In this video we introduce the second most important theorem in all of mathematics (excluding the laws of arithmetic)!It is certainly remarkable that the recognition of the importance of this result (called the Triple quad formula) is only now taking place at the beginning of the 21st century. How does this formula arise? By asking the deceptively simple questions: how do we measure the separation between two points, and then what is the relation between three collinear points?In this video, at a certain point I invite you to discover this crucial formula for yourself. It is highly recommended, especially if you are a serious student of mathematics, that you spend an hour or so to deduce the required result before I tell you what it is. This occurs around 14:30 of the video.
Does mathematics make logical sense? No, it does not. Foundational issues have been finessed by modern mathematicians, and this series aims to turn things around. And it will have interesting things to say also about mathematics education---especially at the primary and high school level. The plan is to start right from the beginning, and to define all the really important concepts of basic mathematics without any waffling or appeals to authority. Roughly we discuss first arithmetic, then geometry, then algebra, then analysis, then set theory. This course is aimed for a general audience, interested in mathematics, or willing to learn.