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
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 or great
math tutors. 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 ether 'language' possibly could, and this fact
supports the topic statements.
However, this 'language' is only available to most people in it's simplest
forms, i.e. arithmetic, algebra and geometry, and these are taught in schools
because they have everyday usage. 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 wide-spread,
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
Pythagoras, Euclid, Archimedes etc advanced propositions which were already
known elsewhere. The West derived it's numbers 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
it's ability to compress ideas, just as a great poet achieves desired effects by
great verbal economy. Second, because it's 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 Stephan Hawking, must be
compressed into infinitesimal space, so are likely to remain the prerogative of
the Creator! |