NYT SCIENCE: Elusive ‘Einstein’ Solves a Longstanding Math Problem
By Siobhan Roberts
Section: Science
Source: New York Times
Published Date: March 28, 2023 at 03:00AM
In less poetic terms, an einstein is an “aperiodic monotile,” a shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. (The term “einstein” comes from the German “ein stein,” or “one stone” — more loosely, “one tile” or “one shape.”) Your typical wallpaper or tiled floor is part of an infinite pattern that repeats periodically; when shifted, or “translated,” the pattern can be exactly superimposed on itself. An aperiodic tiling displays no such “translational symmetry,” and mathematicians have long sought a single shape that could tile the plane in such a fashion. This is known as the einstein problem.
“I’m always messing about and experimenting with shapes,” said Mr. Smith, 64, who worked as a printing technician, among other jobs, and retired early. Although he enjoyed math in high school, he didn’t excel at it, he said. But he has long been “obsessively intrigued” by the einstein problem.
And now a new paper — by Mr. Smith and three co-authors with mathematical and computational expertise — proves Mr. Smith’s discovery true. The researchers called their einstein “the hat,” as it resembles a fedora. (Mr. Smith often sports a bandanna tied around his head.) The paper has not yet been peer reviewed.
By Siobhan Roberts
Section: Science
Source: New York Times
Published Date: March 28, 2023 at 03:00AM
And it all began with a hobbyist “messing about and experimenting with shapes.”
Last November, after a decade of failed attempts, David Smith, a self-described shape hobbyist of Bridlington in East Yorkshire, England, suspected that he might have finally solved an open problem in the mathematics of tiling: That is, he thought he might have discovered an “einstein.”In less poetic terms, an einstein is an “aperiodic monotile,” a shape that tiles a plane, or an infinite two-dimensional flat surface, but only in a nonrepeating pattern. (The term “einstein” comes from the German “ein stein,” or “one stone” — more loosely, “one tile” or “one shape.”) Your typical wallpaper or tiled floor is part of an infinite pattern that repeats periodically; when shifted, or “translated,” the pattern can be exactly superimposed on itself. An aperiodic tiling displays no such “translational symmetry,” and mathematicians have long sought a single shape that could tile the plane in such a fashion. This is known as the einstein problem.
“I’m always messing about and experimenting with shapes,” said Mr. Smith, 64, who worked as a printing technician, among other jobs, and retired early. Although he enjoyed math in high school, he didn’t excel at it, he said. But he has long been “obsessively intrigued” by the einstein problem.
And now a new paper — by Mr. Smith and three co-authors with mathematical and computational expertise — proves Mr. Smith’s discovery true. The researchers called their einstein “the hat,” as it resembles a fedora. (Mr. Smith often sports a bandanna tied around his head.) The paper has not yet been peer reviewed.
Read More at: https://www.nytimes.com/2023/03/28/science/mathematics-tiling-einstein.html
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