| Title | : | Recollections from my PhD days: cruising, sinking, and learning to stay afloat |
| Speaker | : | Nishad Kothari (IIT Madras) |
| Details | : | Fri, Oct 9, 2026 2:30 PM, @ SSB134 |
| Abstract | : | Dedicated to the human spirit in these dark times! ------------------------ Motivations: The (human) pursuit of mathematics (including that of theoretical computer science) is facing a very difficult time due to the irresponsible and unethical (in my honest opinion) behaviour of certain large AI corporations (and of the individuals supporting their destruction of the aforementioned human pursuit). While individual mathematicians (including theoretical computer scientists) may hold different opinions regarding whatever is going on, one thing is certain: each of us is deeply affected, and is facing existential as well as philosophical questions (many of which we haven’t bothered to think about in the past, or at least not to this extent). It is high time that we use this as an opportunity to inculcate more solidarity (despite our many differences and varied opinions); this is the first motivation. Secondly, it is very common amongst us to just talk about the results and the technicalities of our work, while often neglecting the journey and the more human aspects (of that journey); the latter are at least as important (if not more). Many students and postdocs have requested me to give talks about my own PhD journey; certainly I am not the only one receiving such requests. Ergo, I have been thinking about giving such a talk (or a series of them) for a while; it seems that, in light of the preceding paragraph, there can’t be a better time than now! Finally: while there was no AI (at least in the sense that is being discussed here) during my PhD days, there was something far less powerful: sheer computational power that would allow one to exhaustively generate and check all mathematical objects up to a certain finite size. During the second half of my PhD, if I may borrow from Shakespeare (for a change), I was constantly facing the existential question: to compute, or not to compute? This is somewhat reminiscent of the burning question of our times: to AI, or not to AI? ------------------------ Abstract: I was cruising during the first couple years of my PhD due to an early breakthrough while being almost oblivious to the existence of the aforementioned computational power (in the context of my research); however, soon after this, the problems (I was working on) became much harder. Around the midpoint of my PhD journey, I gave in to the temptation of using computations (after resisting their use for a long time) to verify/disprove some of my conjectures; neither did I use computational power to prove anything nor did I know/learn how to do so. However, before I could realize, I had become so dependent on computations, and addicted to them, that it adversely affected my ability to do mathematics (that is, the ability to conjecture, to prove, and most importantly, to patiently struggle in order to gain a deeper understanding through that struggle). At some point, it felt as if I was drowning. Luckily, I had excellent PhD advisors (Joseph Cheriyan and the late U. S. R. Murty) who were genuinely invested in my growth, and they stood by my side while I learnt to stay afloat. Two others (apart from my friends and family) played a key role: Marcelo H. de Carvalho and Cláudio L. Lucchesi (both from Brazil); little did they know that they were being roped into a rescue operation! --------------------------------- There will be a solidarity break around the midpoint; snacks and refreshments will be served. ps --- Do I really need to add that this entire text was written by me without any assistance from AI?! |