Bertrand Russell once said, “It might seem that the empirical philosopher is the slave of his material, but that the pure mathematician, like the musician, is a free creator of his world of ordered beauty.” Several such creators of their worlds of ordered beauties have appeared in the world. They have appeared from unexpected whereabouts and unheard-of descents. One such appearance was that of Prof Abdul Aziz.
Prof Aziz came of a not-financially-poor yet not-highly-educated family. He was born in 1952. He was one of a kind in his family. Not many from his locality were educated. Owing to this state of affairs, it is somewhat unfortunate that his contributions to mathematics, in general, and to Complex Analysis, in particular, were understandable to hardly anyone in his locality. Fortunately, mathematics has an audience neither divided by lands nor separated by tongues. In the words of David Hilbert, “Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.”
Thus, Prof Aziz’s work did not go unnoticed. His expertise in Complex Analysis can be gauged by the fact that one of his contributions culminated into being known after him as Aziz’s Theorem. Mentions of Aziz’s Theorem can still be found in books including that of Victor Prarolov’s book, ‘Polynomials’.
Having rendered his services in the capacity of a teacher, a dean, head of the department, and a supervisor to several researchers, Prof Aziz retired from official services years back in 2010. His retirement did not, however, stop him from following his passion, mathematics. As per one of his family members, Prof Aziz remained immersed with research even after his superannuation at the University of Kashmir. In harness, Prof Aziz breathed his last on June 26, 2021, after having contracted the deadly coronavirus. There is no denying the fact that the world cannot mourn a demise for good. In the words of the Bohemian writer, J.R.R. Tolkien, “In sorrow we must go, but not in despair. Behold! we are not bound for ever to the circles of the world, and beyond them is more than memory.”
Prof Aziz was best known for his contributions in the field of Complex Analysis. Owing to his untiring efforts and God-given acumen, he earned a name and fame for himself. His research papers in Complex Analysis appeared in some of the best journals in the field, including the Journal of Approximation Theory, Glasnik Matematicki, Journal of Mathematical Analysis and Applications, Proceedings of the American Mathematical Society, Indian Journal of Pure and Applied Mathematics, Bulletin of the Australian Mathematical Society and Pacific Journal of Mathematics, to name a few. It is pertinent to mention that these journals are considered to be the best in the business when it comes to maintaining the highest possible standards in mathematical research.
As per Google Scholar, one of his papers titled “Inequalities for a polynomial and its derivative” published in the Journal of Approximation Theory appeared in 1988. This paper has been cited two-hundred times. Pertinent to mention that this paper was co-authored with another son of the soil, Qazi Muhammad Dawood, the son of another son of the soil, Qazi Ghulam Muhammad.
Some people are remembered for long owing to their contributions and their toil. In the words of G. H. Hardy in his ‘A Mathematician’s Apology’, “Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. Immortality may be a silly word, but probably a mathematician has the best chance of whatever it may mean.”In the words of Paul Erdős, “Mathematics is the surest way to immortality. If you make a big discovery in mathematics, you will be remembered after everyone else will be forgotten.” Prof Aziz’s work has been good enough to make him remembered for long, at least in academic circles.
It is not uncommon that the foundations laid and the work done by a mathematician can keep engaged the next generations to come. In the words of Charles Hermite, “Abel has left mathematicians enough to keep them busy for five-hundred years.” Prof Aziz’s work has had profound impact on the mathematics research done in Kashmir. A lot of researchers are busy doing Complex Analysis. The legacy has been continued and several useful and beautiful generalisations have been obtained capitalising on his work. It looks like his work will engage more mathematicians from the valley for some more time if not for very long.
—The writer is Assistant Professor at Government Degree College Sopore. [email protected]