AI use: proofreading and grammar checks with Gemini. See footnote 2 for the full editorial note.
[An alternative version of this essay—given in a less formal tone—is available at my personal blog]
As an aspiring (and far from fully-fledged) mathematician1, I am closely following the current discourse regarding the “dystopia” in mathematics driven by major AI companies. A cursory glance at current social media reveals bold claims from commentators stating that “math is solved.” In this essay, I would like to offer a retrospective on the current situation from a naive student’s perspective.
First, I will be transparent about my sources of thought. In machine parlance, I digested “datasets” to “generate” this essay “organically.” To frame this discussion, I highly recommend that fellow students review the following “datasets” to understand the shifting landscape in mathematical research:
Articles:
- Terry Tao: What should we tell our students? (A highly relevant reflection by A. Lozano-Robledo for students).
- The Dialectical Theorem (An exceptional piece on the future of formalization).
- Summaries of AI Views by Prof. Terry Tao (Essential reading for my take; Parts I-IV are highly recommended for students).
Videos:
- Recent Prof. Terry Tao video on the change of how we view math presented in Numberphile
- A not-so-recent take from Prof. Terry Tao about mathematics in the age of AI presented at the ICM 2026 Public Lectures
- The 3B1B video stating there’s never been a better time to go into math
(Note: My perspective is inclined on the written articles, as I enjoy reading more than watching.)
As of now, it is evident that LLMs still lack the rigor to produce highly polished articles, and they occasionally cause disruption, such as the severe misalignment conducted by AIs. However, I cannot reject the possibility that LLMs will overcome this barrier; in the span of just three years (2023-2026), the growth of AI in mathematics has been exponential. As I realized during my rigorous master’s exams at UNIPD, I am not gifted as an innate genius, but rather, I am gifted as a relentless learner. I survived learning advanced mathematics because I accumulated tools that made complex problems more accessible for myself. However, since I do not possess the intuitive creativity on the level of von Neumann or Terence Tao (or just bring any great mathematician name to the table!), I must disclose that the prospect of machines becoming the ultimate learners in the near future is a daunting reality.
Therefore, my resolve to pursue a PhD has required heavy contemplation. I believe most of my colleagues (initially) know my primary reason for pursuing a PhD is simply to conduct research. Frankly, this alone may not be a sufficient reason. For instance, one can enter the industry to solve complex, research-level problems at companies that primarily hire Master’s degree holders. In my current state, a Master’s degree is entirely adequate if the sole goal is a secure career.
What differentiates aiming for a PhD from a Master’s, then? Simply put, it is the intrinsic reason for doing it.
- One can have a reason as simple as, “I want to do it just because.” This is quite a good reason, provided one has a concrete answer to the specific question (the second one) posed later in this essay.
- One can have noble ambitions, such as wanting to reform the systemic issues of one’s national academic infrastructure with your PhD skillset. Reality check: this is a monumental task, and setting it as a primary, immediate goal can lead to profound burnout. Unless one has been as good as Ngô Bảo Châu.
- One can have a desire to push one’s boundaries so as not to waste one’s potential. However, one can achieve this without a PhD—working in corporate R&D or building a startup serves this purpose well.
- One might pursue it for the prestige of the title. Another reality check: standard PhD research rarely provides an immediate, world-shattering contribution. Rather, it is a beautiful, profoundly personal “zero-to-one” transition—a metamorphosis from a student into an independent craftsman.
- One can hold an extremist view of wishing to “fight” this AI dystopia by competing against the overwhelming tide of machine-generated theorems. However, this is not a contest of sheer volume. Three years is enough for LLMs to surpass human output if volume is the only metric. Just look at the recent mathematical papers released by OpenAI.
Before committing to a PhD, one must realize that spending 3 to 5 years of one’s life running this “marathon” requires a rough answer to a foundational question:
“What do I want to do with this degree?”
A classically poor answer is to use the degree to delay unemployment for another few years. Attempting a PhD as a stalling tactic often limits future career options rather than expanding them.
For me, being able to construct the next question was the turning point in my reasoning:
“Why do I want to do a PhD in this specific topic?”
Stating the general version (“Why do I want to do a PhD?”) is often inadequate and leads one astray. As it is with conducting real research, we should ask specific questions instead of general ones. I personally believe there is no right answer for this question. Simply being able to formulate this specific question confidently is often enough to ensure one will find fulfillment in their doctoral journey. I can say, after being able to formulate this question, I am more than sure I want to do my PhD in my specific topic of interest.
Notice that these reflections do not relate to the AI dystopia at all. That falls into a third, separate consideration:
“How do I view AI for my research?”
My naive perspective here is that the future of academia does not begin with AI, but with how we choose to use it. Thinking that AI will completely “kill” human researchers is not a sound reason to avoid a PhD. If no human is conducting foundational research, how will the AI progress? With the current level of computational inefficiency in tackling problems like the Navier-Stokes equation, I doubt AI will unconditionally replace humans anytime soon. Machines are not yet reliable enough to autonomously verify frontier research outputs, and AI companies are still entirely reliant on human input (if I recall correctly, it is named as reinforcement learning, with industry consensus showing AI requires thousands of human hours in RLHF to evaluate outputs).
On the other hand, one of the main reasons we pursue a PhD is to undergo that zero-to-one transition—starting to do research from nothing. This transition is deeply human and often requires intense academic isolation; a solitary struggle that builds unparalleled resilience. Indeed, one could discreetly use AI to push out multiple papers to fulfill graduation requirements. However, what happens to one’s growth as a real mathematician if their mathematical “art” is not fully their own?
Since I am an avid fan of Prof. Terence Tao (I hope I can meet him someday!), I would love to give the analogy that doing a PhD is as being under an apprenticeship with a master craftsman. I view mathematics as an art of craftsmanship. How can one learn to craft a new masterpiece if one does not understand the mechanics of prior masterpieces? Over time, researchers will naturally use the aid of machines—which in the case of mathematics, is the aid of AI. However, what distinguishes a master craftsman from a fraud is whether they can still conceptualize and create without the aid of fancy machinery. Ethically utilizing AI might limit one’s sheer output, but what will you become if you act as a mere conduit for generating theorems? At the end of the day, your theorem must be yours. I am surprised that within myself, this simple check on whether one’s readiness to use AI follows Tony Stark’s advice to Peter Parker in Spider-Man: Homecoming works well to maintain my ethics:
“If you’re nothing without this suit, then you shouldn’t have it.”
If one is restricted to working without AI and cannot bring even the slightest idea to fruition, one should refrain from over-relying on it. What is the meaning of a PhD if one merely becomes an interpreter for a machine?
I am open about the fact that I utilize AI to aid my study process. It assists in my preparation, note-taking, and streamlining my workflows.2
As suggested by 3Blue1Brown, there has never been a better time to go into math. We can accelerate our growth if we ethically use AI for our work. I personally view AI as an extension—to verify tedious inequalities, streamline reasoning, and conduct surface-level background research, expanding my general knowledge, and problem-solving grasp. If we use AI to extend our horizons rather than replace our cognition, mathematics as a field will thrive in this direction.
Ultimately, I stand on the optimistic side of mathematics in the age of AI, which solidifies my reason to pursue a PhD, with an ounce of realistic take that I will stay vigilant to the current progress of AI (Hopefully, I will start my PhD journey soon as well). Having a fulfilling PhD experience comes down to knowing oneself and asking specific questions. It carries a massive opportunity cost that consumes a major part of one’s twenties (I assume most people do their PhDs in their 20s). Do not fret over AI; assimilate appropriately with it. As long as one remains fond of one’s craftsmanship, one will adapt—because, as Gödel proved, mathematics itself is incomplete.
Received 19 October 2026.
- I am aware this may be taken into account for my PhD (and research career) applications in near-future and I am fully conscious of what I wrote. ↩︎
- Editorial Note: The proofreading, grammar fixes, and flow check of this article’s draft were assisted by Gemini 3.1 Pro, as the author is fully aware of his own lack of tidiness in language matters. ↩︎
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