After 40 years of learning Abstract Algebra (aka Modern Math yet it is a 200-year-old Math since 19CE Galois invented Group Theory), through the axioms and theorems in math textbooks and lectures, then there is an Eureka “AHA!” revelation when one studies later the “Category Theory” (aka “Abstract Nonsense”) invented only in 1950s by 2 Harvard professors.

A good Abstract Math teacher is best to be a “non-mathematician” , who would be able to use ordinary common-sense concrete examples to explain the abstract concepts: …

Let me explain my points with the 4 **Pillars** of Abstract Algebra :

$latex boxed {text {(1) Field (2) Ring (3) Group (4) Vector Space}}&fg=aa0000&s=3$

Note: the above “**1-2-3 & **4″ sequence is a natural intuitive learning sequence, but the didactical / pedagogical sequence is “**3-2-1 & **4″, that explains why most students could not grasp the philosophical essence of Abstract Algebra…

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