On a research-level math problem that seems to involve nothing more exotic than counting, adding, and subtracting.
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My new office space suffers from a shortage of photons, so I’ve been wiring up light fixtures. As I was snaking 14-gauge cable through the ceiling cavity, I began to wonder: Why is it called 14-gauge? I know that the gauge specifies the size of the copper conductors, but how exactly? The number can’t be a simple…
One Thursday afternoon last month, dozens of fires and explosions rocked three towns along the Merrimack River in Massachusetts. By the end of the day 131 buildings were damaged or destroyed, one person was killed, and more than 20 were injured. Suspicion focused immediately on the natural gas system. It looked like a…
Packing up the household for a recent move, I was delving into shoeboxes, photo albums, and file folders that had not been opened in decades. One of my discoveries, found in an envelope at the back of a file drawer, was the paper sleeve from a drinking straw, imprinted with a saccharine message:
Your security and privacy on the Internet (to the extent that such quaint notions still have meaning) depend on the difficulty of factoring certain large numbers. For example, take this 1,024-bit integer:
Babylonian accountants and land surveyors did their arithmetic in base 60, presumably because sexagesimal numbers help with wrangling fractions. When you organize things in groups of 60, you can divide them into halves, thirds, fourths, fifths, sixths, tenths, twelfths, fifteenths, twentieths, thirtieths, and…
When I launched bit-player.org in 2006, displaying any sort of mathematical notation on the web was torture. I would typeset an equation in LaTeX, convert the output to a JPEG image, upload the image file to a directory on the server, and embed a reference to the file in an HTML img tag. The process was cumbersome and…
Please click or tap in the gray square below. It will fill with a jolly tableau of colored disks—first big blue ones, then somewhat smaller purple ones, and eventually lots of tiny red dots.
Fourteen years ago I noted that disk drives were growing so fast I couldn’t fill them up. Between 1997 and 2002, storage capacity doubled every year, allowing me to replace a 3 gigabyte drive with a new 120 gigabyte model. I wrote:
Are the prime numbers sprinkled randomly along the number line, like windblown seeds? Of course not: Primality is not a matter of chance but a product of simple arithmetic. A number is prime if and only if no smaller positive integer other than 1 divides it evenly.