# How Math Is Fundamental to Scientific Progress

Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

From algebra to statistics: learn how math is vital to the study of science, and the all scientific progress. Learn about how mathematical modeling and technology has led to rapid improvements in scientific knowledge.

## Contribution of Math to Scientific Progress

The universe is inherently mathematical. Everything we see can be measured, quantified, and explained. There are patterns everywhere in nature. This is the fundamental goal that makes scientific progress possible. And math is integral to that scientific progress.

Scienceis the attempt to explain the natural world using systematic observation and experiment. Scientists collect data, and the most useful data they collect is usually a number of some kind: it's the masses of fundamental particles, the percentage of absorbed calcium as food passes through the body, the number of base pairs found in DNA, or the number of bonds in a molecule.

Scientists love to put numbers to things because it helps them make logical sense out of what they're observing. The goal is very often to find a mathematical relationship between the two quantities being studied. This is especially true in physics, which has the goal of coming up with equations to explain absolutely everything in the universe. So math is absolutely necessary for scientific progress.

But science uses math in other ways too. Whenever data is collected, scientists have to figure out whether that data is statistically significant. Without this analysis, the entire experiment is worthless. So the topic of statistics is central to every scientific investigation.

## Modeling and Technology

There are more abstract ways that math is applied to improve scientific progress. One is a mode of thinking. Modeling is at the heart of mathematics - everything in mathematics is an abstraction, and science is where those abstractions gain real life applications. Modeling is where you represent a real-life phenomenon with an abstraction of some kind. You can have physical models, computer models, mathematical models - even things like flowcharts are considered to be models. But whether your model is mathematical or merely a pretty picture to help explain a phenomenon, this idea of modeling comes directly from mathematics.

Technology is any application of science that achieves a particular goal for humans. Even something as simple as a campfire is technology, because it applies our knowledge of how to create fire in order to keep people warm. Technology has enabled mathematics to accelerate scientific progress in recent years. Scientists are able to model and simulate things on computers by inputting math equations. The computers can then complete calculations that would take individual humans their entire lives, and improve our understanding of the world faster than ever.

## Examples of Uses of Math in Science

Physics probably has the most practical examples of mathematics. For example, physicists use vectors a lot, so an understanding of vectors is vital for anyone studying or working in physics. Those vectors can point in any direction, and because of that, trigonometry becomes important. A diagonal force can be broken down into x and y components by creating a vector triangle, and using sine, cosine, and tangent. In physics, SOHCAHTOA isn't just for physical triangles; it can be used for any vector quantity.

Because physics is all about rates of change, physicists also use calculus in almost every topic they explore. While in the classroom, calculus is mostly confined to AP Physics C, where students (for example) learn that velocity is the differential of displacement with respect to time, and that acceleration is the differential of velocity. Calculus is also found in electromagnetism, where James Clark Maxwell came up with a set of four partial differential equations that elegantly describe all of electricity, magnetism and light.

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