The mathematically-inclined Arduino enthusiast will enjoy this project by Tim Fraser, who has created a way of interpreting Lambda Calculus - which in his words is:
... a formal system (programming language) developed by Alonzo Church in the 1930's to attack the deepest mathematical problem of the day. This was the Entscheidungsproblem, the question of whether or not there exists an algorithm capable of deciding the truth or falsehood of all statements in mathematics.
Although the Arduino is limited due to the processing and memory capability, this is still an interesting project. For more detailed explanations, sketch and more - visit Tim's project page. And we're on twitter and Google+, so follow us for news and product updates as well.
If you want to recreate this project, you can make it even smaller by using the Freetronics LeoStick:
Apart from being one of the smallest Arduino-compatibles on the market with USB, it also has an onboard RGB LED and piezo which can be used a knock sensor and various tune and sound effects. For more information and to order, click here.