Waldorf students learn that math can be found everywhere, and that math is integral to all life. By the time students are in eighth grade, many can express the universal nature of math. In one of our recent writing assignments, some students in Mrs. McGaunn’s math class share their reflections on selected math quotes:

From Aida DeWeese-Boyd:

“All mathematicians share…a sense of amazement over the infinite depth and the mysterious beauty and usefulness of mathematics.” – Martin Gardner

Often when we think of math we think of textbooks and proven formulas the ancients left for us, but what doesn’t come to mind is math is still being figured out. Every day something new is discovered: a new digit of Pi or formulas are discovered to send probes to the Moon or even Mars; in short, our universe expand everyday, every moment. This is the “amazement over infinite depth.”

But this quote also speaks of the everyday presences of math in our lives. For instance, think of the buildings we live and work in: these were not just constructed, but also designed and planned out. Think of the calculations it took to figure out if a roof would cave from too much weight or fall apart from too little. Our roads, our towns, even nature has geometric perfection, which to me is the biggest mystery. There are many things that “make the world go round” and it is the truth to say that one of those things is mathematics.

My favorite part of this quote “mysterious beauty” means to me that not only is our universe always expanding, but as we solve problems and mysteries are unraveled new questions appear. In fact, that fills me with hope – a hope that there will be things we don’t understand. I would really to study astrophysics for this very reason. This quote reassures me that there will always be new things to discover as long as one wishes to discover them

From Ella Mills:

“Wherever there is number, there is beauty.” – Proclus

If one doesn’t choose to understand what this quote means, it may seem like any other quote you’ve heard someplace or even made up. But with this quote, there is truth. Some people may misinterpret this quote and think Proclus is just saying “math is beautiful”, but the word beauty reminds me of symmetry, and how much math ties into beauty.

In nature, one could pick up a leaf and not know the millions of symmetrical and geometric designs that make up just the spine. There is math everywhere, and much of what we do each day involves math, whether we realize it or not.

“I’m never going to use this!” A lot of kids including myself used to say; and now I understand how ridiculous that sounds. Even if one doesn’t have a career involving math, one still uses math countless times in a day: calculating percentages on items in the grocery store, or when out to dinner calculating the server’s tip. Putting gas in the car and rounding the price, paying for anything and using correct change, and cutting anything precisely. Math is all around us, and most times we may not even realize we’re using it.

Overall, the main message I got out of the quote was that math=symmetry, and symmetry is one of the ways we measure beauty. If math is everywhere, and math=beauty, then beauty can be found everywhere.

From Nathaniel Cosco:

“Math may not teach me how to add love or subtract hate, but it gives me every reason to hope that every problem has a solution”– Anonymous

Math might not be able to teach us all the answers, or prepare us for every situation we come across, but its principles will guide us through our lives forever. Math can solve almost any problem or mystery, be used to warp or manipulate puzzles and obstacles, or even help us better understand the world around us. It’s used day to day, sometimes even unconsciously to help us more accurately perceive the distance, time, and energy. To me, the power of math is extraordinary.

However, there are a lot of things that math alone cannot solve. The one problem that no amount of math or calculating will ever solve, is human emotion. Math alone will never find answers to love, or happiness. Math alone cannot cure depression, anxiety, or any sadness by itself. Math is a powerful tool, but not a limitless one.

That being said, I still believe that math is the most powerful expression of knowledge. Even more so than the written language, or any other expression of speech, because almost anyone, of any culture, can understand and communicate with math. And the power to break down the barriers of language, race, and background, is truly the most powerful tool anyone can possess.

From Simon Rubin:

“The Book of Nature is Written in the Language of Mathematics”—Galileo

There are several ways math is expressed in nature. All forms of nature are connected to math in some way.

Plants, animals and even the sky express math in some form. In ﬂowers, the petals are usually equidistant from each other. All petals are typically the same size. Flowers bloom based on the number of days that have passed, and the time of the season. The tides rise and fall twice a day based on the moon’s twelve hour cycle. When the earth moves to different points in the solar system, the change of gravity is what changes the tides. You can determine different species of trees based on the geometric shape of the leaves. For example, a sugar maple has exactly ﬁve points on its leaves while an oak tree has six points. To tap a maple tree for sap one must drill into the trunk at an approximate 45 degree angle, otherwise sap cannot be collected. In order to get syrup the sap must be boiled at a certain temperature for a certain amount of time. Additionally, it takes about 40 gallons of sap to make 1 gallon of syrup.

These examples prove how math is hidden in nature. Without math, we would not understand how nature works. Nature makes more sense with math.