Slow stream of thoughts caught in hostel’s quiet hours
Inasmuch as Mathematics is concerned, It is a very private experience for me because there is no external human eye that looks after me. I feel myself a culprit of not doing and learning even a quasi-fraction of mathematics as what I had imagined and was (and am) passionate about, and of doing very little of what I had thought. An active assertion of this kind is taken to be a lie by those close to me, for they take it in a manner where we try to explicate some person’s understanding of maths merely by comparing it to his immediate surrounding that considers maths just as an obstacle to life and examination results. Hence, it is true iff considered at a largely personal sense, as a feeling, and not an active assertion. And it is needless to extrapolate the reasoning behind such sort of negative feeling; for the answer generalizes to too many things of life, material and mental, that are already semantically bleached.
In the movie, ‘The Man who knew Infinity’, G.H. Hardy takes the Indian prodigy Ramanujan in his assistance, goes hard on him first but becomes his friend by the end. Sad to say that Ramanujan, a brilliant mathematician of the first kind, dies at a young age. I heard the name ‘Ramanujan’ from my mathematics teacher, Gul Rehmat, in class twelve at Islamia College. Keeping sir’s persona in mind, I say that he barely taught us anything, and he would just sit in the class and talk to us; yet he stirred a desire in me and opened me to mathematics in an original and creative sense — as opposed to my earlier notion of trying to be faster than everyone around me in calculations, being confident merely because of good marks, and not having a coherent idea of the juxtaposition of abstractness and concreteness. To be precise, this openness to creativity started the moment when he stood up from the wooden chair and started writing on the Whiteboard. My sensory apparatus caught a moment of profound insight when I saw such a rare explicative appartus unveiling such an abstract idea. The ‘precise propositional definition of limit’ entered my mind and imagination, and the image of the teacher entered the frame of my heart. I am proud of myself that I chose to concentrate for those thirty minutes and kept my heart, mind, and imagination open and undistracted.
Later, GIKI revived those older childish notions again in a much superficial sense — as the maths taught to undergrads here is just a play of calculators (you missed a decimal point), 20 minute quizzes coming from presentation slides and prepared by students by cramming formulas; either by sitting alone with a fast beating heart, WhatsApp-ing someone who can help them, or by sitting with friends in the little study rooms of the beautiful library — anxiously staring at laptop screens, listening to a friend who finally understood a way out of ‘x’ from an Integration, ordering food near library, and consistently made silent every by the librarian, and laughing at each other when they hear librarian saying to a group that their plagiarism in humanities course report is 85%. We take sighs of relief after leaving the examination hall and heading to the tuc or the hostel, and then home after months.
In his book, ‘A Mathematician’s Apology’ — which I read twice, first in the summer of ’21, and later in December ’23 — Hardy writes (and I summarize):
“The real maths of the ‘real’ mathematicians, of Fermat and Euler and Gauss and Abel and Riemann, is almost wholly ‘useless.’ The metric of judgement of a mathematician is not the practical utility, but something different: that something worth creating was created. High thinking of one kind is always likely to affect high thinking of another — but it has extremely little effect on anything else.
Exposition, criticism, appreciation, is work for second-rate scientists and mathematicians. It is a confession of weakness to talk about ‘writing’ mathematics, instead of doing the actual maths and adding something to maths. What we do may be small, but it has a certain sense of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.
Languages die, but mathematical ideas do not. Greek mathematics is ‘permanent’, more so even than Greek literature. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean. An equation is the same whether it’s written in red or green ink. It makes no difference to a chess problem if the pieces are white and black, or red and green, or whether there are physical ‘pieces’ at all. The chess board and the pieces are mere devices to stimulate our sluggish imaginations, and are no more essential to the problem than the blackboard and the chalk are to the theorems in a mathematical lecture.
One of the finest weapons of a mathematician is the proof by ‘reductio ad absurdum’ (proof by contradiction) — a far finer gambit than any chess gambit: a chess player may sacrifice a piece, but a mathematician offers the whole game.
A man who could give a convincing account of mathematical reality would have solved very many difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all.”
December 7, 2023
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