Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"Infinite Wisdom," by Erica Klarreich. Science News, 30 August 2003.

Klarreich covers "a new approach to one of mathematics' most notorious problems": how many numbers are there? In 1873 Georg Cantor proved "that the real numbers (all the numbers that make up the number line) form a bigger infinity than the counting numbers do." Mathematicians today continue to ask "how much bigger is that infinity?" The article presents a summary of work on the continuum hypothesis and recent work by mathematician Hugh Woodin of the University of California, Berkeley. In sum, Woodin's argument "has proved---apart from one missing piece that still must be filled in---that elegant axioms do exist and, crucially, that every elegant axiom would make the continuum hypothesis false."

--- Annette Emerson