A few months ago, I updated my Mathematics Genealogy page. It was finally updated about two weeks ago and I publicised the page on my FB wall. Some might ask why have I not updated this earlier. Mainly procrastination but before this, I was still wondering whether I will be taking any more students; I was contemplating to get another job even after retirement to help me pay bills. This seems very unlikely now.
Note that the list only contains PhD students who are directly under my main supervision. For completeness, I list down MSc students who are under my main supervision:
- Toh Sing Poh, "Cosmic Crystallography: CCP-Index of Thurston Manifold" (2002)
- Abubaker Ahmed Mohammed Siddig, "Mathematica Packages for Solving Schrodinger Equation with One-Dimensional Rectangular Potentials" (2003)
- Aslam Abdullah, "Extending Bianchi's Classification of Homogeneous Three-Manifolds" (2006)
- Ch'ng Han Siong, "Accelerating Cosmologies with Extended Product Spaces" (2006)
- Nurisya Mohd Shah, "Energy Eigenequation Expansion for a Particle in Singly Punctured Two-Torus and Triply Punctured Two-Sphere Systems" (2008)
- Mazlinda Zainy, "The Discrete Phase Space for 3-Qubit and 2-Qutrit Systems Based on Galois Field" (2009)
- Siti Nurul Ain Hj Zaiton, "Qutrits and Lie Algebraic Structure on Tensor Product of SU(3)" (2010)
- Mojtaba Aliakbarzadeh, "Generating Mutually Unbiased Bases and Discrete Wigner Function for Three-Qubit System" (2011)
- Lam Shi Xiang, "A Network Structural Analysis of Malaysian Stock Market with Edge Density Constraint" (2013)
- Wong Wen Wei, "Geometry of Two-Qubit System and Hopf Fibration" (2013)
- Ahmad Hazazi Ahamad Sumadi, "Canonical Group Quantisation on One-Dimensional Complex Projective Space" (2015)
- Syed Nasrullah Ali Qazi, "Two Fluid Scenario for Dark Energy Models in a Bianchi Type I Universe" (2015)
- Choong Pak Shen, "Characterizing Two- and Three-Qubit Entanglement by Their Tensors" (2016)
- Nor Syazana Shamsuddin, "Maass Cusp Form on Asymmetric Hyperbolic Torus" (2017)
- Zurita Ismail, "Structure of Co-Authorship Network in UPM Journal Publication Database From 2007-2010" (2019)
- Siti Aqilah Muhammad Rasat, "The Role of Compositionality in Constructing Complementary Classical Structures Within Qubit Systems" (2021)
- Ahmad Aqwa Rosli, "Pictures of Processes With Abelian Rotation Symmetry" (2023)
Additional note: It is funny that I missed one of the MSc students in my latest CV. Also, the last MSc student graduated after my official retirement (end of 2022).
In total, I have 10 PhD students and 17 MSc students under my direct supervision. I have not included those students under my co-supervision, despite that there is room for adding second or third advisors in the Mathematical Genealogy page. This is mainly because supervisory committee is simply the necessary requirement of the Graduate School. The intended purpose of a supervisory committee is actually good in ideal contexts, but practically, its role may break down when expertise of members of the committee have very little in overlap. This is particularly true for theoretical physics where we have difficulty in finding supervisory committee members and thus most of the other members have little knowledge of theoretical ideas (likewise, I have very little knowledge on experimental techniques). Of course, there are cases where such supervisory committee actually work. Note that in my case, there are a few of my co-supervised students for which I did actively advising them. Even in my retirement, I still give advices to 'students'; the latest was a staff who is supposed to join UPM Physics Department soon (was surprised by his visit to my home before Ramadhan). Thus, it is best that I exclude the co-supervised students altogether (some do not even fit in mathematics research).
Some may ask about the number of students under my supervision, why that many. Indeed, I felt the same way, but if I compare myself with my colleagues in other fields, the number is pretty averageBut for a theorist, the number seems to be above average. At an early stage, I thought I should avoid taking PhD students given my little experience. I thought to myself, it is better for students to have the PhD research experience abroad where the community is larger. Thus, I begin to take quite a substantial number of MSc students particularly in areas that I would like to experiment on. Note however, my first graduate student was actually a PhD student from Algeria (whose MSc was in nuclear physics), but it was related to the work I do in PhD. More PhD students follow thereafter, (including those who did their MSc with me, even though I forewarned them that staying put with a single supervisor tend to give limited research experience and that they might like to venture elsewhere). I also ventured PhD research in cosmology and quantum field theory, which are not my main research areas. In these cases, I often insist having external supervisors from abroad who have more experience in the area than me.
If one looks at my supervisor (RS Ward) mathematics genealogy page, it seems that I have contributed quite a significant fraction to his (30) descendants.
I have my own reasoning for having the number of students that I have, but I will do a different post for this reason.
Now, if one looks at the picture above, the supervisor of my supervisor is Roger Penrose. I have already felt blessed to note this lineage that includes greats like Penrose even before he won the Nobel Prize. In fact, I was indeed already feeling blessed to have Richard Ward of the Atiyah-Ward transform fame. When I had him as my supervisor, I did not even know that Roger Penrose was his supervisor until very much later on, but I do know that his research involved twistors as a mathematical tool. Having these two intellectuals as part of my academic lineage is already something great to have, but I was told (by Tawfik; I did not check beforehand) later on that this lineage goes even back to Isaac Newton and Galileo! Here I write down my academic ancestors:
- Richard Ward
- Roger Penrose
- John Arthur Todd
- Henry Frederick Baker
- Arthur Cayley
- William Hopkins
- Adam Sedgwick
- Thomas Postlewaite
- Stephen Wisson
- Walter Taylor
- Robert Smith
- Roger Cotes
- Isaac Newton
- Isaac Barrow
- Vincenzo Viviani
- Galileo Galilei
- Ostilio Ricci
- Niccolo Fontana Tartaglia
What is the point of highlighting all these? For me, it is just a matter of recognising the blessings one has. I hope my own students feel the same way too. It is not something to really take pride in since having a great lineage does not necessarily entail one is great. Only doing/establishing a good academic work will determine one's stature and it is not for ourselves to judge or say whether we are doing great (or not). The words of Prof. Lamberto Rondini are always on my mind: (paraphrasing) it is not easy to leave one's mark even in one's own narrow field, let alone for the bigger field of science. My own words to my junior colleague quite recently (without the intent of being derogatory): all of us are trying leave a mark in science internationally (or locally), always on the look out for fresh ideas that are of importance to the (relevant) community. If we are lucky, we will stumble onto one or two works with lasting impact but otherwise we are in the fold of many (average) scientists trying to do something worthwhile or useful.
As a side note, I do dream to have scientific work that have lasting impact in quantum sciences, mathematical sciences particularly those with geometrical and topological ideas. Most of the time, international scientists tend to be more appreciative of such effort in comparison to local ones. Time will tell if any of the things that we do, has some form of impact.
