One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…

"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…

Twelve problems which can be proved by the "mailbox principle" are stated and discussed. (DT)

Examples of unrealistic'' mathematics and mathematical reasoning are presented and discussed. (DT)

Some simple results in partition theory which arise when order is taken into account. (MM)

This investigation concerns the repeated application of the rule "take the sum of the squares of the digits." (MP)

Operations with zero and concepts associated with the use of zero are examined in some detail. Historical practices concerning zero are discussed. (CT)