If you have tried and failed, fear not: many great ones before you have experienced this fortune. What is important is not whether you have failed, but what you have done after such failure. Did you feel sorry for yourself and give up all hope of success? Or did you dust off the sweat and blood, and vow to come back stronger, and eventually win the prize? Depending on your course of action, you may end up another casualty of the ne'er-do-well society, or you just might end up making your mark on life.

If this is the first article of mine that you are reading, then you might not be aware of my background or particular interests. By training, I am an educator, schooled in the fields of mathematics and science. The topic of this article came about as I was doing some reading within a branch of advanced mathematics known as *Group Theory*. This particular branch forms a sub-branch of the Abstract Algebra field, and as such touches upon topics which help us to understand particular mathematical sets and the structures and operations imposed upon them.

For example, the set of polynomials forms an infinite mathematical set with certain properties. Polynomials are algebraic expressions that serve as models for many different real world phenomena, such as problems in motion, electronics, sound, and weather. The quadratic polynomials form a subset and the solutions of such are studied in my article series entitled “Algebra for Dopes: The Quadratic Equation. " One of the interesting problems concerning polynomials is whether one can find solutions for the higher degree ones, particularly those of the fourth and fifth degree. These problems were studied by a young mathematician named Evariste Galois and his famous work laid the work for Galois Theory, a sub-branch of Abstract Algebra, which would conclusively answer the questions regarding whether such fourth or fifth degree polynomials could be solved using formulas involving radicals and such as used in solving lower degree polynomials like the quadratics.

Evariste Galois’ brilliant work put an end to such vexing problems and gave mathematicians food for thought for the next two hundred years. Unfortunately this young genius was killed in a political duel in 1832, at the tender young age of twenty. What is interesting about his life is that Evariste twice failed the entrance exam to the prestigious Ecole Polytechnique, considered to this day one of the ten best universities in the world. That is correct-*in the world*. He eventually studied at a less prestigious university and completed his studies there. Moreover, Evariste's initial mathematical publications were received with less than laudatory fanfare.

Yet when the collected manuscripts of Galois were finally published in 1843, mathematicians realized the soundness of the ideas contained therein and the groundbreaking work that was laid with their contents. What is astounding about the life of this mathematician is the amount of work accomplished in so short a time. God only knows what contributions could have been made had Evariste lived a few more years. And all this from someone who failed to impress the very best with his less than impressive academic muster!

So the next time you think you are a failure because you tried something and failed, think again. Consider the tragic story of this young mathematician. If he failed repeatedly, but finally succeeded because he persisted, with time running so preciously short on him; then imagine what you can do, if you just do not give up. Just imagine. . .

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Joe is a prolific writer of self-help and educational material and an award-winning former teacher of both college and high school mathematics. Joe is the creator of the * Wiz Kid* series of math ebooks,

**, the little classic on the ABC's of arithmetic, the original collection of poetry,**

*Arithmetic Magic***, and the short but highly effective fraction troubleshooter**

*Poems for the Mathematically Insecure***. The diverse genre of his writings (novel, short story, essay, script, and poetry)-particularly in regard to its educational flavor- continues to captivate readers and to earn him recognition.**

*Fractions for the Faint of Heart*Joe propagates his teaching philosophy through his articles and books and is dedicated to helping educate children living in impoverished countries. Toward this end, he donates a portion of the proceeds from the sale of every ebook. For more information go to http://www.mathbyjoe.com .

*March 29, 2008*(773)