What is a crystal?

Almost 25 years have passed since Shechtman discovered quasicrystals, and 15 years since the Commission on Aperiodic Crystals of the International Union of Crystallography put forth a provisional definition of the term crystal to mean ``any solid having an essentially discrete diffraction diagram.'' Have we learned enough about crystallinity in the last 25 years, or do we need more time to explore additional physical systems? There is much confusion and contradiction in the literature in using the term crystal. Are we ready now to propose a permanent definition for crystal to be used by all? I argue that time has come to put a sense of order in all the confusion.Comment: Submitted to Zeitschrift fuer Kristallographi

What is a perverse sheaf?

Three-page article on the notion of perverse sheaf to appear in the "What is?" series in the Notices of the AMS.Comment: to appear in the May 2010 issue of the Notices of the AMS http://www.ams.org/notice

What is a logical diagram?

Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind does exist in Charles Peirce’s conception of iconic signs, but that fully understood, logical diagrams involve a structured array of normative reasoning practices, as well as just a “picture on a page”

What is a composite citation? An introduction

No abstract available

What is a definition for in school mathematics?

This paper discusses the place of definitions in school mathematics, considering official UK curriculum guidance, literature related to definitions in advanced mathematical thinking and to experimental teaching focused on student development of definitions. A two dimensional framework is suggested for considering their functions, the ways in which students are expected to relate to them and their didactic purposes. Two contrasting examples of definitions from textbooks are analysed using systemic-functional linguistic tools