. But some mistakes have worse consequences than others. According to Greek myth, King Sisyphus of Ephyra made the especially big mistake of cheating Hades, the God of Death. Twice. Hades said “Fool me once, shame on you; fool me twice, you have to roll a huge boulder up a hill only to have it roll back down again, forever and ever.” I like to imagine Sisyphus counting his steps, repeatedly reaching the same top number just before the heart-breaking moment when the boulder returns to the bottom and Sisyphus is back at 1 again. Ironically, this kind of cycli ..read more

To err is human; we all make mistakes. But some mistakes have worse consequences than others. According to Greek myth, King Sisyphus of Ephyra made the especially big mistake of cheating Hades, the God of Death. Twice. Hades said “Fool me once, shame on you; fool me twice, you have to roll a huge boulder up a hill only to have it roll back down again, forever and ever.” I like to imagine Sisyphus counting his steps, repeatedly reaching the same top number just before the heart-breaking moment when the boulder returns to the bottom and Sisyphus is back at 1 again. Ironically, this kind of cycli ..read more

“What is The Matrix?” — Morpheus, The Matrix (1999) A matrix is a rectangular array of numbers, but a rectangular array of numbers only becomes a matrix when you think of it in the right way. I’ll get back to Morpheus’ rhetorical question1 in a bit. Matrices are everywhere in science and technology, from ecology to economics to data science. I’ll tell you how to add matrices together (in just the way you would probably expect) and how to multiply them (in a way you probably wouldn’t). What I won’t tell you is how matrix algebra was invented, because it’s just too embarrassing – not for me pers ..read more