What should i write a book about for math?

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wordprof | College Teacher | (Level 1) Educator Emeritus

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If I understand your question, you are seeking a focus point to build a fairly long examination of a mathematics question; you do not mean “a book about fractions” or “a book about decimal points”, but rather “the history of math” or “the development of math in the western world.”  I suggest this central philosophical question:  “Is mathematics a discovery or an invention?”  That is, are mathematical rules built into nature, for us to “discover”, or is Mathematics a “language,” a “system” we have constructed to exchange ideas?  At the base of this complex investigation is the Cartesian duality of mind and body—that is, the relation of “fact” to “perception”.  A good start might be Ouspensky’s thought in Tertium Organum about the relation of our senses to the external world.  You should have a good time exploring these areas of thought.  (Now, if you meant a book report, I suggest "1,2,3, Infinity.")