Mathematics has experienced millennia of glorious advancement. Its accomplishments are among the greatest achievements of humanity. Just over the last hundred years, we have witnessed the extensive mathematization of many aspects of life in general, and of all sciences in particular. No other human endeavor can claim such success. There is no reason to believe that this course will change in the millennia to come.
And all this has been achieved purely on the merit of its intellectual content, without resorting to marketing, propaganda, or persuasion so common in many other human activities.
The conclusion that inevitably follows from this success is that there are profound qualities in the broad field of mathematics. The single quality that must have contributed to its success is the intellectual rigor with which mathematics is developed.
Mathematics has something to offer for everyone. Everyone can benefit from the deliberate practice of rigorous thinking, from clarity and precision in the use of language, and from other intellectual experiences encountered in a well-structured mathematics course at any level.
I want the greatness of mathematics to permeate every class period with my students. I believe that every little piece of mathematics reflects some of its profound qualities, some of its essence. With my students and for my students, I want to make this engaging; I want to make it come alive.