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Does advanced mathematics have a real role in life?
It must be useful. Many science and technology are based on advanced mathematics. As for ordinary life, it can increase your understanding of things, for example, differential equations are very helpful to understand the laws of motion of objects. The car you drive, the games you play, the bridge you cross, the building you live in, and the mobile phone you use. Which one was not designed and made by a group of ordinary people? You think they use addition, subtraction, multiplication and division?