Is Math A Natural Science? Examining The Classification Debate

The question of whether math should be considered a natural science has been debated by mathematicians, philosophers, and scientists for centuries. Some argue math studies abstract systems unrelated to the physical world. Others contend math underpins all natural sciences.

In this 3000-word article, we’ll analyze the merits of both perspectives on this complex issue.

If you’re short on time, here’s the quick answer: While math and natural sciences share some commonalities, math lacks the core feature of empiricism that defines the natural sciences. Most experts today classify math as a formal science rather than a natural one.

Defining Natural Science

In the realm of scientific inquiry, the classification of disciplines has been a subject of ongoing debate. One such debate centers around whether mathematics should be considered a natural science. To delve into this discussion, it is important to understand the characteristics that define natural science and how mathematics fits within this framework.

Empiricism and the scientific method

At the core of natural science is the principle of empiricism, which involves gathering data through observation and experimentation. This approach is complemented by the scientific method, a systematic process that involves formulating hypotheses, conducting experiments, and analyzing results to draw conclusions.

These methodologies are commonly employed in disciplines such as physics, chemistry, biology, and geology.

Studying the natural world

Natural science focuses on the study of the natural world and seeks to understand its fundamental principles and processes. It aims to explain phenomena occurring in the physical universe, from the smallest subatomic particles to the vastness of the cosmos.

By employing empirical methods, natural scientists investigate the workings of nature and strive to uncover underlying patterns and relationships.

Making testable predictions

One key characteristic of natural science is the ability to make testable predictions based on empirical evidence. Through careful observation and experimentation, scientists formulate hypotheses that can be rigorously tested.

The results of these tests either support or refute the hypotheses, leading to the advancement of scientific knowledge. This cycle of prediction and verification is a hallmark of natural science.

Classifications of science

While mathematics is undeniably a critical tool in many scientific disciplines, its classification as a natural science is a matter of contention. Some argue that mathematics, as an abstract field of study, operates under different principles than natural science.

Mathematics is often seen as a formal system that deals with abstract concepts and logical reasoning, rather than direct empirical observation.

On the other hand, proponents argue that mathematics is the language of science and plays an integral role in modeling and describing natural phenomena. It provides the foundation for many scientific theories and allows scientists to make precise calculations and predictions.

In this sense, mathematics can be viewed as an essential tool within the natural sciences.

Arguments for Math as Natural Science

Studies real-world systems

Mathematics may seem abstract, but it plays a crucial role in understanding and describing real-world systems. From the laws of physics to the patterns in nature, mathematics provides a language to express and analyze these phenomena.

For example, the field of fluid dynamics uses mathematical equations to study the flow of liquids and gases, which has numerous applications in engineering and environmental sciences. Moreover, mathematicians often collaborate with scientists from other disciplines to develop mathematical models that accurately represent complex systems.

Essential foundation for science

Mathematics is the backbone of all scientific disciplines. It provides the tools and methods necessary for conducting experiments, analyzing data, and making predictions. Without a solid foundation in mathematics, it would be challenging to understand the fundamental principles and laws that govern the natural world.

Whether it’s calculating probabilities in biology, solving differential equations in physics, or analyzing statistical data in psychology, mathematics is an essential part of the scientific process.

Uses logic and reasoning

Mathematics relies heavily on logic and reasoning to prove theorems and solve problems. This logical rigor is also a characteristic of natural sciences. Just like scientists, mathematicians employ deductive reasoning to establish the truth of mathematical statements based on established axioms and logical rules.

The precision and clarity of mathematical arguments make it a valuable tool for understanding and explaining natural phenomena.

Makes some testable hypotheses

While mathematics is often seen as a deductive science, it can also make testable hypotheses. Mathematicians can formulate conjectures based on patterns or observations and then set out to prove or disprove them.

For example, the famous Goldbach Conjecture in number theory states that every even integer greater than 2 can be expressed as the sum of two prime numbers. Although this conjecture remains unproven, mathematicians have tested it for a vast range of numbers and found no counterexamples so far.

This blending of deductive reasoning and empirical testing aligns mathematics with the scientific method.

Arguments Against Math as Natural Science

Lacks empiricism

One of the main arguments against classifying math as a natural science is that it lacks empiricism. Unlike other natural sciences such as physics or biology, math does not rely on observation or experimentation to establish its principles.

Instead, it is built upon deductive reasoning and logical proofs. While math is undoubtedly a valuable tool for understanding and describing the natural world, it is not based on the same empirical methods used in the natural sciences.

Studies abstract systems

Another reason why some argue against math being classified as a natural science is that it studies abstract systems rather than the physical world. Math deals with concepts such as numbers, sets, and functions, which are abstract and do not have a direct connection to the natural world.

While math can be applied to various scientific disciplines, it is not inherently tied to the study of the physical universe like other natural sciences.

Makes no testable predictions

Unlike natural sciences that make testable predictions, math does not typically make predictions about the natural world. Math provides a framework for understanding patterns and relationships, but it does not make specific predictions about the behavior of physical phenomena.

Instead, math is a tool that scientists use to analyze and interpret data, but it does not itself generate testable hypotheses.

Better classified as a formal science

Given the unique characteristics of math, some argue that it is better classified as a formal science rather than a natural science. Formal sciences, such as logic and computer science, study abstract systems and formal languages.

They focus on the development of formal systems and the rules that govern them. Math fits into this category as it relies on formal logic and abstract concepts to establish its principles.

While the classification of math as a natural science is debatable, it is important to recognize the valuable role it plays in understanding and explaining the natural world. Math provides a powerful toolset for scientists to analyze and interpret data, and its applications in various scientific fields are undeniable.

Whether it is classified as a natural science or a formal science, math continues to be an integral part of scientific inquiry.


In summary, while math and the natural sciences share some similarities, math lacks the core feature of empirical study of the natural world that defines natural science. The debate continues, but most experts today classify mathematics as a formal science rather than a natural one.

However, understanding the merits of both perspectives provides useful nuance on the foundations and epistemology of mathematics.

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