What is the most important element for studying pure mathematics?

One central concept in pure mathematics is the idea of generality; pure mathematics often exhibits a trend towards increased generality. Uses and advantages of generality include the following: 1) Generalizing theorems or mathematical structures can lead to deeper understanding of the original theorems or structures. 2) Generality can simplify the presentation of material, resulting in shorter proofs or arguments that are easier to follow. 3) One can use generality to avoid duplication of effort, proving a general result instead of having to prove separate cases independently, or using results from other areas of mathematics. 4) Generality can facilitate connections between different branches of mathematics. Category theory is one area of mathematics dedicated to exploring this commonality of structure as it plays out in some areas of math.

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