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Science News
October 11, 2003
Ivars Peterson |
Goldbach Computations Goldbach's conjecture that every even number larger than 2 is the sum of two prime numbers remains unproven, but recent research may provide some insight.   |
Science News
June 2, 2001
Ivars Peterson |
Prime Twins Although most mathematicians believe that there are infinitely many twin primes, no one has yet proved this conjecture to be true. Indeed, the twin prime conjecture is considered one of the major unsolved problems in number theory... |
Science News
March 20, 2004
Ivars Peterson |
Deriving the Structure of Numbers The study of prime numbers has long been a central part of number theory, a field traditionally pursued for its own sake and for the mathematical beauty of its results. |
Science News
July 16, 2005
Ivars Peterson |
Closing the Gap on Twin Primes Euclid proved that the set of primes is infinite in size more than 2000 years ago, but no one has yet proved whether there is an infinite number of twin primes, or pairs of primes that have a difference of two. There's now hope that that matter will finally be resolved. |
Science News
April 24, 2004
Ivars Peterson |
Progressive Primes In one step toward elucidating certain primal mysteries, two mathematicians have now apparently proved that the population of primes contains an infinite collection of arithmetic progressions. |
Science News
December 2, 2000
Ivars Peterson |
Zeroing In on Catalan's Conjecture 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, a venerable problem involving relationships among whole numbers... |
Science News
July 17, 2004
Ivars Peterson |
Waring Experiments The different ways of expressing whole numbers as sums of parts has long fascinated both professional and amateur mathematicians. |
Science News
August 6, 2005
Ivars Peterson |
Playing with Ruth-Aaron Pairs Mathematicians have taken the home run records of Hank Aaron and Babe Ruth and made the fascinating discovery that the numbers have more in common than just baseball. |
Science News
June 22, 2002
Ivars Peterson |
Conquering Catalan's Conjecture Preda Mihailescu of the University of Paderborn in Germany finally may have the key to a venerable problem known as Catalan's conjecture, which concerns the powers of whole numbers. |
Science News
September 25, 2004
Ivars Peterson |
Euler's Sums of Powers For anyone fascinated by powers and integers, there's no shortage of problems to tackle, whether by ingenious logic or massive computer search... PUzzle of the Week... |
Science News
August 28, 2004
Ivars Peterson |
More Progressive Primes In July, Markus Frind, Paul Jobling, and Paul Underwood announced that they had discovered the first sequence consisting of 23 prime numbers in arithmetic progression. This surpasses the previous record of 22 primes in arithmetic progression, set in 1993. |
Salon.com
September 5, 2002
David Appell |
Math = beauty + truth / (really hard) Explaining what the winners of the world's top awards in mathematics actually do isn't as easy as adding 2+2. But we'll give it a try. |
Science News
May 11, 2002
Ivars Peterson |
Song-and-Dance Fermat Fermat's Last Tango, a musical based on the story of Fermat's last theorem and the quest to prove it, is cheerful, clever, and entertaining. Its varied music is engaging. It puts mathematics on display as an intensely human endeavor... |
Science News
May 4, 2002
Ivars Peterson |
Prime Spirals There is truly not only mystery but also beauty in the distribution of prime numbers... |
Science News
January 11, 2003
Ivars Peterson |
A Remarkable Dearth of Primes The pursuit of prime numbers -- integers evenly divisible only by themselves and 1 -- can lead to all sorts of curious results and unexpected patterns. In some instances, you may even encounter a mysterious absence of primes. |
Science News
August 27, 2005
Ivars Peterson |
Primes, Palindromes, and Pyramids Many questions about palidromic prime pyramids remain open. Is there a better way than exhaustive search for finding the tallest pyramids with fixed step sizes? Can you prove that fixed step size pyramids are finite? |
Science News
March 30, 2002
Ivars Peterson |
Rainbow Randomness The branch of pure mathematics known as Ramsey theory concerns the existence of highly regular patterns in sufficiently large sets of randomly selected objects. Patterns can arise out of randomness in a variety of ways... |
Science News
November 14, 2008
Julie Rehmeyer |
How To (really) Trust A Mathematical Proof Mathematicians develop computer proof-checking systems in order to realize century-old dreams of fully precise, accurate mathematics. |
Science News
January 14, 2006
Ivars Peterson |
Team Mersenne A Central Missouri State University computer identified the 43rd Mersenne prime, setting the record for the largest known prime number. This behemoth, 2 30402457 - 1, runs to a whopping 9,152,052 decimal digits. |
