This paper explores universal relations, i.e., meta-mathematical concepts that mathematicians seem to employ in all domains of mathematical reasoning. This paper presents precise mathematical definitions for three universal relations: isomorphism (type identity), essential property , and isoonticity . Although no formal explanation is given as to how universal relations expedite mathematical re...

24 NOTICES OF THE AMS VOLUME 52, NUMBER 1 I n the discipline known as folkloristics [D1] (the study of folklore), a folk is defined as any group whatsoever that shares at least one common linking factor. The factor could be nationality, ethnicity, religion, or occupation. Members of a profession would also qualify as a folk group. Hence, mathematicians constitute a folk. And, like all folk grou...

In this paper we provide a brief overview of the two mathematical constructions presented by Yves André during the first two session of Ircam’s “Mathematical School for Musicians and other Non-Mathematicians”. After discussing a musical application of Operator Theory we try to suggest the possible connection between Jean-Yves Girard’s Geometry of Interaction (based on a special case of von Neum...

An excellent introduction to the theory of automorphic representations and the relations with number theory is the Corvallis proceedings, Automorphic Forms, Representations and L-Functions, Parts 1 and 2, Proc. Sympos. Pure Math., vol. 33, 1979. Although composed mainly of survey articles, the proceedings are already rather formidable. They are a measure of the breadth of the field. They will b...

Unsolved problems are the lifeblood of mathematics. Unfortunately, as the frontiers of our field are being pushed ever further, it is becoming more and more difficult for mathematicians from even mildly disparate research areas to find common ground. However, there is a wealth of elementary unsolved problems which any person with a working knowledge of mathematics should be able to understand a...