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'Everything that has a beginning has an end.'
'Everything begins with choice.'
"When children first learn arithmetic, they need to relate the symbols back to concrete objects in the real world, so they start with associating numbers with fingers, or beads. In later years, however, most children are happy to carry out mathematical operations entirely abstractly, even to the extent of using X and Y in place of specific numbers. Those who go on to advanced mathematics learn about other types of numbers (e.g., complex) and operations (e.g., matrix multiplication), which obey strange rules that don’t obviously correspond to anything familiar in the real world. Still, the student can readily learn how to manipulate the abstract symbols that denote the unfamiliar objects and operations, without worrying about what, if anything, they actually mean. So mathematics becomes more and more a question of the formal manipulation of symbols. It begins to seem as if mathematics is nothing but symbol manipulation, a point of view known as formalism.”
by Paul Davies , pg 100