The word "elegance" traces its roots back to the Latin "elegantia," signifying refinement and taste. Initially, it carried a connotation of affected refinement, but over time, it evolved to denote genuine grace and sophistication. By the Middle Ages, "élégance" had entered the French language, and subsequently, English. Early English usage often linked elegance to refined writing and speech, as exemplified by classical authors like Cicero and Virgil. 

Modern Conceptions of Elegance 

Today, elegance encompasses a wider range of qualities. It can refer to a person's appearance, behavior, or even a solution to a problem. 

Personal Elegance: Grace, sophistication, and good taste characterize an elegant individual. 

Problem-Solving Elegance: An elegant solution is simple, efficient, and often involves a creative or insightful approach. 

A prime example of elegant problem-solving is a technique attributed to young Carl Gauss. When tasked with summing integers from 1 to 100, Gauss paired numbers (1+100, 2+99, etc.), recognizing that each pair totaled 101. With 50 such pairs, the total sum is simply 50 * 101 = 5050. This elegant solution showcases simplicity, efficiency, and a clever insight. 

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