Is the ability of so-called “artificial intelligence” and, indeed, mathematics in general, to predict how economic systems behave ultimately flawed?

How high school student Hannah Cairo has shown the limits in predicting systemic behavior

There is no doubt that artificial intelligence or “AI” has been touted as enabling systems to run more efficiently and particularly for software to monitor and project (and even ultimately control) the behavior of systems.  But as a slew of recent articles point out (see Slacker at https://stacker.news/items/1080616 and Breitbart at https://www.breitbart.com/economy/2025/08/14/breitbart-business-digest-what-a-new-math-breakthrough-means-for-economics/), mathematical assumptions that underlie the idea that data from part of the system may predict outcomes in another part of the system can be just that:  a mere assumption.  This is because a high school student named Hannah Cairo has apparently disproven the Mizohata–Takeuchi conjecture, which is, in a nutshell, that the lack of movement or “amplitude” in one part of a system could be used to presume quietness in the rest of the system.  

As Slacker explains:

In February, a high school student from California who goes by the name Hannah Cairo accomplished what top mathematicians had failed to do for more than 40 years: disprove the Mizohata–Takeuchi conjecture. The breakthrough arrived in a 14-page preprint posted online, and its consequences stretch far beyond the realm of pure mathematics. Economists, policymakers, and risk managers would be wise to take note.
The Mizohata–Takeuchi conjecture had long been a comforting idea in mathematical analysis. It proposed that for certain kinds of ideal systems—linear partial differential equations with real analytic coefficients—local quietude implied global stillness. In other words, if the solution to one of these equations vanished on some open patch of space, then it had to vanish everywhere. That elegant rule served as a foundation for intuition about how waves, signals, and other smooth systems behave.
The new work destroys that foundation. Cairo constructed a counterexample: a solution that is identically zero in some open region—perfectly flat, no signal at all—but distinctly nonzero elsewhere. All the required conditions are met. The equation behaves according to the supposed rules. And yet the rule fails.
This disproof doesn’t just matter to analysts of the abstract. It should unsettle anyone who builds models or draws conclusions from partial observations—especially in macroeconomics, finance, and policy.

This may mean, for example, that the blatantly flawed predictions about economics may result, at least in part, from the fact that our assumptions about the system based upon part of the system are flawed.  Perhaps this also explains why “climate change“ predictions, based upon incomplete data of what climate systems are doing today, have been so wrong when making predictions about the near and medium-term future.

Put in a broader context, this mathematical breakthrough may indicate that predictions an AI agent and/or other autonomous software can predict how a system, including economic systems and computer networks, will behave based upon data from one part of the system, simply does not follow.  For those who believe we can predict the climate based upon our incomplete data, this has broad implications.  Again, a quote from Slacker:

For those of us that thought that mathematical models of economy or weather or lots of other complex systems would not work well all the time, this is one of the reasons that they do not work.
 

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