The Economic Implications of Silent Deception

In February, a California high school student, Hannah Kylo, accomplished something a leading mathematician couldn’t achieve in over four decades. Mizohata has successfully disproven Takeuchi’s theory. This significant breakthrough was shared in a 14-page preprint, extending its relevance beyond pure mathematics. Economists, policymakers, and risk managers would do well to take note.

Takeuchi’s theory has been a widely accepted notion within mathematical analysis. It proposed a specific kind of ideal system, namely linear partial differential equations with real analytical coefficients. The idea was that if a solution disappeared in some areas, it must vanish everywhere—suggesting local stability implied global stability. This elegant concept informed many intuitions regarding the behavior of waves, signals, and other smooth systems.

However, recent discoveries challenge that foundation. Cairo presented a counterexample: a uniform zero solution in certain open areas, which appears perfectly flat—indeed, showing no signal—yet in other regions, the solution is clearly not zero. All the requisite conditions are satisfied, and the equations behave as expected. Yet, the rules collapse.

This counterargument might not concern abstract analysts as much as it should, but it certainly raises alarms for those designing models or drawing conclusions from partial data, particularly in areas like macroeconomics, finance, and policy.

A significant portion of economic reasoning relies on inferences drawn from incomplete information. For example, if headline inflation seems mild, that’s based on the assumption that inflation expectations remain stable. If payroll numbers plateau, inference suggests that the labor market is in a steady state. If a systematic risk indicator is favorable, it leads to the conclusion that the banking system is robust. These assessments often hinge on the belief that stable systems do not conceal difficulties beneath the surface.

The World is More Complex Than We Thought

So, when Mizohata disproves Takeuchi even within the most straightforward mathematical frameworks, how can we be confident in the more complex environments of the real world?

Consider inflation: Policymakers frequently focus on “core” measures that exclude food and energy prices, relying on various categories to inform financial strategies. But what if hidden pressures—like margin compression or shifting consumer behaviors—emerge outside the narrow range being tracked? The surface may look calm, while deeper changes are in motion.

Now, think about the labor market: steady unemployment rates might obscure declines in working hours or participation rates, or a rise in gig economy workers. Everything appears stable until revisions disclose the hidden realities, at which point the floor could drop from beneath us.

And then there’s financial regulation: Supervisors often monitor a limited number of major institutions and overt indicators. Meanwhile, risks can build up in off-balance sheet entities or in unregulated credit channels. Just because everything seems well-managed doesn’t guarantee that the system is functioning smoothly.

This counterexample illustrates that a system might seem dormant in one region while actually surging elsewhere, and there might not be a reliable mathematical method to uncover such activity based solely on areas of perceived calm.

Economics has long grappled with the limitations of known data. Mizohata’s findings sharpen these concerns. Even the most meticulously crafted equations reveal blind spots, hidden zones, and quiet turbulence.

That doesn’t imply the need to turn away from models entirely. Instead, it suggests we should avoid the pretense of absolute knowledge. Inferences ought to be approached with caution, acknowledging data gaps. Local tranquility should not be mistaken for global stability.

Mathematics has informed us that silence might serve as evidence. Now, though, it teaches us something different: silence can be deceptive.