# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Formally speaking," by John L. Casti. *Nature,* 31 May 2001, page 527.

In this article, Casti writes on the formalization of language and how attemptsat formalization have led to different branches of mathematics. Withoutformalization, it is hard to prove theorems. Yet no matter how rigorous thedefinition, mathematicians cannot "suffocate" language: "the objects ofmathematics really do mean something, and that meaning cannot be replaced bypure syntax alone." Casti uses work done by Gödel, Russell and Turing asexamples of formalization.

*--- Mike Breen *