What is mathematics?

Mathematics is a fantastically broad, beautifully intricate, complexly connected concept of numbers and symbols.  Most days I think mathematics is problem solving, some days I have no idea what mathematics is because it tries to define the infinite.  As mathematicians we find relationships between these numbers and laws that already exist and make a language to help define them.  One of these concepts is infinity.

Infinity is a something that doesn’t exist.  No one can reach infinity and no one knows where it is.  It’s something humans created to try to grasp the concept of forever, the end of the number line.  It is a hypothetical construct that frankly, hurts to think about.  Although, the concept of infinity may be impossible to totally grasp, it is still captivating.
 
Mathematics is one of the few disciplines that even attempts to explain such a lofty concept.  In turn, there are many mathematicians who looked at infinity through logical thinking in subjects such as astronomy, geometry, and engineering.  They discovered key concepts that define the way we look at mathematics. 

There are a plethora of moments that could be argued are the greatest discoveries in mathematics, but here are the moments I think are the greatest.  First I think Al-Khwarismi and his book The Compendious Book on Calculation by Completion and Balancing was the most influential moment for mathematics.  The book summed up all of algebra at the time and opened the door for algebra in Europe.

Second, Euclid’s parallel postulate defines the way we look at geometry.  It challenged mathematicians to define geometry into subcategories and create proofs from these subcategories.

Third, the Pythagorean Theorem is among the most important discoveries in mathematics.  The Pythagorean Theorem gives us what we know about right triangles.  This is one of the first theorems we learn a children and for  good reasons.

The next greatest moment in mathematical history is the discovery of the First Fundamental Theorem of Calculus.  As the other discoveries define a category of mathematics, so does the First Fundamental Theorem of Calculus, which obviously created the way mathematicians look at calculus.

Finally, the discovery of Quadratic Equation hits the last spot of the top five.  It gives mathematicians a neat and concise way of looking at parabolas, but coming in at number five, it doesn’t define a huge category of mathematics.   Throughout history, the mathematicians that discovered these concepts helped us define what we call today, mathematics. 

*This post is thanks to all of my mathematics professors at GVSU for teaching me so much over my years here.  Special thanks to John Golden because of all he taught me I had to rework my top 5 greatest moments.  His worksheet also helped me write the section about Al-Khwarismi.