Biology, Chemistry, Physics, and Mathematics

Editors’ note: This section is based upon work from[1]

To become a biologist or health-care professional, you have to study a variety of scientific disciplines — biology, chemistry, physics, and math. You might have noted that the world doesn’t actually divide itself in this way. Rather, the disciplines historically have been a way of choosing a sub-class of the phenomena that occur in the world and looking at a particular aspect of them with a particular purpose in mind. Different disciplines have different sets of tools and ways of knowing. Looking at something from different disciplinary perspectives adds a richness and depth to our understanding — like taking two 2-D pictures and merging them into a 3-D image.

Your introductory science and math classes often provide you with some basics — tools, concepts, and vocabulary — but may not give you a perspective on what each discipline adds to what you are learning and how they all fit together. Each discipline has its own orientation and perspective towards the development of a professional scientist. Here’s a brief (and oversimplified) overview of the different disciplines that you encounter in studying biology.


Biology, as you well know, is the study of living organisms. The approach taken by biology is guided by and constrained by the fact that the subject is about living organisms.

  • A lot of biology is complex Because of the complexity, the first steps in biology (and in other sciences of the complex) are often about identification, classification, and description of phenomena. Whenever a science considers a complex phenomenon it does this — whether it’s biology, organic chemistry, or plasma physics. In biology, it is important to describe the traits, structure, and behavior of a biological phenomenon before looking toward explanations of how it works. So it was important to do Linnaean classification and morphology before the ideas of evolution could be worked out; and an understanding of the nature of organic chemistry and biological molecules was necessary before the molecular functioning of biological systems could be disentangled. This results in biology having a huge vocabulary and many concepts to learn.
  • Biology depends on history — By this, we don’t mean the history of how the science of biology developed, but the history of how organisms developed. All biological organisms are connected through a common, unbroken, history – a chain or web of lifeforms – that affects how things are today. What has happened over time matters in biology and affects how things are today. This is like geology, and unlike chemistry, physics, or math. (Though when biology gets down to the mechanism of how things actually happen, it is very much like chemistry and physics, and uses math.) The properties of organisms that are currently alive and their relationships to their environments and to each other depend a lot on what happened to their ancestors in the distant past. The history of an organism is written in its genome. Knowledge of evolutionary processes is often an important tool to “explain” why a particular organism solves a biological problem in a given way.
  • Biology looks for mechanism — Biology is not just about “What is life?” It’s also about “How does it work?” At one level, you might look at the organs and parts of either an animal or a cell and figure out what their function is for the organism. Today, using the tools of chemistry and physics (and using math), biology has gone down to the atomic and molecular level, figuring out the biochemistry of genes and proteins. Today, such quantitative measurements can be carried out simultaneously on thousands of genes or proteins in an organism. This has opened a new frontier of science, “Systems Biology”, which aims to find mechanisms in these huge datasets and describe how thousands or millions of components work together in a biological system such as a cell, an organism, or a population.
  • Biology is multi-scaled — an organism can be considered at many scales, for example, the atomic and molecular scale (biochemistry), in terms of the internal structure and functioning of its organs and parts (physiology), and as a part of a much larger system both in space (ecology) and time (evolution). The relation between these scales can be treated by reductionism or emergence — going to smaller scales to explain something (reductionism), or seeing new phenomena arise as one goes to a larger scale (emergence).
  • Biology is integrative– Biological phenomena emerge from and must be consistent with the principles of chemistry, physics, and math. In other words, chemistry and physics constrain how an organism can behave or evolve. Therefore biologists must understand how physics and chemistry manifest themselves in biological organisms and higher-order systems. Increasingly, biologists searching for mechanisms of complex biological behavior are finding it valuable to use mathematical, physical, and chemical models in their research.


Chemistry starts with the idea that all matter is made up of certain fundamental pieces – atoms of about 100 different kinds (elements) – and is about the ways those elements combine to form more complex structures – molecules. But chemistry is not just about building molecules. It’s about what you can do with that knowledge in our macroscopic world.

  • Chemistry is about how atoms interact to form molecules — Understanding the basic principles of how atoms interact and combine is a fundamental starting point for chemistry.
  • Chemistry is about developing higher-level principles and heuristics — Because there are so many different kinds of molecules possible, chemistry develops higher-level ideas that help you think about how complex reactions take place.
  • Chemistry frequently crosses scales — connecting the microscopic with the macroscopic, trying to learn about molecular reactions from macroscopic observations and figuring our what is possible macroscopically from the way atoms behave. The connections are indirect, can be subtle, and may involve emergence.
  • Chemistry often assumes a macroscopic environment — Much of what chemistry is about is not just idealized atoms interacting in a vacuum, but is about lots of atoms interacting in an environment, such as a liquid, gas, or crystal. In a water-based environment, the availability of H+ and OH- ions from the dissociation of water molecules in the environment plays an important role, while in a gas-based environment, the balance of partial pressures is critical.
  • Chemistry often simplifies — In chemistry, you often select the dominant reactions to consider, idealize situations and processes in order to allow an understanding of the most important features.

For a chemist, most of what happens in biology is “macroscopic” – there are lots and lots of atoms involved – even though you might need a microscope to study it. In introductory chemistry you often assume that reactions are taking place at standard temperature and pressure (300 K and 1 atm).


The goal of physics is to find the fundamental laws and principles that govern all matter — including biological organisms. Those laws and principles can lead to many types of complex and apparently different phenomena. Physics as traditionally taught at the introductory level tends to explicitly introduce four scientific skills that may seem different to what you see in introductory biology and chemistry classes, but these four skills will prove valuable for your career.

  • Physicists often spend a lot of time working out the simplest possible example (“toy model”) that illustrates a principle — even if that example appears not particularly interesting, relevant, or realistic. This lets you understand clearly and completely how the principle works. This understanding then can be woven into more complex situations to produce a better sense of what’s going on (although the embedding of the simplicity in a realistic, relevant, and complex situation is often omitted in traditional introductory physics classes).
  • Physicists quantify their view of the real world — Although there is a lot of conceptual and qualitative reasoning in physics, physicists tend not to be satisfied until they can quantify what they are talking about. This is because purely qualitative reasoning can sometimes be misleading. While you can come up with an argument that says A happens, if you think carefully, you might also come up with an argument that says something different happens — B. It’s not until you can figure out that effect B is 1000 times bigger than effect A that you really know how to describe what’s going on. This is just as true in biology and chemistry as physics, but physicists tend to introduce quantification sooner in the curriculum and more extensively than chemistry, which does it more in introductory classes than biology does.
  • Physicists think with equations — This is more than just calculating numbers: physicists use equations to both organize their qualitative knowledge about what affects what and how, and to reason with in order to determine how things happen, what matters, and how much. Physicists go back and forth repeatedly between thinking conceptually about a problem and thinking mathematically about a problem, so that each of these ways of thinking sheds light on the other.
  • Physicists deal with realistic situations by modeling and approximating — This means identifying what matters most in a complex situation and building up a fairly simple model that lets you get a good picture of what’s happening. This is where the art lies in physics: in figuring out what can be ignored without losing what you want to look at. Einstein got it right when he said: “Physics should be as simple as possible, but not simpler.” All sciences do this, but because physics is about “anything and everything”, physicists often assume that they can get away in introductory classes with choosing systems that may seem to be simplified to the point of irrelevance. In this class, we’ll try to be more explicit in modeling complex examples than in traditional physics classes.

This way of doing science is a bit different from the way biology is often done — but elements of this approach and the constraints imposed on biology by the laws of physics are becoming increasingly important both for research biologists and health-care professionals. For more discussion, see the page, What Physics Can do for Biologists.


Math is a bit different from the sciences. In its essence math is about abstract relationships. Since math is about abstract relationships and how they behave, it’s not “about” anything in the physical world. But it turns out that a lot of relationships in science can be modeled by relations that obey mathematical rules, often very accurately. (If you think this is surprising or strange, you aren’t alone. For fun, take a look at the interesting article by the Nobel Prize-winning nuclear and mathematical physicist, Eugene Wigner, entitled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.“)

Math as taught in math classes often is primarily about the abstract relationships — learning how to use the tools of math. Making the transition to using math in real-world situations may be quite jarring as there are now additional things to pay attention to other than the math itself — such as figuring out how the elements of the real-world system get translated into a mathematical model and worrying about whether the mathematical model is good enough or not. I like to think of it this way: in math class you learn the “grammar” of the language of science. Here, and in your other science courses, you need to start learning “vocabulary.” With grammar and vocabulary together, you can begin to describe the Universe.

Bringing these disciplines together

Bringing these all together to permit coherent and productive thinking is a challenge! In this class we expect and encourage you to bring to bear knowledge you have from your other science classes — to try to see how they fit together, support each other, and to learn to identify when a particular disciplinary approach might be most appropriate and useful.

While these different scientific disciplines are all ultimately working to the same end: understanding the Universe. They did evolve semi-independently historically. As such, there are cultural differences between the sciences just as there are cultural differences between countries (driving on the right or left, for example). These cultural differences are not about “right” or “wrong” ways of doing things. They are just different. In fact, these differences in perspective are a strength! The different viewpoints between disciplines have often led to many important discoveries throughout history and are still where many of the most exciting advancements are being made. They can, however, be confusing. We have, therefore, worked with biology, chemistry, and mathematics instructors here at University of Massachusetts – Amherst. These discussions have resulted in some common language used in this book, which might, therefore, be different than in other physics text you may look at. Even so, there are sometimes places where we need to leverage the strength of a different viewpoint. We will point out these differences using boxes like the one below.

A Venn-diagram showing the different sciences

We will use boxes like this to point out important differences between disciplines. Again, these differences are not “right” or “wrong” ways of doing things. They are simply artifacts of the different sciences evolving independently for centuries with influences from different cultures from across the globe.

  1. E.F. Redish, “The disciplines: Physics, Biology, Chemistry, and Math,” in Introductory Physics for the Life Sciences I - NEXUS Physics, University of Maryland, College Park, 2013.


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Physics 132: What is an Electron? What is Light? by Roger Hinrichs, Paul Peter Urone, Paul Flowers, Edward J. Neth, William R. Robinson, Klaus Theopold, Richard Langley, Julianne Zedalis, John Eggebrecht, and E.F. Redish is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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