The Beauty of Mathematics

I am writing this letter with reference to the article entitled “Convergence in Pure Thought” which appeared in Greater Kashmir on August 13, 2020. The article provides an abysmal comparison of certain mathematical entities with different poetic or philosophical aspects. Any person having a sound exposure to higher Mathematics could easily infer that the content is misleading. I strongly oppose the overemphasized and sloppy correlation between different poetic or philosophical aspects with the mathematical entities. For instance, while the author mentions the unevenness of the summer rainfall via the Kashmiri saying “wehrach manz chu dandus aksei hengus rood pyomut,” he points out an analogy with the notion of Continuity/Discontinuity, which is one of the celebrated concepts of both Mathematics and Physics. In the sequel, the author also claims certain strange analogies between some poetic verses and different mathematical notions. Such self-proclaimed analogies are completely erroneous and lack the merit of being appreciated by any knowledgeable reader. Even unpleasant  is the assertion that such analogies are a testimony to the beauty of Mathematics.   The author turns a blind eye towards the fact that the beauty of Mathematics lies in its ultimate truth and the befitting modelling of natural phenomenon. Nevertheless, beauty in appearance is also a vital part of any mathematical theory. It is pertinent to mention that the significance of a mathematical theory is distributed into beauty in appearance and its applications to different branches of science and engineering.  Although beauty in appearance is the first test, the applicability of a mathematical theory is the main driving force behind it. For instance,  Paul Dirac, an English theoretical physicist, says: “The main reason that the theory of relativity is so universally accepted is its mathematical elegance.” Here “elegance” refers to its apt modelling of physical phenomenon.

In my opinion, the aforementioned article is flawed mainly due to two reasons: first, there are several vague interpretations of the logical and profound mathematical ideas; second, even more off putting, the author proclaims that the applications of mathematical theories across various branches of science and engineering are of secondary importance. The irony is that the author opines that the beauty of Mathematics does not lie in its applications to different scientific, social and economic aspects but somewhere else (probably, the poetic and philosophical analogies pointed out by the author). Although there are many aspects where some elementary mathematics is used for recreational purposes, that is none of the businesses of a mathematician and has nothing to do with the beauty of Mathematics. The true beauty of Mathematics can be ascertained from a rhetorical question of Albert Einstein: “How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?”  Even the pure mathematicians like G.H. Hardy, Srinivasa Ramanujan and many others strongly admire the applications of mathematical theories in unveiling the mysteries of nature. One of the quotes of G. H. Hardy reads: “A Mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.” This quote completely denounces the author’s vague interpretations as it lucidly points out that the elegance of pure Mathematics lies in the logical ideas involved in the formulation of mathematical theories. To add to my arguments, I shall point out another quote of Srinivasa Ramanujan, the mathematical genius of India: “An equation means nothing to me unless it expresses a thought of God.” What does “…thought of God” refer to? Surely, the entire universe in itself is a composite thought of God; the thought which the humans try to explore. The testimony to this quote lies in the fact that, nowadays, some of the results formulated by Srinivasa Ramanujan are being applied to study the behaviour of Black Holes; a region of space-time from which gravity prevents anything, including light, from escaping. Nevertheless, Ramanujan’s Mathematical theories are also widely applied in various aspects of signal processing. These references suffice to infer that the elegance of Mathematics mainly lies in its extraordinary power to analyze and explain different aspects of nature. As a human endeavour, Mathematics has grown into a profound branch of knowledge which has influenced all aspects of life and there is hardly any field of science where mathematical theories are not being invoked. That is the main reason why the subject of Mathematics has been enthroned as the queen of science.

Azhar Yousuf is Researcher, Mathematics (Wavelet Theory), South Campus, University of Kashmir, Anantnag.