Applied mathematicians Steven Strogatz and Alex Townsend are addressing the shift in modern computation with their new book, Big Math: The Hidden Codes That Run Our World. The work explores how the rise of large language models and massive datasets has fundamentally moved mathematics beyond the capacity of human cognition.
The Externalization of Calculation
Mathematics has long served as the invisible infrastructure for everything from weather prediction to medical diagnostics. While humans once relied on finite mental capacity to solve complex problems, the discipline has increasingly shifted toward computational outsourcing. This trend is not entirely new; it represents a 2,000-year-old evolution of moving math outside the human brain and into physical tools.
“What the abacus did for arithmetic, the fangcheng board did for systems of linear equations,” Steven Strogatz told Ars Technica. This ancient rectangular array allowed for the manipulation of linear systems using bamboo sticks, effectively externalizing logic into a tangible interface. Today, that externalization has reached a point where the scale of variables—often numbering in the billions—renders human-led calculation obsolete.
Risley Hall Collaboration
The genesis of Big Math lies in the professional intersection of two generations of mathematicians at Cornell University. Strogatz, a senior faculty member known for his work on chaos theory and the dynamics of small-world networks, began mentoring Townsend, a specialist in numerical analysis and deep learning.
Their regular lunches at Risley Hall provided the backdrop for a project that evolved from a course on the top 20 algorithms of the 20th century into a broader examination of matrix-based computation.
Strogatz’s previous work includes studying the synchronicity of fireflies and the London Millennium Bridge. By pairing his expertise in nonlinear dynamics with Townsend’s focus on deep learning, the authors aim to bridge the gap between pure mathematical theory and the applied reality of modern computing.
Steven Strogatz and Alex Townsend's new book, Big Math: The Hidden Codes That Run Our World, is hugely prescient. It's the story of the math that underpins so much of our lives and how we got to our AI-suffused moment, and brilliantly anticipates the current crisis facing… pic.twitter.com/gSdJDANNOQ
Scaling Math to AI
The core argument of the book posits that much of the mathematics developed over the last several centuries is inherently scalable. While the parameters of modern LLMs have expanded significantly, the underlying matrix operations remain grounded in classical mathematical principles.
The challenge, according to the authors, is that the class of really big problems with billions of variables or parameters is something that you just can’t approach in your head. Computers have enabled a transition from conceptualizing math to executing it at a scale previously considered theoretical.
The Future of Algorithmic Complexity
As the “hidden codes” described by Strogatz and Townsend are already running the world.
“There are so many books about pure math, as if computers didn’t exist,” Strogatz told Ars Technica.
“Alex and I are both very applied mathematicians. We thought there should be a book on computers and math, especially the class of really big problems with billions of variables or parameters that you just can’t approach in your head.”
