Tag: math

An “Academic Transformation” Takes On the Math Department
Entertainment

An “Academic Transformation” Takes On the Math Department

About twenty years ago, Olgur Celikbas attended a conference on algebra in Turkey. He and his then girlfriend, Ela Özçağlar, had recently graduated from college in Ankara; both had studied math. At the time, the University of Nebraska-Lincoln had one of the top commutative-algebra programs in the world, and professors at the conference sold Olgur on the idea of going to America for grad school. Ela was less sure. “I was, like, ‘Where’s Nebraska?’ ” she recalled. She asked her father, a geography professor. He said something about a corn ocean.Ela and Olgur got married, moved to Nebraska, and obtained Ph.D.s in mathematics. They began looking for academic positions, but finding jobs in the same place felt like “the most difficult two-body problem in the world,” Ela said. They got temporary...
A New Proof Moves the Needle on a Sticky Geometry Problem
Technology

A New Proof Moves the Needle on a Sticky Geometry Problem

The original version of this story appeared in Quanta Magazine.In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate it so that it points in every direction in turn. What’s the smallest area the needle can sweep out?If you simply spin it around its center, you’ll get a circle. But it’s possible to move the needle in inventive ways, so that you carve out a much smaller amount of space. Mathematicians have since posed a related version of this question, called the Kakeya conjecture. In their attempts to solve it, they have uncovered surprising connections to harmonic analysis, number theory, and even physics.“Somehow, this geometry of lines pointi...
The Lawlessness of Large Numbers
Technology

The Lawlessness of Large Numbers

The original version of this story appeared in Quanta Magazine.So far this year, Quanta has chronicled three major advances in Ramsey theory, the study of how to avoid creating mathematical patterns. The first result put a new cap on how big a set of integers can be without containing three evenly spaced numbers, like {2, 4, 6} or {21, 31, 41}. The second and third similarly put new bounds on the size of networks without clusters of points that are either all connected, or all isolated from each other.The proofs address what happens as the numbers involved grow infinitely large. Paradoxically, this can sometimes be easier than dealing with pesky real-world quantities.For example, consider two questions about a fraction with a really big denominator. You might ask what the decimal expansio...