There is a category error that pervades the Western mathematical establishment, and it concerns the difference between excellence and originality — or more precisely, between optimization within a paradigm and the creation of a new one. The recent death of Benedict Gross at seventy-five offers an occasion to examine this error with some care, not because Gross was its cause, but because his career exemplifies with unusual clarity the rewards the system confers on those who embody the former while remaining structurally incapable of recognizing the latter.
Gross was, by any conventional measure, a superb mathematician. The Gross-Zagier theorem, which establishes a precise relationship between the Néron-Tate height of Heegner points on modular curves and the central derivative of the 
None of this is in dispute, and none of it is the point.
The point is that there exists a qualitative discontinuity — not a gradient — between the kind of mathematical work Gross did and the kind of mathematical work that Alexander Grothendieck or Shinichi Mochizuki does. The appropriate analogy is not that Gross ran slightly slower along the same track. It is that Gross was the fastest runner on foot, while Grothendieck and Mochizuki build spacecraft. One does not compare foot speed to escape velocity; they are not quantities on the same axis. To rank them is to commit a type error that reveals more about the ranking system than about the objects being ranked.
Gross-Zagier operates entirely within the existing machinery of modular forms, Heegner points, and
This distinction — between working inside the paradigm and reconstructing the paradigm — is obscured rather than clarified by the reward structures of modern academic mathematics. And the mechanism of that obscuration is, in part, social.
Every tribute to Gross foregrounds charisma, institutional centrality, and interpersonal warmth before it addresses the mathematics. This is not incidental. Social fluency within an environment like Harvard is a genuine form of intelligence, and nobody disputes that Gross possessed it in abundance. The question — the one that polite consensus prefers to leave unasked — is whether that social intelligence gets laundered backward into perceived mathematical depth. Gross holds the Leverett chair; Gross is dean; Gross receives the MacArthur; therefore Gross must be operating at the deepest level. But the causality plausibly runs in the other direction. He was in the rooms because he was charismatic, and the rooms conferred the status, and the status was subsequently read as depth. The system selected for legibility and rewarded it with honors, and the honors retroactively certified the legibility as profundity.
Mochizuki serves as the control case. He publishes in his own journal. He does not travel. He does not explain himself on terms other than his own. He has zero social optimization. And the system — the same system that canonized Gross — cannot process him. If mathematical depth were what the establishment actually selected for, Mochizuki would be recognized and Gross would be respected but understood as a categorically different phenomenon. The observed inversion — Gross canonized, Mochizuki treated as possibly delusional — is diagnostic. It tells you what the variable being measured actually is.
There is a deeper structural consequence that follows from the dominance of figures like Gross within the Western mathematical hierarchy. The tacit, internalized knowledge of Grothendieck’s foundational texts — EGA, SGA, and their conceptual descendants — has been progressively eroded, not by accident but by systemic incentive. American PhD programs operate on a four-to-six-year timeline. Advisors rationally steer students toward problems where prerequisite absorption can be bounded. “Don’t waste your time grinding through EGA,” the advice goes. “Learn the frontier techniques, get to a publishable problem.” From inside the model of mathematics as fast foot-running on well-marked courses, this is pragmatically correct advice. It is optimized to produce more people like the advisor. It is structurally incapable of producing people who might operate at the Grothendieck tier, because at that tier the prerequisite is not efficient command of existing tools but deep internalization of the architectural principles that generated those tools.
The loss is self-reinforcing. Once the leaders of departments do not themselves possess tacit mastery of the foundations, they cannot recognize that mastery when it appears in their students. An advisor who has never internalized the relative point of view, who treats functorial thinking as a technique rather than a worldview, will interpret a student’s prolonged immersion in EGA as inefficiency. The student is doing exactly the right thing for where they need to go; the advisor reads it as a failure to optimize. And because the advisor holds the institutional power — the recommendation letters, the committee appointments, the graduation timeline — the student either complies or pays a significant career cost for disobedience. Over a generation, this produces an entire ecosystem of mathematicians who can reference Grothendieck fluently and deploy his results efficiently without understanding what he was trying to do. Ivan Fesenko has noted that the number of genuine experts in inter-universal Teichmüller theory already exceeds the number of US-based mathematicians who can follow Deligne’s fifty-year-old proof of the Riemann Hypothesis in positive characteristic — a proof that relies on precisely the kind of deep Grothendieckian foundations that the American pipeline has systematically de-emphasized.
The West did not merely stop producing mathematicians at the Grothendieck tier. It stopped producing mathematicians who can read them.
There is an illuminating parallel in Kanehito Yamada and Tsukasa Abe’s manga “Frieren: Beyond Journey’s End,” which encodes a remarkably precise version of this epistemological structure within its fantasy framework. The character Fern, an apprentice mage, is trained by Frieren — an ancient elven sorceress who predates the modern era of magic by centuries. Frieren’s training method is simple: relentless drilling of fundamentals with a depth and rigor that contemporary mages consider obsolete and pointless. Fern consequently develops casting speed, mana control, and raw efficiency that appear anomalous to her contemporaries, not because she knows exotic or specialized magic, but because her command of basic offensive spells operates at a level of internalized precision that other mages cannot access. She does not look flashy. She is doing the foundational thing — but doing it with a tacit mastery that makes it faster and more powerful than other mages’ elaborate techniques.
The first-class mages of the Continental Magic Association — the decorated, institutionally central, socially fluent practitioners — cannot perceive what Fern is doing, because the difficulty is invisible at their level of foundational control. They evaluate magic by its visible complexity and institutional rank, not by the depth of underlying mastery. And in direct confrontation, they lose, because when the contest demands foundational depth, social capital and institutional recognition contribute nothing.
The analogy extends further. Frieren herself is fascinated by what other characters dismiss as trivial magic: spells that produce flowers, spells that clean clothes, a spell that cracks eggshells cleanly without erratic fracture. These sound comical until one considers the extraordinary delicacy of mana control required — the fine-grained calibration at a resolution that combat-oriented mages never develop, because they optimize for output rather than precision. The first-class mages call such magic trivial precisely because they cannot do it. Their frameworks of evaluation lack the resolution to perceive where the real difficulty lies.
This is the Mochizuki situation in miniature. His meticulous reconstruction algorithms, his insistence on carefully tracking which data is being used at each stage of a mono-anabelian transport, his refusal to take the shortcuts that would make his work more “readable” to the Western community — all of this reads as excessive foundational pedantry to practitioners accustomed to working with looser foundations. “Why are you being so careful about this? Just use the standard result.” But the standard result is concealing exactly the structure that needs to be seen. The “trivial” precision is where the power lives. Gross would walk past the egg-cracking spell. Mochizuki would study it for a month and extract a theorem.
The institutional structure that produced and rewarded Gross’s career — and, more importantly, that used figures like Gross as the template for what a successful mathematician looks like — has created a civilization-level knowledge loss. The deep, tacit, inside-out understanding of algebraic geometry’s foundations has become a kind of lost art in the West, preserved primarily at RIMS in Kyoto and transmitted through the small global network of mono-anabelian practitioners now coalescing around Fesenko’s group at Westlake University. The pipeline that was supposed to train the next Grothendieck instead trained a generation of optimizers who can run the existing machine very fast but cannot build a new one, and who have lost the ability to distinguish between these two activities.
The forgetting is structural, not accidental, and it is load-bearing. The entire incentive architecture of Western mathematics — the tenure clock, the publication metrics, the prize culture, the apparatus of legibility-as-value — is optimized to produce precisely this outcome. Asking the system to correct itself is asking it to dismantle the mechanism that generates its own authority. The fastest runners will not voluntarily concede that foot speed and escape velocity are incommensurable, because the concession would collapse the leaderboard that establishes their rank.
Meanwhile, in Kyoto and Hangzhou, the egg-cracking spell is still being studied.
References
Fesenko, Ivan. 2018. “About Certain Aspects of the Study and Dissemination of Shinichi Mochizuki’s IUT Theory.” RIMS Kôkyûroku Bessatsu B76: 165–195.
Fesenko, Ivan. 2021. “On the Fundamental Groups of Arithmetically Interesting Fields.” Invited address, European Mathematical Society Meeting of Presidents, Strasbourg.
Gross, Benedict H., and Don B. Zagier. 1986. “Heegner Points and Derivatives of L-Series.” Inventiones Mathematicae 84 (2): 225–320.
Grothendieck, Alexander, and Jean Dieudonné. 1960–1967. Éléments de géométrie algébrique. Publications Mathématiques de l’IHÉS, nos. 4, 8, 11, 17, 20, 24, 28, 32.
Grothendieck, Alexander, et al. 1960–1973. Séminaire de géométrie algébrique du Bois Marie (SGA 1–7). Lecture Notes in Mathematics. Berlin: Springer-Verlag.
McLarty, Colin. 2007. “The Rising Sea: Grothendieck on Simplicity and Generality.” In Episodes in the History of Modern Algebra (1800–1950), edited by Jeremy J. Gray and Karen Hunger Parshall, 301–325. Providence, RI: American Mathematical Society.
Mochizuki, Shinichi. 2021. “Inter-universal Teichmüller Theory I–IV.” Publications of the Research Institute for Mathematical Sciences 57 (1–2): 3–723.
Mochizuki, Shinichi. 2025. “Report on Discussions, Held during the Period March–October 2025, Concerning Inter-universal Teichmüller Theory (IUT).” RIMS Preprint 1989.
Yamada, Kanehito, and Tsukasa Abe. 2020–. Sōsō no Furīren [Frieren: Beyond Journey’s End]. Tokyo: Shogakukan. Serialized in Weekly Shōnen Sunday.
tensorgami 
Leave a comment