The undergraduate mathematics course at Cambridge is called the Mathematical Tripos, and it has a long and distinguished history. The word Tripos refers today to a Cambridge degree course in any academic subject, which is examined by written papers. In fact, mathematics was the first Cambridge Tripos. It started in the 18th century, although its origin dates from earlier times when oral examinations were held (conducted by an examiner known as Mr Tripos, allegedly because of the three-legged stool on which he sat!). Periodically, radical changes have been made in the Mathematical Tripos, when perceived to be desirable in the light of either external events or changing emphases within the subject. A famous revolution took place in 1910, one of whose consequences was the abolition of the order of merit in which the Wranglers (candidates awarded first class honours) were placed in numerical order. The last major overhaul occurred in 1964, when the present structure was created. A similar such wholesale review has been taking place here over the last few years, with the result that a completely new course will begin in October 1991. This short article aims to describe some of the thinking behind these proposals.