Twelve hours at the Math Lab made it clear.

I taught the review session at 7PM. We talked about sequences, L'Hopital's Rule, and improper integrals. It took only 2 hours, but I had work to do. I spent the next hour in my office working on the application exam. We had decided to remove the Taylor expansion, and I was sad. I labored for the next hour in TeX, and then closed the lab. I didn't feel like leaving. Neither did some students who had been in my review session. The room cannot be locked, so they stayed and did homework. I helped them some and mused on other ideas for the test. Then they asked which math classes were good to take after integral calculus.

I was off like a shot.

In under five minutes I had rattled off all the interesting math classes I knew of at our university. I extolled the merits of multivariable calculus and mentioned the five axioms of geometry. I talked about analysis and how cool proving the fundamentals of calculus is. I instilled a healthy fear of partial differential equations. Then one of them mentioned that he didn't really get imaginary numbers. I didn't hesitate to grab a marker and introduce the fundamentals of complex analysis. That took an hour, and I got to talk about how complex numbers relate the hyperbolic sine wave to the normal sine wave. It was glorious. I also got to explain how integrals worked in multiple dimensions, and how the line and surface integrals are just extensions of the definite integral into functions of vector variables.

Then one of them asked if I knew about how the natural numbers were countable and the real numbers weren't. Did I ever!

The next hour was spent discussing cardinality, the sizes of varying infinities, and Cantor's diagonalization proof of the continuum. Explaining how infinity exists but we can't count that high was exhilarating. (Cantor's proof, by the way, is sheer genius.) By the time I got to the end of the proof I could not stop smiling. I spent the rest of that night, until 7AM, doing and teaching math.

Yes, twelve hours at the Math Lab made it obvious.

You see ladies and gentlemen, I love math. I think it is the most glorious discovery of man. As has so famously been quoted,

"The Book of Nature is written in the Language of Mathematics." -- Galileo Galilei

The fact that numbers can quantify and evaluate the world around is powerful (Arithmetic). The fact that five postulates can govern how the world fits together is amazing (Geometry). Our ability to manipulate unknown quantities to obtain a meaningful answer is intriguing (Algebra). Being able to deal with infinity in a clear and logical way, and that doing so underlies all of mathematics, is unbelievable (Set Theory). The existence of pretend numbers that matter in the real world boggles the mind (Complex Analysis). And, the fact that infinitely small changes follow the same fundamental laws as their finite counterparts is nothing short of stupendous (Calculus).

And you know what? It can happen to you.

If you don't like math, it is not because you are not smart. It is not because you are just "not interested" in math. Does everyone not appreciate beauty? Mathmatics supports, upholds, and surrounds beauty. It is beautiful. If you do not enjoy math, I suspect that you are the victim of poor math teachers, poor math books, or both. I have taught math to thousands of students -- and the more they understand, the more they enjoy. So can you.

Here's how:

  1. Learn the logic of mathematics.
  2. If you learn the logical basis of mathematics, it will become much clearer and simpler for your brain to comprehend. Many reading this probably had bad experiences with proofs in high-school geometry. Fortunately, proofs are much nicer than that. Study them, and you will see.

  3. Find a good book to learn from.
  4. There are abundant poor math texts, and a few rare superior books. I recommend a thorough perusal of a university or online bookstore, or a recommendation from a trusted friend. If a book can explain mathematics your learning process will be much more enjoyable as you read and comprehend concepts as they arise. In my particular area of love, calculus, I recommend Calculus 8th Edition by Varberg, Rigdon, and Purcell (ISBN 0130811378). The text is complete, rigorous, well-structured, clear, and brief. It makes an excellent text to learn from and to reference. I am sure similar books in other subjects exist and await your discovery.

  5. Discover the meaning of the numbers.
  6. As you begin to learn about why mathematics works and how it fits together, you will begin to grasp the meaning of these things in the world we live in. In addition, knowing how basic mathematics connects with the world around us will allow you to take the relationships in advanced mathematics and conceptualize a world that we cannot even perceive (such as n-dimensional space or the complex plane.) This is the true beauty and excitement of mathematics, and through understanding you can make the connections that will broaded your mind and enhance your understanding.

I love mathematics. I know, that someday soon, you can too.

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