# Number Theory

This page provides references and capsule descriptions of my recent articles on number theory.

Primed for Success, *Smithsonian *Special Issue, Fall 2007, 74-75.

Terence Tao has made one of the most difficult of all transitions: he is the rare prodigy who lives up to his early promise. At age 32, he has already won a MacArthur “genius grant” and the most prestigious prize in math, the Fields Medal, and has made major advances in several branches of mathematics. And he’s still just beginning.

‘Cranky’ Proof Reveals Hidden Regularities, *Science*, 1 April 2005, 36-37.

The fallout from Andrew Wiles’ 1994 proof of Fermat’s Last Theorem will probably last for decades. A group of three mathematicians uses Wiles-like methods, together with an elementary “binning” procedure, to uncover some neat patterns in a classical function of number theory, the partition function.

Hardy’s Prime Problem Solved, *New Scientist*, 8 May 2004, 13.

A prime progression is a sequence of prime numbers that are all equally spaced — such as 5, 17, 29, 41, 53. Mathematicians have have never found one with more than 22 terms. Now, two young number theorists (Terry Tao and Ben Green) have proved that prime progressions of

anylength exist.

Prime Proof Helps Mathematicians Mind the Gaps,* Science*, 4 April 2003, 32.

Dan Goldston of the U.S. and Cem Yildirim of Turkey prove that prime numbers are like weeds — they occur in clumps. Unfortunately, since this article was published a gap has appeared in their proof, so its current status is unclear. Come back to this page for updates. [

July 2005 update: Goldston's work was finally vindicated a month or two ago, with an even simpler proof.]