Last week I read an amazing book on the biography of Zero. There were a mishmash of thoughts that occured to me throughout the reading, which I would like to share on this blog.
Indians are famed for quantitative skills but fall short of numerical creativity
Ever wondered why a large proportion of Indians are engineers, programmers, quant people? Very few plan to become artists or philosophers. To be an engineer, one has to be comfortable with numbers, more precisely algorithms. That takes hard work and number crunching. To be an artist, one must have (apart from aesthetic sense) a geometric sensibility. A true mathematician, I feel, would also have the intuition of a philosopher, artist or architect (Brunelleschi, Da Vinci, etc..). Why? Well, mathematics involves not only adding subtracting multiplying and manipulating numbers, but also visualizing shapes and spaces that are represented by these numbers.
Perhaps this Indian (relative) weakness in geometry is historic. Ancient Indians stripped numbers from their geometric significance. Unlike the Greeks they did not visualize multiplication of two numbers as the area of a rectangle. Their operations were purely a manipulation of numbers – like a number game. This mentality is pervasive in current day India as well; as a high school student in India I saw fellow students and teachers alike who devoted several hours to mastering the various maneuvers of mathematical operations. Inspite of all that, it is apparent that people don’t see beyond the numbers. There is no geometrical significance to algorithms – it was just an application of various formulas that one memorizes. Pure algebra. Differentiation of x2 is 2x. Few people care how this result came to be. Even fewer concern themselves with its history (Newton, in deriving the rate of change of functions, approximates (x-h)2 –x2 and assumes h to be so small that h squared is almost zero).
Personally, I am experiencing an entirely different system of learning calculus after coming to the US. Math here makes more sense because it explains how calculus is applicable in real life. I enjoy it.