# 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*