On a late-spring evening in Boston, just as the sun was beginning to set, a group of mathematicians lingered over the remains of the dinner they had just shared. While some cleared plates from the table, others started transforming skewers and hunks of raw potato into wobbly geodesic forms. Justin Solomon, an assistant professor at M.I.T., lunged forward to keep his structure from collapsing. “That’s five years of Pixar right there,” he joked. (Solomon worked at the animation studio before moving to academia.) He and his collaborators were unwinding after a long day making preparations for a new program at Tufts University—a summer school at which mathematicians, along with data analysts, legal scholars, schoolteachers, and political scientists, will learn to use their expertise to combat gerrymandering.
The school, which began on Monday, is the brainchild of a young Tufts professor named Moon Duchin, who specializes in geometry. It has drawn participants from France, Israel, Japan, Singapore, and forty U.S. states. Some of Duchin’s students plan to train as expert witnesses, or to run for office. One mathematician enrolled out of a Christian sense of justice; another cited the day-to-day frustrations of living in a severely gerrymandered Florida district. Yet another applicant wrote, “Until very recently, I thought doing anything about this was a hopeless cause.” At the dinner, Duchin acknowledged that she was “kind of devastated by this election,” but both she and her colleagues were careful to point out that their venture is strictly nonpartisan. It was inspired by a simple question: What if there are well-researched areas of math that could simplify, or at least systematize, the fraught process of redistricting?
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Gerrymandering has been a thorn in the side of the U.S. political system since before the very first Congress was elected.
Gaze deeply into the eye of a chicken, and what do you see? Some see terrifying stupidity. But researchers at Princeton University and Washington University in St. Louis say they see in the bird’s eye the first known biological occurrence of a strange state of matter known as “disordered hyperuniformity.”
The potentially new state of matter is the result of the way five photoreceptor cells of different sizes are packed into the retina, the light-sensitive layer at the back of chickens’ eyes, according to a written statement describing the research.
In other animals, these “cone” cells are often arranged in a regular pattern, according to LiveScience. Insect cones, for example, are arranged in a hexagonal grid.
It took two major expeditions charting the solar eclipse of 1919 to verify Albert Einstein’s weird prediction about gravity — that it distorts the path of light waves around stars and other astronomical bodies, distorting objects in the background. Now, researchers have created the first precise analogue of that effect on a microchip.
Any large mass distorts the geometry of space around it, for instance making parallel light rays diverge or converge. One consequence, described by Einstein’s general theory of relativity, is that objects behind a body such as the Sun may look magnified or distorted as the optical path of light goes through the region of warped space.
Metamaterials scientist Hui Liu of Nanjing University in China and his colleagues mimicked this ‘gravitational lensing’ — which affects light in the vacuum of space — by making light travel through solid materials instead. Different transparent media have different indexes of refraction, causing light to bend. One example is at the interface between water and air, a familiar effect that makes a pencil look broken when it is half-dipped in water. But if a medium has an index of refraction that varies gradually rather than abruptly, it will make the the paths of light rays curve as they travel through it.
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The warping of the empty space around a massive star means that the shortest path of light around a star is a ‘curved’ one — but the bending of light rays in a medium can mimic the same effect. | Nature Photonics
Stumped? Shakuntala Devi, the woman known as the “Human Computer,” could tell you, and probably faster than any mathematical computer could.
Devi, who passed away on April 21 at age 83 in her hometown of Bangalore, India, toured the world as a prodigy for much of her life, making appearances on radio, television and in theaters, the New York Times reports.
In a 1977 appearance at Southern Methodist University in Dallas, Devi found the 23rd root of a 201-digit number in just 50 seconds, besting a slowpoke Univac computer that took 62 seconds to make the same calculation. The root of a number (“X”) is equal to another number (“Y”) that can be multiplied by itself a given number of times to equal “X.” So the 23rd root of “X” equals “Y” multiplied by itself 23 times.
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Shakuntala Devi (November 4, 1929 – April 21, 2013), Indian mental calculator known as the ‘Human Computer,’ has died.
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It’s the sort of abstract puzzle that keeps a scientist awake at night: Can you predict how three objects will orbit each other in a repeating pattern? In the 300 years since this “three-body problem” was first recognized, just three families of solutions have been found. Now, two physicists have discovered 13 new families. It’s quite a feat in mathematical physics, and it could conceivably help astrophysicists understand new planetary systems.
The trove of new solutions has researchers jazzed. “I love these things,” says Robert Vanderbei, a mathematician at Princeton University who was not involved in the work. He says he, in fact, spent all night thinking about the work.
The three-body problem dates back to the 1680s. Isaac Newton had already shown that his new law of gravity could always predict the orbit of two bodies held together by gravity—such as a star and a planet—with complete accuracy. The orbit is basically always an ellipse. However, Newton couldn’t come up with a similar solution for the case of three bodies orbiting one another.
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Solutions to the three-body problem, such as the “figure eight” and “yarn,” can be viewed on an abstract shape-sphere.
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After a century of studying their tangled mathematics, physicists can tie almost anything into knots, including their own shoelaces and invisible underwater whirlpools. At least, they can now thanks to a little help from a 3D printer and some inspiration from the animal kingdom.
Physicists had long believed that a vortex could be twisted into a knot, even though they’d never seen one in nature or the even in the lab. Determined to finally create a knotted vortex loop of their very own, physicists at the University of Chicago designed a wing that resembles a delicately twisted ribbon and brought it to life using a 3D printer.
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Shourryya Ray, a 16-year-old German student, has cracked a puzzle that has stumped mathematicians since Sir Isaac Newton first posed the problem more than 350 years ago.
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