In 1898, Marie and Pierre Curie discovered radium. Claimed to have restorative properties, radium was added to toothpaste, medicine, water, and food. A glowing, luminous green, it was also used in beauty products and jewelry. It wasn’t until the mid-20th century we realized that radium’s harmful effects as a radioactive element outweighed its visual benefits.
Unfortunately, radium isn’t the only pigment that historically seemed harmless or useful but turned out to be deadly. That lamentable distinction includes a trio of colors and pigments that we’ve long used to decorate ourselves and the things we make: white, green, and orange.
The shortest math paper ever reminds us why mathematicians think that P doesn’t equal NP, even if they can’t yet prove it. It’s much easier to check solutions to problems (P) than it is to actually solve them (NP).
Below you can see how a CDC 600 computer looks like around 1964-1969.
On the night of January 1, 1801, Giuseppe Piazzi, a priest in Palermo, Italy, was mapping the stars in the sky. Over three nights, he’d look at and draw the same set of stars, carefully measuring their relative positions.
That night, he measured the stars. The next night, he measured them again. To his surprise, one had moved. The third night, the peculiar star had moved again. This meant it couldn’t be a star at all.
It was something new, the first asteroid ever discovered, which Piazzi eventually named Ceres. Asteroids are bits of rock and metal that orbit the Sun. At over 900 kilometers across, Ceres is a very large asteroid. But through a telescope, like Piazzi’s, Ceres looked like a pinpoint of light similar to a star. In fact, the word asteroid means star-like. You can tell the difference between stars and asteroids by the way they move across the sky. Of course, Piazzi knew none of that at the time, just that he had discovered something new. To learn about Ceres, Piazzi needed to track its motion across the sky and then calculate its orbit around the Sun.
So each clear night, Piazzi trained his telescope to the heavens. Night after night, he made careful measurements, but from his observations he learned that Ceres was only visible in the sky during the day. It would take another year and a lot of astronomers to nail down Ceres’ path, but we haven’t lost track of it since.
Today, we can do something that Piazzi could only dream of: send spacecraft to study asteroids up close. One spacecraft called Dawn journeyed billions of kilometers over four years to the main asteroid belt. There, it visited Ceres and another asteroid, Vesta. Dawn’s stunning images transformed Piazzi’s dot of light into a spectacular landscape of craters, landslides, and mountains.
My first code in Mathematica goes back to V2 (1991) for the first reliable graphical environment from Microsoft (Windows 3.0, 3.1), lab reports improved instantly. Many things have changed in three decades in the world of computer algebra systems, even to the point to be of (irremediably) minority use, mostly because there are plenty alternatives both for high (Matlab, Octave, Sage) and low level (C, C++, Fortran…), or both (Python, Java, R…). But for people of a couple of generations (those born in the 60s and 70s or so) coming from an almost purely analogical world, seeing a pioneer (back then and now) of that generation as Stephen Wolfram (1959), posting this about the software that he himself had developed from the scratch before his 30 birthday, well, it makes us… happily nostalgic.
At the height of their power, infamous Caribbean pirates like Blackbeard and Henry Morgan commanded as many as ten ships and several hundred men. But their stories pale next to the most successful pirate of all time, Madame Zheng, who commanded 1,800 vessels, made enemies of several empires, and still lived to old age.
If walls could talk, Turkey’s Hagia Sophia would have an abundance of stories to tell. Once a church, then a mosque, and now a museum, this world marvel has stood the test of time and war, surviving centuries of conquest by some of history’s greatest empires.
The Hagia Sophia was finished in the year 537, only 5 years after construction began. On this day (May 7) in the year 558, the dome collapse following a major earthquake. It was rebuilt – in the first of many modifications made to the structure!
If you can’t imagine life without chocolate, you’re lucky you weren’t born before the 16th century. Until then, chocolate only existed in Mesoamerica in a form quite different from what we know today. As far back as 1900 BCE, the people of that region had learned to prepare the beans of the native cacao tree. The earliest records tell us the beans were ground and mixed with cornmeal and chili peppers to create a drink – not a relaxing cup of hot cocoa, but a bitter, invigorating concoction frothing with foam.