The theme of this session – understanding new trends, new results - invites reflection on two small Anglo-Saxon words: “new” and “news.” “New” has several distinct meanings: not existing before; not known before; fresh; different; not old; of recent origin. “News” refers to tidings - to information about recent events.

The two words, in our context, reflect two professions: mathematician and journalist. Mathematicians deal with the new; journalists with news. Despite the common etymology of these words, in practice they have almost opposite meanings to the mathematician and the journalist. To understand new trends and new results, we have to examine how mathematicians and journalists differ in their perceptions of what's new and of what's news.

NEW MATHEMATICS

What is new to the mathematician? For some it is theorems - proofs of old conjectures or discoveries of new results. In 1983 it was Gerd Faltings' proof of the Mordell conjecture; in 1985 it was Louis De Branges' proof of the Bieberbach conjecture. In 1988 it was, for a short time, Yoichi Miyaoka's claim that he had proved Fermat's Last Theorem.

For others, what is new in mathematics are trends in research. For a good part of the 1970's, catastrophe theory was new; now attention has shifted to fractals and chaos. Forty years ago, many new trends in mathematics were expressed in the collective work of Nicholas Bourbaki as the culmination of David Hilbert's agenda to provide a complete logical portrait of known mathematical theory.