The Essence of MathematicsIt is in mathematics that we are able to capture truthTo address the question “What actually constitutes a genuine mathematical enterprise” where what we seek is intrinsic beauty of the subject and the fundamental unity of its parts on the one hand, and its applications outside of mathematics on the other, one can’t do better than invoke Bertrand Russel and Roger Penrose - two of the greatest thinkers of the twentieth century - whose ideas on mathematics when read in tandem define the essence and raison d’etre of mathematics in no uncertain terms.Their apparently contrasting views which are commensurate with the actual practice of mathematics are summed up in the immortal words of Russel that “Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere, like that of sculpture” and matched in equal measure by the remarkable words of Penrose when he says that “The more we understand about the physical world and the deeper we probe into the laws of nature, the more it seems as though the physical world almost evaporates and we are left only with mathematics"