SideShow Post #64 To which I replied in Post #67 The above prompted SideShowBob Post #71 The above remarks by you indicate that you do not realize that calculus & mathematics beyond algebra & Euclidean Geometry require a lot of prerequisite knowledge. It would be interesting to try to teach Differential Geometry to the 8-year old without first teaching Euclidean geometry & differential calculus. Why do you think that subjects like Differential Geometry (aka Metric Geometry) are not usually taught prior to the 4th year in college? The reason is that mathematics is analogous to a building which requires a foundation as well as stories 1-10 below the eleventh story. You seem to view mathematics courses as analogous to history. You can learn American history with no knowledge of European or ancient history. You cannot learn calculus or Differential Geometry without several prerequisite courses. To teach the 8-year old such disciplines would require first teaching quite a few prerequisite courses. It would require the equivalent of several semesters of other mathematics.