No Country for Mediocre Mathematicians

Reflections on the white lies of AI and the struggles of a geometer By garvy | Aug 17, 2026

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The Art of the Academic Fib

In the realm of mathematics, communication often requires a certain level of dishonesty strategic framing.

Whether it is convincing the NSF that our research is of paramount importance or simplifying our life stories for strangers, lying is a tool. It is far simpler to gesture vaguely and claim, "I have a deep-seated passion for the laws of existence," “I love learning the laws of life,” than it is to recount the twenty specific, grueling milestones that led to my PhD in Arithmetic Geometry from Gainesville.

Because "What do you do?" is the default social icebreaker, I spend my time choosing between:

1. A tedious, hour-long autobiography.
2. A convenient little lie.

(To this day, no one knows about my time at puzzle camp.)

"Lying is a sin, and small fibs accumulate into a significant moral debt."

To balance the scales, I am brutally honest when asked about my post-PhD plans. While other mathematicians confidently answer "more math," I simply shrug.

The Aura of Genius

I have encountered the "true" mathematicians—the ones inhabiting universities, conferences, and the depths of Twitter. When you are physically close to the most brilliant minds on Earth, you don't necessarily feel an overwhelming sense of intellectual inferiority. Instead, you feel a striking realization: this person genuinely loves math.

In academia, passion, talent, and ego are a braided cord. My own passion, unfortunately, has always been in short supply.

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The Path of Least Resistance

When I first met my advisor, Jeremy, I told him I had no intention of pursuing a career in academia. I lacked the necessary momentum and the requisite ego. Jeremy agreed, and for four years, we pursued knowledge at a leisurely pace.

By the end of my doctorate, I had accidentally achieved a respectable set of milestones:

• Solo publication in a reputable journal.
• Presentation at a major conference.
• Financial gains via several teaching awards.

The Market Shift

Thirty years ago, my CV would have been a "golden ticket." Today, the landscape is different. Competition has accelerated to a breaking point.

The Post-Doc Checklist (Modern Era):

• Solid publication
• Conference presentation
• Triple the amount of conferences
• Two additional high-impact publications
• Unwavering ego

I wasn't a bad candidate; I was just a weak one. I entered a brutal market as a mediocre student turned mediocre mathematician.

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The Prodigy Complex

Jealousy is an unattractive trait, which explains why my modeling career never took off. I find myself comparing my life to those who possess a singular, focused devotion.

I watched Alysa Liu shoot to stardom and the public swoon over her passion (and her proximity to the idol glaive). I’ve only stepped on ice twice, yet I envied her devotion. Similarly, when Hannah Cairo’s preprint hit arXiv, the world buzzed about her age and brilliance. I, meanwhile, existed in silence.

Comparison is the thief of joy, and since I leave my doors unlocked (practicing a form of hyperstition for a high-trust society), joy is stolen from me frequently.

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The Philosophy of "Small Ball"

However, there is a different way to view contribution. Mathematics is a frontier that can be explored but never fully conquered.

$\text{My Work} < \text{Advisor's Work} < \text{Sarnak's Work} < \text{Ramanujan's Work}$

Even if the scale is vastly different, the nature of the act—contributing—is the same. A physicist friend once asked: Why bother with research if someone like Terence Tao could solve your entire dissertation in a fraction of the time?

The answer is simple: Terence Tao did not solve that specific, small, open problem.

By finding a bite-sized result, I experienced the exhilaration of touching the edge of the unknown. I discovered structure within the labyrinth.

The Value of the Incremental

"Small ball" mathematicians are the unsung heroes of the field. For every landmark theorem, there are thousands of incremental results that build the necessary intuition.

At BARD (a computational number theory conference), I learned that there is outsized power in the "grunt work":

# The "Small Ball" Approach:
# While the giants theorize, we program the experiments.
def numerical_experiment(conjecture):
    for n in range(1, 1000000):
        if not verify(n):
            return "Counterexample found!"
    return "Intuition supported."

By performing the numerical experiments that the "greats" only theorize about, the small ball player can shift the entire direction of the field without ever becoming a household name. I don't need to be Andrew Wiles or George Andrews.