Unsolved Problems

Solved and unsolved problems in generalized notions of Connes amenability

We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signicance of any solutions to them to the development of the eld.

Memory for impasses during problem solving.

Three experiments were conducted to investigate the relative memorability of solved versus unsolved problems in long-term memory. In each experiment, subjects worked on a set of potentially solvable word problems, with the time spent on each problem held constant. Problem memorability was then measured with a free-recall task. In Experiment 1, in which a majority of problems were solved, unsolv...

Norman Do More Unsolved Problems for Young and Old

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...

An Infinity Of Unsolved Problems Concerning A Function In The Number Theory AN INFINITY OF UNSOLVED PROBLEMS CONCERNING A FUNCTION IN THE NUMBER THEORY

Unsolved Problems Related to the Covering Radius of Codes*

Some of the principal unsolved problems related to the covering radius of codes aredescribed. For example, although it is almost twenty years since it was built, ElwynBerlekamp’s light-bulb game is still unsolved. [Added later: this problem has since beensolved — see P. C. Fishburn and N. J. A. Sloane, ‘‘The Solution to Berlekamp’sSwitching Game,’’ Discrete Math., Vol. 74, 1989,...