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Strictly speaking, a language is a verbalized means of communication, enabling
the speaker to convey thought to another person. However, the more complex
the thoughts or ideas, the harder or more cumbersome the language becomes.
To explain verbally why 'the square on the hypotenuse of a right-angled triangle
equals the sum of the squares on the other two sides' would require a long and
tedious paragraph. And this is the simplest possible example; anything more
complicated would be unmanageable. So in this way mathematical symbols
which nowadays are universally accepted, compress information in a way that
no other language possibly could, and this fact supports the topic statement.
However, this language is only available to most people in its simplest forms,
i.e. arithmetic, algebra and geometry, and these are taught in schools because
they have everyday usages. The shop assistant needs arithmetic, unless there
is an automatic cash till, and technicians of all kinds need the other two;
perhaps more, such as trigonometry, logarithms and the calculus, should he
or she be dealing with quantities that vary in time and space. In this sense, of
course, mathematics is a minority language, a language intelligible only to the
specialists of all nations.
The time may come when knowledge of higher mathematics is far more
widespread, however. The new mathematics is now being taught in many
schools, sometimes alongside the traditional approach, and younger students
find the new methods more intelligible. The principles of course have not
changed; merely the setting out. However, there are great developments
available to younger students enabling them to see the subject as a whole
rather than as a series of separate compartments, and this should engender
more interest in those whose natural bent is in the direction of the arts.
Mathematics has been described as 'the spearhead of natural philosophy', and
this was certainly true up to about 1800. The subject grew up independently
in China, India, the Arab world and Europe. For example, many of the Alexandrian and Greek schools of geometricians, represented by Thales of
Miletus, Pythagoras, Euclid, Archimedes etc advanced propositions which were
already known elsewhere. The West derived its number system from the
Hindu-Arabic world, which reached Europe in about 1000 AD. The West learnt
mathematics from the Arab world and, from the 15th century, great
developments took place.
Descartes revived algebraic geometry, Napier invented logarithms, Newton and Leibnitz the calculus. Lobachevsky developed non-Euclidian geometry, and
was followed by Einstein, though the latter was more of a physicist than a
mathematician. From Newton onwards, mechanics and astronomy began to
use advanced mathematics and, later on, physics came in for the same
treatment. Both pure and applied mathematics became the indispensable
tools of progress. Pure maths reaches conclusions by means of the deductive
process, and may be independent of need. Applied maths consists of
developments to meet the requirements of science and technology.
So mathematics has become a beautiful language in several senses. Firstly,
in its ability to compress ideas, just as a great poet achieves desired effects by
great verbal economy. Second, because its tools, the symbols, are
internationally accepted. Third, because it is entirely objective, and completely
exact, allowing no room for prejudice or human emotion. Fourth, because it
constantly provides the ground for new hypotheses. These in turn are checked
by logic and observation. Often as with Pythagoras, mathematical conclusions
can be checked by other means. So mathematics can lead man closer to
absolute truth than any other means, that is in the categories of discovery in
which it can operate.
Mathematics means facts , verified by experiment, and these facts are true
within the four dimensions in which the human mind can operate. The other
dimensions, perhaps six according to Stephen Hawking, must be compressed
into infinitesimal space, so are likely to remain the prerogative of the Creator!
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