Mathematics Behind Jujutsu Kaisen - Gojo Satoru’s Infinity - Essay Competition 2026

Aug 25, 2026

100

A mathematical essay treats Gojo Satoru’s Infinity from Jujutsu Kaisen as a precise description of infinite subdivision rather than a purely fictional defense. It contrasts Gojo’s claim of never being reached with Zeno of Elea’s Achilles paradox, then identifies the flaw in assuming an infinite sequence cannot be completed. Using geometric series convergence and insights from Lebesgue measurement, the work argues why infinite stepping can yield finite totals and why this matters for defeating Infinity.

LanguageEnglish

CategoryLiterature

FormatPDF

Pages10

Reading Time15 min

AccessFree to download

Introduction

Zeno’s Paradoxes

Geometric Series

Mathematics Behind Jujutsu Kaisen: Gojo Satoru’s Infinity Achmad Roykhan Sabiq Oxford University Mathematics Essay Competition 2026 March 2026 1 Introduction In Jujutsu Kaisen, there is a scene that Gojo Satoru, the most powerful sorcerer alive, explains his technique with unsettling calm: Infinity. The concept is simple. Between any attacker and Gojo, thereis always a distance. That distance can be halved, then halved again, then again, forever. No matter how fast the attack travels, it must first cross half the remaining distance, then half of that, then half of that, an infinite sequence of steps that, Gojo claims, can never be completed. Every attack slows asymptotically, and he is never reached. Figure 1: Gojo Satoru’s Infinity stopping an incoming attack. Image source: Jujutsu Kaisen Wiki (Fandom), Limitless, retrieved March 2026 . Original work by Gege Akutami, Shueisha. It sounds like the perfect defence. It also sounds deeply familiar to anyone who knows Zeno of Elea. The ancient Greek philosopher made the same argument, and mathematicians eventually proved him both right and wrong in ways far subtler than either he or Gojo Satoru fully appreciated. Gojo’s Infinity 1 ··· Attacker Gojo Distance is always halved again. The attacker never arrives. Zeno’s Paradox t1 A T t2 A T A T t3 A = Achilles T = Tortoise Figure 2: The same mathematical structure, separated by 2500 years. Left: Gojo’s Infinity subdivides the distance to the attacker indefinitely, each step covering half the remaining gap. Right: Zeno’s paradox places Achilles (A) and the tortoise (T) in the same logical trap: at each stage, Achilles reaches the tortoise’s previous position, only to find it has moved on. In both cases, infinitely many steps stand between the pursuer and the target, and in both cases, the same mathematical question arises: can an infinite sequence of steps ever be completed? What follows is an attempt to take Gojo’s Infinity seriously as a mathematical object. The question is what mathematics actually says about infinite subdivision of space, and the answer, built from geometric series and a remarkable theory of measurement due to Henri Lebesgue, will reveal that Infinity is stranger and more fragile than it first appears. It will also explain, with some precision, why Ryomen Sukuna was able to defeat it. 2 Zeno’s Paradoxes Around 450 BCE, the Greek philosopher Zeno of Elea proposed a series of paradoxes designed to prove that motion is an illusion. The most famous involves Achilles, the greatest runner in the ancient world, and a tortoise given a head start in a race. Achilles, being faster, will obviously catch up. But consider what must happen first. Before Achilles can reach the tortoise, he must cover half the distance between them. Then, from that new position, he must cover half the remaining distance. Then half again. And again, forever. At every stage, the tortoise has moved a little further. Achilles must complete an infinite number of steps before he can draw level, and how can anyone ever complete an infinite number of anything? The argument is logically watertight. It is also, as everyone knows from experience, completely wrong in its conclusion: Achilles does catch the tortoise, and we do cross rooms without difficulty. Gojo Satoru’s technique places exactly this paradox between himself and anyone who tries to reach him. The distance is always halved. The steps are always infinite. The attacker, like Achilles, is always just short of arrival. In the world of jujutsu sorcery, the paradox is a weapon. And to understand whether it can be defeated, we need to understand what is wrong with Zeno’s argument and what is right about it. | 12 | 14 | | | --- | --- | --- | | | 18 | | | | · · · | 1 16 | 12 + 14 + 18 + 116 + ··· =? Figure 3: Each region represents one term of the series ~~1~~2 + ~~1~~4 + ~~1~~8 + ··· The subdivisions fit together to tile the unit square without

FAQs

What is Gojo Satoru’s Infinity and how does it relate to Zeno’s paradox?

Infinity subdivides the remaining distance to an attacker endlessly by repeatedly halving it, creating an infinite sequence of steps. Zeno’s Achilles paradox uses the same logical structure of infinitely many intermediate stages before arrival.

Why does Zeno’s argument fail in practice?

Zeno’s conclusion assumes that completing infinitely many steps is impossible. The essay shows that the infinite subdivision can still produce a finite total, which is why Achilles can catch the tortoise.

How do geometric series resolve the infinite-step problem?

The time (or step) lengths form a geometric series where each term is half the previous one. Because the series converges, the sum of all infinitely many steps is finite, allowing completion in a finite total time.

Aug 25, 2026

100

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