The Importance of Math

September 13, 2007

The Importance of Math
By: Gary Hammock

When was the last time you've heard the phrase, "I hate math." You may have even said this statement in the past. While the intricacies of mathematics may be, at times, hard to grasp, one can never dismiss it entirely.

Mathematics plays an important part in our everyday lives whether we choose to acknowledge the fact or not. Many of our daily activities are done without thought of the underlying mathematics. We not only use mathematics for the obvious tasks like balancing accounts, telling time, and percentage rate calculation; but we also use math in esoteric ways every time we make use a GPS locator, visit a web site, view digital pictures, and even watch DVDs!

Think about the nuances that happen every time you make a sound on a cellular phone. Essentially (and most simplistically), the microphone converts the analog signal of your sound wave (which can be represented as a continuous mathematical function) into a digital/binary representation of bytes. After transmission and reception, the bytes have to be processed through a digital to analog conversion function to reconstruct the sound wave to be output by the other phone's speaker. The mathematical conversions make this possible.

What about when you order a book from Amazon.com? Your browser opens an SSL (secure sockets layer) connection to Amazon's servers which encrypts your payment information. Encryption (and the subsequent decryption) is a highly mathematical operation that is used intensively by web traffic to help deter man-in-the-middle exploits and protect your personally identifying information.

Most digital cameras have the ability to produce images in the JPEG format. This requires the use of "discrete cosine transformation" and "Huffman tables" to reduce the file sizes of the image information. These are matrices stored by the image that require the computer to—in a sense—calculate the color of every pixel in the image. This means that the file sizes are smaller at the expense of the computer processor doing a little extra work. Mathematical operations make the image compression possible.

Many of the mundane things we do (especially when computers are involved) require some usage of mathematics. In the computer industry, two of the most ubiquitous operations are data-encryption and data-compression. These operations can't be done without mathematical manipulation of the input data set. Merely clicking the "Log In" button on a web site doesn't make you secure by itself, it takes math!

In fact, the computer industry in general has mathematicians to thank. Charles Babbage—an English mathematician—designed both the Difference Engine and the Analytical Engine in the early 19th century. Both devices were essentially developed to be mechanical computers. Lady Ada Byron—a mathematical enthusiast and the namesake of the Ada programming language—is credited with creating the first computer program (which was designed to compute Bernoulli numbers on Babbage's Analytical Engine). Alan Turing—an English mathematician and cryptanalyst—designed electro-mechanical machines to break German cryptography during World War II and designed the "Automatic Computing Engine" in 1946. The list of contributions by mathematicians to the computing industry continues still today.

The mathematics field is still very active. Simply because many of the "common" principles have been known for centuries, (or only decades as the case with computers and numerical analysis) doesn't mean that there aren't mathematicians looking for new ways to implement mathematics. Mathematicians are always looking for ways to improve algorithms, solve complex systems (such as E8), and build new encryption protocols.

Simply because the mathematics in our lives is largely unseen, never believe that it's not impressive and far reaching.

Author's Comments

Math can also make really cool images! The video below is the output of the Julia fractal set. I wrote this simple fractal generation program with references from Michael Barnsley's book, Fractals Everywhere. Feel free to download the application, source code, images, and the movie itself!

Application and Source Code

Download the Application and Source Code Here!

Video

Julia Set Animation - Quicktime Video (.mov)

Wallpapers

Fractal Fern
Fractal Fern Image
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Sierpinski Gasket/Triangle
Sierpinski Gasket (Triangle) Image
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Mandelbrot Set
Mandelbrot Set Image
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Julia Set Image #1
Julia Set Image #1
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Julia Set Image #2
Julia Set Image #2
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Julia Set Image #3
Julia Set Image #3
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Julia Set Image #4
Julia Set Image #4
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