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Calculating Swarms
The frenetic scurrying of ants around a nest may seem like much ado about nothing. There's method in their madness, however.
All this activity adds up to ingenious strategies for collectively working out the shortest path to a food source, combining forces to move a large, unwieldy object, and performing other functions crucial to an ant colony's wellbeing.
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Math Trek
Zeroing In on Catalan's Conjecture
Fermat's last theorem is just one of many examples of innocentlooking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat's scribbled conjecture, for instance.
Now, Preda Mihailescu of the Swiss Federal Institute of Technology in Zurich has proved a theorem that is likely to lead to a solution of Catalan's conjecture, another...

Math Trek
Mathematical Art on Display
The term "mathematical art" usually conjures up just one name–that of Dutch graphic artist M. C. Escher (1898–1972). Many people are familiar with Escher's endless staircases, hyperbolic tilings, Möbius ants, intricate tessellations, and other creations. They may also be aware of the intertwining of mathematics and art during the Renaissance, with the development of perspective...

Feature
The Power of Partitions
Just a year before his death in 1920 at the age of 32, mathematician Srinivasa Ramanujan came upon a remarkable pattern in a special list of whole numbers.
The list represented counts of how many ways a given whole number can be expressed as a sum of positive integers. For example, 4 can be written as 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. Including 4 itself but...

Feature
Great Computations
Computers at home or in the office often sit idle for minutes, hours, or days at a time. The Internet now allows researchers to take advantage of this enormous reservoir of unused computer power.
More than 1.6 million people have downloaded software to sift through signals collected by the Arecibo radio telescope in Puerto Rico as part of a search for signs of intelligent...

News
Searchers capture a champion megaprime
A participant in the Great Internet Mersenne Prime Search (GIMPS) has identified the largest prime number yet. When printed out, its digits would fill more than 450 pages of Science News.
Discovered by 20yearold Michael Cameron of Owen Sound, Ontario, the new champion prime is 213,466,917 – 1, which runs to 4,053,946 decimal digits.
A prime is a whole number evenly divisible by...

Feature
Surprisingly Square
For many decades, the study of the sums of squares was a stagnant backwater of mathematical research. This state of affairs changed unexpectedly in 1996 when mathematician Stephen C. Milne of Ohio State University in Columbus unveiled powerful new formulas for enumerating representations of numbers as the sums of squares.
Milne's discoveries "came as a great...

Math Trek
White Narcissus
The elegant, swooping forms carved out of wood by sculptor Robert Longhurst often resemble gracefully curved soap films that span twisted loops of wire dipped into soapy water. Alhough these abstract sculptures bear an uncanny resemblance to mathematical forms known as minimal surfaces, they emerge from Longhurst's imagination rather than from mathematics.
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