Column

Math

Disorder in the Deck

Card players sometimes get lazy, shuffling a deck fewer times than necessary to randomize the cards. Indeed, persistently sloppy shuffling can have a significant impact on play–an effect that experts (and gamblers) can exploit to their advantage. However, the problem lay not in the computer but with human expectations. Subsequent research showed that hands in […]

Math

Disorder in the Deck

Card players sometimes get lazy, shuffling a deck fewer times than necessary to randomize the cards. Indeed, persistently sloppy shuffling can have a significant impact on play–an effect that experts (and gamblers) can exploit to their advantage. However, the problem lay not in the computer but with human expectations. Subsequent research showed that hands in […]

Math

Staying in Step

Late in the winter of 1665, an ailing Christiaan Huygens (1629–1695) was confined to his room for a few days. The Dutch physicist whiled away the hours of his confinement by closely observing and pondering the odd behavior of two pendulum clocks he had recently constructed. Huygens had obtained a patent on the first pendulum […]

Math

Planes of Budapest

Nearly every Sunday during the winter of 1933 in Budapest, a small group of students would meet somewhere in the city at a park or cafe to discuss mathematics. The gathering typically included Paul Erdös (1913–1996), who was attending the University of Budapest, György (George) Szekeres, a recent chemical engineering graduate of the Technical University […]

Math

Plato’s Molecule

In his dialogue Timaeus, the Greek philosopher Plato (427–347 B.C.) carefully laid out his reasoning for ascribing certain geometric shapes to the minuscule particles that constituted the four elements of matter. In his view, these elements–fire, air, water, and earth–were all aggregates of tiny solids, each one having the shape of one of the regular […]

Math

Plato’s Molecule

In his dialogue Timaeus, the Greek philosopher Plato (427–347 B.C.) carefully laid out his reasoning for ascribing certain geometric shapes to the minuscule particles that constituted the four elements of matter. In his view, these elements–fire, air, water, and earth–were all aggregates of tiny solids, each one having the shape of one of the regular […]

Math

Defending the Roman Empire

Years ago, when I was in high school and college, the board games Risk and Diplomacy served as wonderful playing fields where I could develop and exercise my tactical and negotiating skills. One issue that often came up in my forays into international intrigue was how to deploy my limited forces to defend far-flung territories […]

Math

Möbius at Fermilab

Fermilab’s Wilson Hall. Courtesy of Fermilab. Soaring into the sky like a medieval cathedral, the twin towers of the structure known as Wilson Hall dominate the flat countryside surrounding the Fermi National Accelerator Laboratory (Fermilab) in Batavia, Ill. Named for physicist and accelerator builder Robert Rathbun Wilson (1914-2000), the building celebrates Wilson’s vision and skill, […]

Math

Solving Yahtzee

Sometimes described as poker with dice, Yahtzee is an immensely popular game. Its manufacturer, Hasbro, claims that as many as 100 million people worldwide play the game regularly. Yahtzee involves rolling five dice with the aim of obtaining favorable scoring combinations. For example, rolling five of a kind scores 50 points, whereas rolling three of […]

Math

Scrambled Grids

Amazingly simple mathematical operations can lead to intriguingly complex results. Consider, for instance, the iterative geometric process of creating flaky pastry dough. Flatten and stretch the dough, then fold it over on top of itself. Do it again and again and again. Repeating the pair of operations–stretch and fold–just 10 times produces 1,024 layers; 20 […]

Math

Goldbach’s Prime Pairs

Like the elements in chemistry, prime numbers serve as building blocks in the mathematics of whole numbers. Evenly divisible only by themselves and one, primes are a rich source of speculative ideas that mathematicians often find simple to state but difficult to prove. The Goldbach conjecture is a prime example of such a conundrum. In […]

Math

Software’s Origin

One of the main functions of the venerable and massive Oxford English Dictionary is to record the earliest known use of a word (or sense of a word) in English. The current edition of the dictionary dates the word software back to 1960, though researchers have discovered an 1850 occurrence of the term in a […]