Volume 42


In this issue we are delighted to reproduce three award-winning articles on Cryptography by Professor Nuno Crato. These articles were awarded first prize in a special competition organized by the European Mathematical Society on Raising Public Awareness in Mathematics.

The safety of electronic commerce is secured by an innovative mathematical method: a public key that allows you to lock messages in a safe, but a safe that can only be open with another device - a secret key!

It sounds like science fiction, but it is a reality: the most bizarre properties of subatomic particles allow us to create unbreakable ciphers.

Internet communication is based on coding mechanisms that guarantee privacy in the exchange of messages. Mathematics makes this possible without having the people involved agree on a secret key.

Sometimes in these columns I will allow myself the liberty of straying outside the domain of History, properly so called, in order to look at somewhat wider issues.

The following ad appeared in The Australian on 25 March 2006.

In the popular Hitch Hiker’s Guide to the Galaxy series Douglas Adams plays with the Ultimate Answer to the great mystery of Life, the Universe and Everything.

Q1221. Complete the mathematical equations below by inserting the least number of mathematical symbols from the table

Q1211. Solve
$$(2+\sqrt{2})^{\sin^2x} - (2+\sqrt{2})^{\cos^2x} + (2-\sqrt{2})^{\cos2x} = \left(1+\frac{1}{\sqrt{2}}\right)^{\cos 2x}$$