”What is math – and why learn it?” Two questions you want me to answer, my dear nephew.
0. What does the word mathematics mean?
In Greek, ‘mathematics’ means ’knowledge’. The Pythagoreans used it as a common label for their four knowledge areas: Stars, music, forms and numbers. Later stars and music left, so today it only includes the study of forms, in Greek called geometry meaning earth-measuring; and the study of numbers, in Arabic called algebra, meaning to reunite. With a coordinate-system coordinating the two, algebra is now the important part giving us a number-language, which together with our word-language allows us to assign numbers and words to things and actions by using sentences with a subject, a verb and a predicate or object:
“The table is green” and “The total is 3 4s” or “T = 3*4”. Our number-language thus describes Many by numbers and operations.
1. Numbers and operations are icons picturing how we transform Many into symbols
2. Placeholders
3. Calculation formula predict
4. Reverse calculations may also be predicted
5. Double-counting creates per-numbers and fractions
6. Change formulas
7. Use
8. Conclusion