One of the questions I am often asked is exactly what do mathematicians do. The short answer is that they look at different mathematical structures, try to deduce their properties, and think about how they might apply to the real world. Math Without Numbers (Dutton, 2020) does a wonderful job of explaining what mathematical structures are, and does so in a fashion that even readers who are uncomfortable with the process of doing mathematics can appreciate and enjoy. There are courses in music and art appreciation, and if there ever are courses in math appreciation, this book would certainly be at or near the top of the reading list.
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