Math

Math

Conquering Catalan’s Conjecture

Innocent-looking problems involving whole numbers can stymie even the most astute mathematicians. As in the case of Fermats last theorem, centuries of effort may go into proving such tantalizing, deceptively simple conjectures in number theory. Now, Preda Mihailescu of the University of Paderborn in Germany finally may have the key to a venerable problem known […]

Math

Algebra, Philosophy, and Fun

I don’t often encounter the words “philosophy” and “fun” right next to the term “algebra.” Nowadays, these words don’t seem to fit together comfortably. However, the three terms do appear in the title of an engaging little book called Philosophy and Fun of Algebra, written by Mary Everest Boole (1832–1916) and published in 1909. I […]

Math

Squares, primes, and proofs

Mathematicians have proved the so-called local Langlands correspondence, a broad generalization of a surprising connection between prime numbers and perfect squares.

Math

Losing to win

Two games of chance, each guaranteed to give a player a predominance of losses in the long term, can add up to a winning outcome if the player alternates between the two games.

Math

Fractal Roots and Artful Math

The term “mathematical art” usually conjures up images of M.C. Escher’s endless staircases, Möbius-strip ants, and mind-boggling tilings. Or it might remind one of the intimate intertwining of mathematics and art during the Renaissance with the development of perspective painting and eye-teasing stagecraft. A view of the recent MathArt/ArtMath show at the Selby Gallery in […]

Math

Fractal Roots and Artful Math

The term “mathematical art” usually conjures up images of M.C. Escher’s endless staircases, Möbius-strip ants, and mind-boggling tilings. Or it might remind one of the intimate intertwining of mathematics and art during the Renaissance with the development of perspective painting and eye-teasing stagecraft. A view of the recent MathArt/ArtMath show at the Selby Gallery in […]

Math

Candy for Everyone

Several students are sitting in a circle. Each student has an even (though not necessarily the same) number of wrapped pieces of candy. On a signal, each student passes half of his or her trove to the student on his or her right. Between signals, the teacher (reaching into an inexhaustible goody bag) gives any […]

Math

A Stranger from Spaceland

“It was the last day of the 1999th year of our era. The pattering of the rain To a Flatlander, a sphere passing through Flatland appears as a line of changing length. had long ago announced nightfall; and I was sitting in the company of my wife, musing on the events of the past and […]

Math

Setting Records Randomly

A wide variety of factors can influence the winning time of a race. For a given event over the course of a year, for example, the results may depend on the quality of the runners, the race location, weather conditions, and so on. In a 1985 article in the Journal of the American Statistical Association, […]

Math

Crystal Möbius

Take a ribbon of paper, twist one end 180 degrees, and attach it to the other end. The resulting surface, called a Möbius strip, has only one side and one edge. Scanning electron microscope image shows niobium selenide crystals in a Möbius-strip conformation (top). In the schematic diagram (bottom), a white ribbon represents a niobium […]

Math

Prime Effort: Powerful conjecture may be proved

A mathematician may have finally proved Catalan's conjecture, a venerable problem in number theory concerning relationships among powers of whole numbers.

Math

A Lawyer’s Math Library

“Strangely enough, anyone wishing to write about Galois in Paris would do well to journey to Louisville, Kentucky.”–Leopold Infeld, Whom the Gods Love LOUISVILLE, KY. French mathematician Evariste Galois (1811–1832), whose death in a duel at the age of 20 cut short a remarkably productive career, is only one of many mathematicians represented in a […]