September 10, 2001
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June 25, 1999
In these notes, based on lectures given in Istanbul, we give an introduction both to Monstrous Moonshine and to the classification of rational conformal field theories, using this as an excuse to explore several related structures and go on a little tour of modern math. We will discuss Lie algebras, modular functions, the finite simple group classification, vertex operator algebras, Fermat's Last Theorem, category theory, (generalised) Kac-Moody algebras, denominator identiti...
February 21, 2004
Twenty-five years ago, Conway and Norton published their remarkable paper `Monstrous Moonshine', proposing a completely unexpected relationship between finite simple groups and modular functions. This paper reviews the progress made in broadening and understanding that relationship.
May 1, 2003
It is rare to succeed in getting mathematics into ordinary conversation without meeting all kinds of reservations. In order to raise public awareness of mathematics effectively, it is necessary to modify such attitudes. In this paper, we point to some possible topics for general mathematical conversation.
April 7, 2020
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
July 25, 1994
We summarize four different versions of our course notes on the limits of mathematics.
March 25, 2020
This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season of lockdown, I modestly try to contribute to scientific interaction at a distance. Therefore all comments and exchange of information are most welcome.
October 13, 2000
Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and afterwards. They have more an educational interest, because make the students think different! For each "solution" a funny logic is invented in order to give the problem a sense.
January 25, 2016
The idea of meaning as use in language is explored in a mathematical and physical context. Two possible scenarios of further analysis are presented: Ordinal arithmetic and String theory.
September 5, 2004
We announce the solution of 4+21+1/2 (!) problems posed in earlier issues of the SPM Bulletin; the ``1/2'' standing for a ``consistently yes'' answer of Zdomsky to the last issue's Problem of the Month.
December 22, 2018
Mathematicians occasionally discover interesting truths even when they are playing with mathematical ideas with no thoughts about possible consequences of their actions. This paper describes two specific instances of this phenomenon. The discussion touches upon the theme of the unreasonable effectiveness of mathematics as well as the ethical obligations of mathematicians.