Madras College takes its name from the system of education devised by the school's founder the Rev Dr Andrew Bell. He was born in St Andrews in 1753, the son of a local magistrate and wig-maker. He studied at the University where he distinguished himself in mathematics. He became a clergyman of the Church of England and took up an appointment as chaplain to the regiments of the East India Company in Madras. One of his duties was to educate the soldiers' children. Because there was a shortage of teachers, he used the older boys, who had been taught the lesson by the master, to instruct groups of younger pupils. The pupils who assisted the teacher were called 'monitors'. This method of education became widely used in schools at home and abroad. After his return from India, Dr Bell made it his life's work to travel the country and encourage schools to adopt 'the Madras system', as it had come to be known. By the time of his death in 1832, over 10,000 schools were using his methods.

To make sure that his educational ideas would be preserved for the future, he made arrangements for the fortune his success had brought him to be used to found a school in his native town of St Andrews. By selling some land he owned he was also able to give money to the neighbouring town of Cupar so that in the end he founded two schools. One is the present Bell Baxter High School in Cupar which was originally called Madras Academy. The other is Madras College in St Andrews. The senior part of the school is still on the original site in South Street where the modern school has grown up behind the impressive 1833 quadrangle.