From evolutionary biology to AI-driven mathematical discoveries, researchers are uncovering how what things are shaped like determines what they can do
Look at your hand. Notice the elegant curve of your fingers, the clever opposition of your thumb, the intricate network of bones and tendons beneath your skin. Its form—the shape and structure—enables its function—the ability to grasp, create, and feel. This same relationship exists throughout nature and human innovation: the aerodynamic form of a bird's wing enables flight; the architectural form of a bridge determines what loads it can bear; even the molecular form of a protein dictates its role in your body.
The quest to understand how form and function relate represents one of science's most fundamental pursuits. From the evolution of biological structures over millions of years to the AI-generated discoveries now expanding mathematical frontiers, researchers across disciplines are uncovering how things are shaped and what they can do as a result.
This isn't merely an academic concern—understanding these principles helps us design better technologies, cure diseases, and even comprehend the very fabric of reality. Join us as we explore how scientists are decoding the eternal dance between form and function, revealing hidden connections between a cat's tongue, a mathematical puzzle, and perhaps the future of innovation itself.
How evolution shapes organisms for optimal function
Design principles inspired by natural forms
Algorithms discovering new mathematical forms
To navigate the world of form and function, we must first understand what these terms mean across different disciplines. At its simplest, form refers to what something is—its shape, composition, and structure. Function describes what something does—its purpose, operation, and application 1 .
The relationship between form and function isn't always straightforward. While they often complement each other perfectly, sometimes they exist in tension. A beautifully designed chair (form) may be uncomfortable to sit on (function), just as a grammatically correct sentence (form) may fail to communicate effectively (function) 7 .
| Discipline | Form (What It Is) | Function (What It Does) | Example |
|---|---|---|---|
| Linguistics | Word classes (nouns, verbs), phrases, clauses | Subject, object, adverbial roles in sentences | The word "fortunately" has the form of an adverb but functions as an "Adverbial" 1 |
| Product Design | Materials, shape, appearance, color | Practical use, usability, purpose fulfillment | A smartphone's sleek form enables communication, internet access, and photography |
| Biology | Anatomical structures, molecular shapes | Survival advantages, biological processes | Mako shark's flexible scales reduce drag, enabling speeds up to 80 mph 2 |
| Mathematics | Equations, algorithms, code structures | Problem-solving, pattern identification | FunSearch AI discovered new algorithms for mathematical problems 5 |
When practical needs dictate design, resulting in objects optimized for their intended use.
When aesthetic choices or structural possibilities drive utility and application.
For biologists, form and function represent one of nature's most exquisite dialogues, shaped over billions of years. The incredible fit between a flower's structure and its pollinator, or between a predator's physiology and its prey, seems too perfect to be accidental. But how does such precise alignment emerge?
A groundbreaking perspective suggests that thermodynamic principles guide this process, with organisms optimizing their form to extract energy from their environment as efficiently as possible 9 .
Under the second law of thermodynamics and the principle of least action, living systems develop forms that maximize their energy efficiency. The mako shark's streamlined body and specialized scales represent nature's solution to moving through water with minimal resistance—a form perfectly adapted to its function as a swift predator 2 .
Physical and chemical principles shape organisms, with genes serving as implementation templates 9 .
Organisms develop forms that maximize energy efficiency according to thermodynamic laws.
Computer modeling shows how simple components following basic rules can generate complex systems 9 .
Sophisticated biological forms and functions emerge through natural processes without top-down design.
Flexible scales reduce drag by preventing flow separation 2
Porous structure creates separated vortex ring for efficient flight
Layered spit and flower oil create rate-sensitive adhesion
If you think form and function only apply to physical objects, consider this: mathematical and computational problems also have "forms" (algorithms and code structures) that determine their "functions" (problem-solving capabilities).
In a stunning breakthrough from Google DeepMind, an AI system called FunSearch (short for "searching in the function space") has been discovering new mathematical forms that solve previously unsolved problems 5 .
FunSearch doesn't work like traditional search engines or calculation systems. Instead, it employs an evolutionary approach that pairs a large language model with an automated evaluator 5 .
Researchers write a description of the problem in code format, including evaluation procedure and initial "seed" program.
The system selects best-performing programs and feeds them to the LLM, which generates new variations.
Each new program is automatically run and evaluated, with promising candidates added back to the pool.
This creates a self-improving loop where programs evolve toward increasingly effective solutions 5 .
The results were extraordinary. For the cap set problem—which involves finding the largest set of points in a high-dimensional grid where no three points lie on a line—FunSearch discovered the largest cap sets ever found, representing the largest increase in two decades 5 .
In the bin-packing problem, where the goal is to pack items of different sizes into the smallest number of bins, FunSearch developed algorithms that outperformed established human-designed heuristics 5 .
The system produced solutions represented by highly compact programs—what computer scientists call low Kolmogorov complexity 5 . These elegantly simple forms effectively solved extremely complex problems.
| Problem Type | Problem Description | Human Solutions | FunSearch Solutions |
|---|---|---|---|
| Theoretical Mathematics | Cap set problem: find largest point sets with no three points on a line | Best known sets before FunSearch | Largest cap sets discovered in 20 years |
| Practical Computing | Bin-packing: efficiently pack items into minimal bins | Established heuristic algorithms | More efficient algorithms that use fewer bins |
| Interpretability | Understanding the solution approach | Often opaque intuition | Working programs that show the solution method |
The implications of understanding form and function extend far beyond academic curiosity. This knowledge is driving innovation across countless fields:
Engineers are studying the form of cat tongues—which feature hollow, scoop-shaped papillae made of keratin—to create better hairbrushes, and potentially new robotics and cleaning technologies 2 .
The mantis shrimp's impact-resistant armor, with its unique spiral-shaped microstructure, has inspired new composite materials for sporting equipment, body armor, and aerospace applications 2 .
Photopharmacology represents another frontier, where scientists design light-sensitive molecules (form) that can be activated precisely within the body (function) 8 .
| Natural Form | Functional Advantage | Potential Applications |
|---|---|---|
| Mako shark scales | Flexible scales reduce drag by preventing flow separation | Aircraft surfaces, swimwear, marine vessels |
| Dandelion seeds | Porous structure creates separated vortex ring for efficient flight | Tiny drones, air pollution monitors |
| Bee pollen pellets | Layered spit and flower oil create rate-sensitive adhesion | Tunable adhesives, waterproof cosmetics, drug delivery |
| Cat tongue papillae | Hollow, scoop-shaped structures efficiently distribute saliva | Improved hairbrushes, robotics, cleaning technology |
What makes current research particularly exciting is how cross-disciplinary insights are accelerating discovery. Understanding how forms emerge in nature helps computer scientists design better algorithms, while computational approaches are now helping mathematicians discover new theoretical forms.
Across these diverse fields, researchers employ specialized tools and materials to study form and function. Here are some key "research reagents" and their functions:
| Reagent/Material | Function in Research | Field of Application |
|---|---|---|
| Synthetic photoswitches (e.g., azobenzenes) | Control biological pathways with light | Photopharmacology, neuroscience 8 |
| 3D wind tunnels | Test aerodynamic properties of structures | Biomechanics, aerospace engineering 2 |
| Computer models with "atoms" | Simulate emergent behavior from simple rules | Artificial life ecosystems, complexity science 9 |
| Large Language Models (LLMs) | Generate creative solutions in code form | AI-driven discovery, mathematical sciences 5 |
| High-pressure chemistry setups | Create predicted hydrocarbon structures | Materials science, nanotechnology 8 |
| Randomized control trials | Isolate causal relationships between variables | Experimental psychology, medicine 6 |
From wind tunnels to high-pressure chemistry setups, researchers use specialized equipment to test how forms behave under different conditions.
AI systems and computer models allow scientists to simulate and explore form-function relationships in virtual environments.
The quest to understand form and function represents one of science's most enduring and productive pursuits. From the elegant logic of evolution to the cutting-edge discoveries of artificial intelligence, we continue to uncover how what things are shaped like determines what they can do—and conversely, what needs to be done often influences how things take shape.
What makes this field particularly exciting today is its increasingly cross-disciplinary nature. Biologists inform engineers, computer scientists assist mathematicians, and insights from one domain spark breakthroughs in another.
The fundamental relationship between form and function appears to be a universal principle operating across scales—from the molecular machinery inside our cells to the vast algorithmic landscapes of mathematical space.
Sustainable Energy
Disease Treatment
AI Discovery
As research continues, each answered question reveals new mysteries to explore. How do we apply these principles to tackle humanity's greatest challenges? What undiscovered forms await discovery in the natural world? And as AI systems like FunSearch expand human capability, what new relationships between form and function will we uncover? The dance continues, and its music beckons us forward into ever-deeper understanding.