This is what seemed super-exciting to me nearly a year ago. To be honest, I still think it is exciting (go ahead and call me a nerd :):) )
My final year as an undergraduate at U of T was full of exciting academic events. I went to numerous Fields Undergraduate Network events and to a larger conference at Penn State. One of the highlights of that academic year was the process of applying for graduate programs. It was a challenge to choose a sample of writing that was required for all the graduate applications. I took a course called Writing in Mathematics and wrote an essay on Mobius Transformations which later won the Dean’s Award for Writing. Unfortunately, a purely mathematical essay would not satisfy the History and Philosophy of Sciences committee. A philosophical perspective was needed. I have never taken a course in philosophy (other than Modern Symbolic Logic described in one of the previous posts), so I was allowed to submit a paper I wrote in one of my pedagogy-related classes in addition to my math essay. Several months later I was accepted to the History and Philosophy of Science and Technology Graduate program , History of Mathematics doctoral stream at U of T.
The most memorable course of my final year was called History of Mathematics after 1700. There I learned a lot of mathematics that was not taught in my previous math classes. For instance, the Vibrating String Controversy. I also got a chance to read some primary sources written by Euler and Bishop Berkley. An interesting theme that could be traced throughout the course was the absence of ‘revolutions’ in mathematics. A scientific revolution is a phenomenon when an old paradigm is abandoned and replaced by a new one, more suitable to solve problems posed in a certain science. For instance, once upon a time people thought that the Earth is the centre of the entire Universe. Then they learned that it is not true. That is a scientific revolution. We no longer use the knowledge from the previous paradigm and we know that it was wrong. In mathematics we do not have such drastic changes. For instance, we still use Pythagoras Theorem and the papers that were written thousands of years ago are still valid.