Problem Solving Story

That summer, I read a historical note in the margin of my precalculus textbook.It told the story of Evariste Galois, who solved a longstanding problem in mathematics while in his teens.

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When it came time for trigonometry, the teacher drew a chart on the board that was the values of sin, cos and tan at these angles, but it did not make sense to me. He drew something on the board that I did not expect. I could see what radians were, and that sin and cos were coordinates.

I started missing class to try to read the book, but I only got more lost. He said, if you can understand how to draw the unit circle from memory, then you can solve any problem in trigonometry.

Now, I wish I could say that everything was perfect once I changed my major, and that I became a mathematician overnight, but nothing could be further from the truth. In my mind I still believed that I wasn’t good enough.

I didn’t know about things like AP Calculus, so when I saw my classmates getting the answer right way, I thought there had to be a mistake and that I wasn’t actually good at math.

I proved the formula and gave it to my MAT 300 professor, and he invited me to present it at an undergraduate research conference. The last thing a math professor told me was that Bill Gates never gave up doing what he loved, and that I shouldn’t give up mathematics because maybe my path was meant to be different.

I ended up leaving the university, but I didn’t give up. I started learning all these beautiful things I had never learned before, like matrices, absolute value, and the rational roots theorem.

It was clear that the way I understood math was different.

I was drawn to the proofs that were in the textbook but at the same time, I lacked the experience to do clever algebraic manipulations.

I realized that math was not about getting grades, it was about contributing. I solved one of the featured problems in the back, and the way I solved it was to build a bunch of similar smaller problems.

I lucked out because I conjectured a formula that would solve any problem of that type. I had a desperate need to be good which led to severe testing anxiety.

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