World Mathematical Year 2000

In 1992 the International Mathematical Union designated the year 2000 as World Mathematical Year. Several countries issued special stamps with a mathematical theme, including Monaco (with a variety of mathematical images), Belgium (Stokes’ theorem, Fermat’s last theorem and the Ishango bone), Korea (numerical symbols), Croatia (the ‘Blanusa snark’ from graph theory), Italy (Archimedes’ sphere and cylinder), Luxembourg (the WMY 2000 logo and the Riemann zeta function) and Spain (the geometer Julio Rey Pastor).
 [Belgium 2000; Croatia 2000; Italy 2000; Korea 2000; Luxembourg 2000; Monaco 2000; Spain 2000]

Statistics

We have already noted several contributions to probability and statistics: de Witt’s applications of probability to economics, Huygens’ formal probability text, Jakob Bernoulli’s ‘law of large numbers’. and Condorcet’s theory of voting.
In the early 19th century the ‘method of least squares’ was developed by Gauss and by Adrien-Marie Legendre. Given a range of data arising from an experiment, the aim is to find the best-fit curve of a given type (such as a straight line or quadratic curve) that most closely fits them. Gauss was led to this method while trying to predict the orbit of the newly discovered asteroid Ceres.
Adolphe Quetelet (1796–1874) was supervisor of statistics for Belgium, pioneering techniques for taking the national census. His desire to find the statistical characteristics of an ‘average man’ led to his compiling the chest measurements of 5732 Scottish soldiers and observing that the results were distributed normally around a mean of 40 inches. Quetelet’s investigations helped to lay the foundations of modern actuarial science.
Florence Nightingale (1820–1910) was strongly influenced by the work of Quetelet. Remembered as the ‘lady with the lamp’ who saved many lives through her sanitary improvements in Crimean War hospitals, she was also a fine statistician who collected and analysed mortality data from the Crimea and displayed them using her ‘polar diagrams’, a forerunner of the pie chart. A number of stamps have featured statistical themes, such as a graph showing the Norwegian gross national product from 1876 to 1976, and one depicting the decline in malaria.  
[Australia 1974; Belgium 1974; British Virgin Islands 1983; Israel 1962; Norway 1976]

The low countries

In 1585 the Flemish mathematician Simon Stevin (1548–1620) wrote a popular book De Thiende [The Tenth] that explained decimal fractions, advocated their widespread use for everyday calculation, and proposed a decimal system of weights and measures. Stevin also wrote an important treatise on statics that included the first explicit use of the triangle of forces.
Johan de Witt (1625–1672) was a talented mathematician and political leader whose concern with Holland’s financial problems led to his writing a treatise on the calculation of life annuity payments, an early attempt to apply probability theory to economics. His important text Elementa Curvarum Linearum [Elements of Linear Curves] was one of the earliest accounts of analytic geometry. He was murdered by an angry mob for political reasons.
The scientific contributions of Christiaan Huygens (1629–1695) were many and varied. He expounded the wave theory of light, hypothesised that Saturn has a ring, and invented the pendulum clock and spiral watch spring. In mathematics he analysed curves such as the cycloid (the arch-like path traced out by a piece of mud on a bicycle tyre) and the catenary (the shape formed by a hanging chain), and wrote the first formal probability text, introducing the concept of expectation.
[Belgium 1942; Comoro Islands 1979; Netherlands 1929, 1947, 1962]

Map-making

Nautical explorations played a major role in the renaissance of map-making. The problem of representing the spherical earth on a flat sheet of paper led to new types of map projection and to improved maps for navigators at sea. The Greek astronomer Ptolemy, the Portuguese cosmographer Pedro Nunes, the Flemish cartographer Gerard Mercator and his friend Abraham Ortelius all played a role in this story.
The first ‘modern’ maps of the world were due to Gerard Mercator (1512–1594), obtained by projecting the sphere outwards on to a vertical cylinder and then stretching the map in the vertical direction in such a way that the lines of latitude (horizontal) and longitude (vertical) appeared as straight lines and all the angles (compass directions) were correct, as on the Canadian stamp.
In 1570 the illustrious Belgian cartographer Abraham Ortelius (1527–1598), geographer to the king of Spain, produced his Theatrum Orbis Terrarum, a collection of seventy maps that is usually considered to be the first atlas. The word ‘atlas’ was coined by Mercator for his three-volume collection of maps in 1585–1595.
[Belgium 1962, 1994; Bophuthatswana 1992; Canada 1898; Cuba 1973]

The invention of printing

Johann Gutenberg’s invention of the printing press around 1440 enabled classic mathematical works to be widely available for the first time. At first the new books were printed in Latin for the scholar, but increasingly vernacular works began to appear at a price accessible to all; these included texts in arithmetic, algebra and geometry, as well as practical works designed to prepare young men for a commercial career.
Important among the new printed texts was the Summa de Arithmetica, Geometrica, Proportioni et Proportionalita of Luca Pacioli (1445–1517), a 600-page compilation of the mathematics known at the time; published in 1494 it included the first published account of double-entry bookkeeping. In Germany the most influential of the commercial arithmetics was by Adam Riese (c.1489–1559); it proved so reputable that the phrase ‘nach Adam Riese’ [after Adam Riese] came to refer to a correct calculation.
The invention of printing led gradually to the standardisation of mathematical notation. The arithmetical symbols + and – first appeared in a 1489 arithmetic text by Johann Widmann and the equals sign was introduced in a 1557 algebra book by Robert Recorde. The symbols × and ÷ were not in general use until the 17th century.
[Belgium 1973; Colombia 1968; Finland 1942; Germany 1959, 1992; Italy 1994]