These can be summarised as follows:
- The fall of the Roman Empire and the subsequent loss of knowledge and educational practises due to the succession of wars that followed this event.
- The efforts of a few key people, Charlemagne and Alcuin being probably the foremost among them, to improve educational standards and the knowledge of the general populace and the clergy. Pope Sylvester II also played his part in improving the Church's opinion of Mathematics in the later period of the Dark Ages.
- The increase in knowledge thanks to texts saved and recovered by the Arabs. Brought to Europe by knights on crusades, and the work of Fibonacci in introducing and promoting the new and improved numerical systems.
- The rise in commerce and navigation during the Renaissance which meant that people with a good level of mathematical knowledge were sought after as tutors for individuals, or teachers for schools of trade and navigation that were beginning to appear.
- The invention of the printing press which led to a much wider dissemination of knowledge and mathematical advances thanks to the reduced cost of buying or acquiring books and texts.
- The foundation of further universities as centres of knowledge and learning.
- The effect of the Reformation of the Church in both Scotland and England had far reaching consequences for educational standards. Scotland experienced a rise in both the number of schools, and the quality of education supplied by them, and England saw the added effect of the Act of Uniformity in the establishment of the Dissident Academies, many of whom were more open to the mathematical sciences then the traditional Grammar Schools and Universities. Scottish Councils copied this with the foundation of several mathematically strong Academies in Perth, Dundee and other cities.
- Finally the effect of the industrial revolution with the increased numbers of immigrant workers from the rural areas which because of the rise in illiteracy and lack of numerate skills highlighted the lack of education available there and the insufficient services in the cities.
All of these factors and events influenced the position of Mathematics in society and education, and the opinions of the public to the subject. The struggle to highlight the importance of a sound mathematical understanding needed in today's world continues with efforts aimed at improving the image of the subject being sponsored and run by both governments and public organisations.
Article by: J J O'Connor and E F Robertson based on a University of St Andrews honours project by Elizabeth Watson submitted May 2000.