II. What is Math?

II : What is Math?
      (Contd. A journey to the wonderland of math by Ajay Kumar Chaudhuri) 
 
        What is the meaning of the word "Mathematics"? Is it expressible in words?  The answers seem simple, obvious and very trivial. But is it so in a real sense? Let us go to the core of the "Wonderland of Math" for a quest of these queries and subsequently perceive the versatility and ubiquity of this apparently well known but inexplicable word.

“Beauty is truth, truth beauty” – these unforgettable words of John Keats about inseparable relation between beauty and truth in his famous poem, ‘Ode on a Grecian Urn’ is equally true for Mathematics also; for it has inner truth and intrinsic beauty in itself. Mathematics, as many of us think, it is a subject of computation of numbers applying first four rules, namely, addition and subtraction along with their inverse processes of multiplication and division respectively. But it has much more deeper meaning, wider sense, supreme beauty, aesthetic patterns, and so many aspects those we cannot express in words of language.

There are diverse views of mathematicians, scientists, philosophers, writers, poets, artists, in fact, persons of every sphere of life about the true aspect of mathematics.

Let us cast a glance at some famous quotes of such luminaries of various fields, as to the exact scope, aspect and definition of mathematics, starting from the age of ancient Greek Philosophers right up to the present age.

Plato (428/427 BC – 348/347 BC) ancient Greek philosopher, student of Socrates, teacher of Aristotle and founder of the Academy in Athens, the first institution of higher learning in Western World, was so fond of his Academy and loved mathematics (geometry in particular) so much that he inscribed the words “Let no man ignorant of geometry enter here” at the entrance of his Academy. Once he said, “The highest form of pure thought is in mathematics.”

Aristotle (384 – 322 BC) Another ancient great Greek philosopher, scientist, one of the greatest intellectual figures of Western history described mathematics as “the science of quantity”.

The rarest genius on Earth of all times Leonardo Da Vinci (1452 – 1519) an Italian polymath whose area of interest included invention, painting, sculpting, architecture, anatomy, geology, astronomy, botany, writing history and cartography. His world famous paintings like ‘Mona Lisa’, ‘The last supper’, ‘The Vitruvian Man’, ‘Lady with Ermine’ still make us spell bound with bewilderment. Such a man opined about mathematics, “No human investigation can be called real science if, it cannot be demonstrated mathematically.”

Galileo Galilei (1564 – 1642), an Italian astronomer, physicist, engineer, natural philosopher and mathematician who played a major role in scientific revolution during Renaissance. He is actually regarded as ‘the father of modern science’. His discoveries with the telescope revolutionized astronomy. He viewed mathematics as “The universe cannot be read until we have learned the language and become familiar with the characteristics in which it is written. It is written in mathematical language and the letters are triangles, circles and other geometrical figures, without which it is humanly impossible to comprehend a single word. Without these, one is wandering about in a labyrinth.”

William  Wordsworth (1770 – 1850), a major English romantic poet who with his friend, Samuel Taylor Coleridge, another great English poet, helped to launch the Romantic Age in English literature with their joint publication Lyrical Ballads. Wordsworth was best known for his deepest love for nature had also some feelings for mathematics. Thus he said, “[Mathematics] is an independent world created out of pure intelligence.”

Carl Friedrich Gauss (1777 – 1855) or better known simply as Gauss, a German by birth was generally regarded as one of the greatest mathematician of all times for his contribution in number theory, geometry, probability theory, geodesy (a branch of Applied math and earth sciences) planetary astronomy, the theory of functions, potential theory including electromagnetism. He was called ‘Prince of Mathematics’. His princely remark about mathematics was, “The Queen of the Sciences”.

Nikolai Lobachevsky (1792 – 1856) or simply Lobachevsky was a Russian mathematician and geometer known primarily for his work on hyperbolic  geometry or Lobachevskian geometry, as it is popularly known, he is sometimes called ‘Copernicus of Geometry’ due to the revolutionary character of his work. Let us get a glimpse of idea about mathematics from his famous quote, “There is no branch of mathematics, however abstract, which may not someday be applied to phenomena of real world.”

Charles Robert Darwin (1809 – 1882) or commonly known as Darwin, an English naturalist and geologist, best known for his contributions to evolutionary theory. He established that all species of life have descended over time from common ancestors. His famous book on this is ‘on the origin of species’. We may get a bit sense of humour about mathematician or mathematics from his words, “A mathematician is a blind man in a dark room looking for a black cat which is not there.”

Let us share a sense of supreme beauty and an eternal truth mingled with mathematics from the perception of Bertrand Russell, (1872 – 1970), the famous British philosopher, logician, mathematician, historian, writer, social critic and political activist who won many awards including the Nobel Prize. He expressed his pleasure in mathematics by the words, “Mathematics rightly viewed possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.”

Albert Einstein (1879 – 1955), A German born theoretical physicists who developed the general theory of relativity, one of two pillars of modern physics (along   with quantum mechanics). He is best known for his mass – energy equivalence E = mc², the world’s most elegant, simplest and famous equation. Not only was he a genius but had a wicked sense of humour. Only two of them are quoted here. One is, "Mathematics are well and good but Nature keeps dragging us around by nose" and the second  goes like this, “If A is success in life,then A is equal to X plus Y plus Z.Work is X; Y is play; and Z- keeping your mouth shut".

Paul Erdos (1913 – 1996) was a Hungarian Jewish, prolific mathematician of the 20^th century was of view that the very essence of mathematics cannot be expressed explicitly in spoken words or language. It is evident when he said, “Why are numbers beautiful? It is like asking, why is Beethoven’s ninth symphony (one of the best known works in classical music) beautiful? If you don’t see why, someone can tell you. I know numbers are beautiful, if they aren’t beautiful nothing else.”

So, just we have viewed the views on mathematics of at least some personalities of highest stature in their respective fields. But now if it is asked, ‘Have we got a clear picture of what mathematics is?’ I think the answer will be emphatically a big ‘No’; for it is like the mystic portrait of Mona Lisa sketched by the great artist Leonardo Da Vinci. As a fall out we are in a quandary to express "Mathematics" explicitly in words. Moreover for its somewhat abstract
character it is not expressible.But interestingly we have free access to its majestic empire, since we live in a world ruled by it.
 
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