Not Quite. Your are confusing the current status-quo which is a cumulative development and a standardization for ease of teaching, with the Original Discoverer

Not Quite. Your are confusing the current status-quo which is a cumulative development and a standardization for ease of teaching, with the Original Discoverer's process of arriving at his results. They are very different. From https://en.wikipedia.org/wiki/New_Math https://en.wikipedia.org/wiki/New_Math : In his book, Why Johnny Can't Add: The Failure of the New Math, Morris Kline says that certain advocates of the new topics "ignored completely the fact that mathematics is a cumulative development and that it is practically impossible to learn the newer creations, if one does not know the older ones." Furthermore, noting the trend to abstraction in New Math, Kline says "abstraction is not the first stage, but the last stage, in a mathematical development." What is being taught today is merely a statement of results and algorithms to mindlessly apply them. Hence the failure of "Mathematical Education" (eg. https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament https://en.wikipedia.org/wiki/A_Mathematician%27s_Lament). By following the Original Discoverer's writings, even if it is outdated (in the light of later discoveries) you understand the What and the Why being explained Organically and Coherently by a single Mind towards one particular set of "Results". This is the crux of "Understanding". Once this is grasped, it becomes easier to follow later developments on the evolution of the same set of "Results" to current-day standards.