I read once that mathematics is the true language that can explain our Universe. My first reaction was, “Cool, so how does it work?” Most of the people who surround me have incredible math anxiety so trying to get people to even enter into a creative and abstract conversation about mathematics proves to be extremely difficult. So, since my friends who are mathematicians are extremely busy teaching or running for public office, I decided to investigate this one on my own. (If any of my mathematician friends reads this and would like to chime in with your perspective, please do so!)

Normally, we describe the world around us by using our senses. They sky is grey and blue. The air smells of sod and rainwater. The sun is setting atop the mountain in the horizon. Well, that last one we know that the sun isn’t the sphere setting, it is our earthly sphere that spins. In addition to describing the world using our senses, we also describe it with reason, that is, what we know to be mathematically true. If you were to ask ten different people to describe the sunset, you would likely get ten different answers. That is because people have different perspectives, they notice different things and they disagree on many ideas and descriptions as a result. All of these ideas and descriptions are based on differently people’s perspectives and can therefore be called “variables,” or, things that change. In order to be sure we communicate exactly what we intend to and in order for everyone to describe something the same way over great expanses of space and time, we need to use “constants,” or things that don’t change. Almost everything in our world changes except mathematics. 7+4 has always been 11 and in 1,000 years it will still be 11. For a clearer understanding, here is a quote from a most intriguing and thought-provoking book I’m reading by Jostein Gaarder called Sophie’s World: A Novel About the History of Philosophy:

“Plato found mathematics very absorbing because mathematical states never change. They are therefore states we can have true knowledge of. But here we need an example.
Imagine you find a round pinecone out in the woods. Perhaps you say you “think” it looks completely round, whereas Joanna insists it is a bit flattened on one side. (Then you start arguing about it!) But you cannot have true knowledge of anything you can perceive with your eyes. On the other hand, you can say with absolute certainty that the sum of the angles in a circle is 360 degrees.” (pp 86-87).

Another enlightening book I found is a mystical, historical and scientific view of mathematics. It is a fascinating book authored by Michael S. Schneider called A Beginner’s Guide to Constructing the Universe: The mathematical archetypes of nature, art, and science- A Voyage from 1 to 10. Schneider takes the reader on a journey through each of the numbers 1-10. For example, chapter five is entitled “Pentad” the Greek philosophers term for the number five. The reader discovers connections from the number five to Fibonacci numbers, the golden mean, pentagonal symmetry in architecture, religion, ritual and more. Slice open an apple and you will see five seeds in the shape of a star. More living things from nature have pentagonal designs such as a sand dollar, starfish, sea cucumber, human body and a microscopic radiolarian skeleton. This book is stuffed to the brim with information that aids the reader in thinking about mathematics in a whole new light and understand in a deeper way, how mathematics describes the universe (and vice versa!).

One of the popular debates about mathematics is which came first, mathematics itself and then humans “discovered” it, or was it non-existent until a human thought it up and developed from that idea into what it is today?

E-mail me with your thoughts or make a comment below if you have something to add.

Three worthwhile articles:
http://www.boston.com/bostonglobe/ideas/articles/2009/02/08/a_talk_with_mario_livio/
http://www.fdavidpeat.com/bibliography/essays/maths.htm
http://en.wikipedia.org/wiki/Mathematics_as_a_language