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There are visual components of mathematics that are vital to the learning of the subject and should be a focus for its teaching. One aspect is the impressive capacity of the brain to visualise, an important element in the discovery process of some prominent mathematicians and scientists. The pedagogical importance of diagrams in mathematics is considered, with examples showing their role in problem-solving, elucidation, persuasion and decision making, concluding with some particularly stimulating and revealing diagrams for use in the classroom.

Rolled high tensile strength steel wire mesh for above-ground surface retention of landslides, oversteepened slopes, pit slopes and roadway exposures has been used globally for decades with high success and has become a standard of practice. Underground mining applications of the Geobrugg rolled mesh are now being used internationally in major block caving and other mining operations with good success and with well-documented performance tests. (Bucher et al. 2013) Furthermore, several other mine site-specific evaluations of cycle-time have documented efficiency improvements (Tonkin 2011). Canadian mines are seeing the need for improved surface support as mining depth increases. A working site evaluation of the rolled mesh is underway at an underground mine in Sudbury, Ontario. Here, a lighter version rolled mesh is being mechanically installed with an Epiroc Boltec boom bolter fitted with an unrolling device on the screen-handling boom. The first phase of this evaluation is intended to provide proof of concept specific to the mine. Key performance indicators are operator hazard exposure, cycle times and other efficiency measures, such as drilling time requirements, consumption of rockbolts, mesh, shotcrete and corrosion resistance, post-blast rehab requirements other effects on operations have been documented. The MINAX® 80-3 mesh used thus far is a lighter version intended for gravity conditions. A heavier version MINAX® 80-4 mesh is ideal for high-stress and bursting ground conditions and will be tried later after this initial proof of concept. An additional consideration was to be able to prove that mild steel galvanised welded wire mesh (GWWM), or sheet mesh could still be installed on the blasted face with the same machine setup as for the rolled mesh. All indications thus far are that the mesh and mesh installation represent a viable alternative to current surface support processes, which can improve both safety and efficiency of operations at the minimum while providing the opportunity for improved surface support performance in high-stress ground conditions. The initial results and observations of this first Canadian evaluation of the high tensile rolled mesh will be reported when complete.

A chance encounter at Bournemouth between Francis Galton and John Venn has lain in some obscurity because of a slip by Galton himself and a second mistake by Karl Pearson. The contact with Venn provides insight into the development of Galton's perception of statistical dispersion, his disenchantment with the notion of ‘probable error’ and adoption of population variability.

This paper considers the question of how Francis Galton came to devise the quincunx, a pin-board that simulates the effect of a large number of Bernoulli trials to yield an empirical normal curve. It suggests that the likely inspiration for the design was some variant of bagatelle. The argument forms a small part of an Open University doctoral thesis (May 2005), which revealed the extent of the support Galton received from George Howard Darwin as he developed the concept of statistical regression.

Home to just over five million souls, Scotland is the most sparsely populated part of Britain. The people are overwhelmingly white (some 98.7%) and English speaking. Levels of deprivation vary considerably across the country as a whole. Some 20% of the school population was entitled to free school meals in 1995, though the figure was twice as high in the City of Glasgow, where life expectancy is 10 years below that of affluent parts of the south of England. In July 1997 proposals were presented for the creation of a Scottish parliament. Whilst the Westminster parliament would ‘remain sovereign’, many powers would be devolved to Edinburgh, including those relating to virtually every aspect of education. So today, the Scottish Executive Education Department (or SEED) administers Scottish Executive policy for pre-school and school education in co-operation with local authorities that are responsible for providing school education in their areas. No less than 96% of youngsters are educated in state schools. Schools associated with religious groups including the Roman Catholic Church were incorporated into the state system in the 1920s. The annual cost of running the whole education system is a little under £5 billion or some 9% of Scottish GDP [1, p. 17].

In the first part of this paper we traced the early development of quaternions in the hands of Hamilton’s successor, Peter Guthrie Tait, Professor of Natural Philosophy in the University of Edinburgh from 1860 to 1900. Tait had neither the intuitive feel for physical concepts that Maxwell possessed nor the entrepreneurial talent of Thomson (Lord Kelvin) and yet he fulfilled a pivotal role in nineteenth century British physics through his correspondence with the former, with whom he went to school, and his collaboration with the latter. Though ambivalent towards quaternions, Maxwell was chivvied by Tait into drafting his 1873 Treatise on Electricity and Magnetism in both Cartesian and quaternion form.

Two days before his death in the summer of 1901 Peter Guthrie Tait gave his son some handwritten notes on quaternions for safekeeping. Though he had distinguished himself in many areas of mathematical physics and had influenced the work of Thomson and Maxwell it was his evangelical promotion of quaternions which would be remembered in the years to follow and it was fitting that his last energies be devoted to the cause.

The eminent physicist, Peter Guthrie Tait, having constructed mathematical models of the flight of a golf-ball and having carried out an extensive series of experiments to evaluate their parameters, specified the maximum distance a golf ball could be made to carry by the most accomplished golfer. He was then upstaged by his son who hit a monumental drive which pitched even further. The golfing press of the day - what there was of it - was happy to run the story and scientists themselves seemed to enjoy the joke at Tait’s expense. Macfarlane, for example, related the anecdote in the following terms in a lecture delivered just eight months after Tait’s death:“He […] communicated his results to the Royal Society of Edinburgh and there stated definitely the longest distance to which a golf ball could possibly be driven […] but the champion golfer upset his father's calculations […] by driving a ball five yards further.”

Among the ways in which a teacher can kindle a pupil's interest in mathematics is by invoking spirits from the subjects past: spirits of men full of imagination and determination; enterprising individuals brimming over with new ideas; pioneers who not only changed their particular discipline, but who in some cases even altered our perception of the world. The Scots have a heritage of which to be proud in science and mathematics. This article discusses four pioneers in statistics.