Throughout history, some of our greatest scientific advancements have come from stepping back and viewing complex systems through the lens of theory and mathematics. When Isaac Newton applied mathematical principles to explain the movement of the planets, he illuminated not just celestial mechanics but the profound idea that the universe operates according to discoverable laws. Centuries later, Albert Einstein expanded on these insights with general relativity, revealing that space and time themselves bend and curve in response to mass. Each of these breakthroughs relied on the power of theoretical models to bring clarity to phenomena that had, until then, been opaque and mysterious.

The brain, with its billions of neurons and trillions of connections, is perhaps the most intricate system we have ever encountered (and, of course, I’m not discounting the vast cosmos). It is a dynamic, evolving network where structure and function are deeply intertwined. Just as physics and mathematics have unlocked nature’s most profound secrets, computational and theoretical approaches are poised to do the same for the brain.

Here, I should mention an article by Hans Frauenfelder titled “Ask not what physics can do for biology—ask what biology can do for physics.” As amusing as the title is, it highlights a fundamental truth: theoretical models often illuminate patterns across disciplines, bringing new dimensions to the study of life, and neuroscience stands to benefit from this very union.

Why Theoretical Models

The brain cannot be understood purely through observation. Neuroimaging technologies, for all their advancements, capture only snapshots of this dynamic organ. They tell us where neurons are, where blood is flowing, and how regions activate. But the true function of the brain lies in its connectivity—how these regions communicate, how signals propagate across vast networks, and how local interactions give rise to global behaviors.

This is where computational tools become indispensable. Mathematics allows us to capture the relationships between different elements of the brain and express them in the form of models. While raw data from experiments provide valuable insights, data alone cannot explain how the brain works as a system. Theory gives us the framework to not only interpret this data but also to make predictions. Through modeling, we can explore how changes in connectivity might impact cognition, how disruptions in structure might lead to dysfunction, and how the brain reorganizes itself in response to learning or injury.

A Long Tradition in Science

The idea of using mathematical and computational tools to explain complex systems is not new, nor is it unique to neuroscience. Physics, chemistry, and biology have long benefited from the application of theory. James Clerk Maxwell, for instance, used theoretical equations to unify electricity, magnetism, and light into a single set of laws. What made Maxwell’s work revolutionary was not just its elegance, but the way it revealed hidden connections that were previously invisible to experimentalists.

In neuroscience, the application of graph theory, fractal geometry, and machine learning models can unveil patterns and principles that are not apparent through direct observation. It excites me to think that we are now at a stage where these theoretical approaches can be fully harnessed to understand the brain.

For example, computational tools like the Morphometric INverse Divergence (MIND) network offer the opportunity to view the brain not merely as a collection of isolated regions but as a highly integrated network. Graph theory abstracts the brain into a network of nodes and edges, revealing how regions interact and how disruptions in these interactions can give rise to cognitive deficits. Fractal geometry allows us to quantify self-similar patterns in cortical folding, which may be key to understanding how the brain optimizes space for efficient information processing. These tools are not just analytical—they are generative. They allow us to make predictions about how the brain might behave under different conditions and offer insights into phenomena that would be difficult, if not impossible, to grasp through experiment alone.

Why It Matters

What excites me most about this approach is the promise of unification. In the same way that the great theories of physics unified disparate forces into a coherent framework, I believe computational tools in neuroscience have the potential to unify our understanding of the brain. The brain is not just a biological organ—it is a physical system that operates according to laws we have yet to fully understand. By leveraging mathematical and computational models, we can begin to uncover these laws.

At its core, the study of the brain through theoretical approaches is about identifying the fundamental principles of organization that govern neural activity. How do networks of neurons coordinate to produce thought? What are the mathematical rules that govern plasticity, the brain’s ability to adapt? Can we predict the emergence of consciousness from the interaction of complex networks? These are the questions that drive me and many others in the field, and I believe that with the right tools, we can start to answer them.

Looking forward, the integration of theory with experimental neuroscience is where the most exciting discoveries will occur. Theoretical models will help us bridge the gap between neuroscience and artificial intelligence. AI systems, in many ways, mimic the brain’s networks, but their capacity for learning and adaptation is still far below that of biological systems. By studying the brain’s computational principles, we may unlock new ways to design self-learning systems that more closely mimic natural intelligence.

The application of theory to the brain is the continuation of a long tradition of using mathematics to reveal the hidden structures of nature. Just as mathematical models have deepened our understanding of the cosmos and the physical world, they now offer the possibility of revealing the brain’s secrets. The idea that, in time, the mysteries of this vast inner ‘cosmos’ might be understood, piece by piece, by those daring enough to seek, fuels my excitement for this field.